From eb2bd9b867c54baf907d028b95a6db672928111e Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 18:56:46 +0800 Subject: [PATCH 01/80] =?UTF-8?q?=E6=96=B0=E5=BB=BA=20submission?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-3/submission/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-3/submission/.keep diff --git a/assignment-3/submission/.keep b/assignment-3/submission/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From 9f1c7a58e8fb0a3a97f9183e52f8a75fc6e715ee Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 18:57:38 +0800 Subject: [PATCH 02/80] =?UTF-8?q?=E6=96=B0=E5=BB=BA=2019210680053?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-3/submission/19210680053/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-3/submission/19210680053/.keep diff --git a/assignment-3/submission/19210680053/.keep b/assignment-3/submission/19210680053/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From 28a0720eaf950402e97b63a6a49f7f4e4c2bec85 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 19:02:23 +0800 Subject: [PATCH 03/80] =?UTF-8?q?KMeans=E4=BB=A5=E5=8F=8A=E4=B8=80?= =?UTF-8?q?=E7=BB=B4=E4=BA=8C=E7=BB=B4=E6=95=B0=E6=8D=AEGMM=E7=9A=84?= =?UTF-8?q?=E5=AE=9E=E7=8E=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-3/submission/19210680053/source.py | 157 ++++++++++++++++++ 1 file changed, 157 insertions(+) create mode 100644 assignment-3/submission/19210680053/source.py diff --git a/assignment-3/submission/19210680053/source.py b/assignment-3/submission/19210680053/source.py new file mode 100644 index 0000000..4155b56 --- /dev/null +++ b/assignment-3/submission/19210680053/source.py @@ -0,0 +1,157 @@ +import numpy as np +from scipy.stats import multivariate_normal + + +class KMeans(object): + def __init__(self, n_clusters): + self.cluNum = n_clusters + + def fit(self, train_data): + # first set the initial centers by random selection + self.train_data = train_data + numSamples, dim = self.train_data.shape + # step1: init the center + self.centroids = np.zeros((self.cluNum, dim)) + for i in range(self.cluNum): + index = int(np.random.uniform(0, numSamples)) + self.centroids[i, :] = self.train_data[index, :] + clusterAssment = np.mat(np.zeros((numSamples, 2))) + clusterChanged = True + + while clusterChanged: + clusterChanged = False + ## for each sample + for i in range(numSamples): + minDist = 100000.0 + minIndex = 0 + ## step 2: find the centroid who is closestfor each centroid + for j in range(self.cluNum): + distance = self.euclDistance(self.centroids[j, :], self.train_data[i, :]) + if distance < minDist: + minDist = distance + minIndex = j + + ## step 3: update its cluster + if clusterAssment[i, 0] != minIndex: + clusterChanged = True + clusterAssment[i, :] = minIndex, minDist ** 2 + ## step 4: update centroids + for j in range(self.cluNum): + pointsInCluster = np.array(self.train_data[np.nonzero(clusterAssment[:, 0].A == j)[0]]) + if len(pointsInCluster) != 0: + self.centroids[j, :] = np.mean(pointsInCluster, axis=0) + + + def predict(self, test_data): + self.test_data = test_data + numSamples, dim = self.test_data.shape + m_res = [] + for i in range(numSamples): + distance = [self.euclDistance(self.test_data[i, :], self.centroids[j, :]) for j in range(self.cluNum)] + clus_type = distance.index(min(distance)) + m_res.append(clus_type) + return np.array(m_res) + + def euclDistance(self, vector1, vector2): + return np.sqrt(sum(np.power(vector2 - vector1, 2))) + + +class GaussianMixture: + # covariance: ndarray + + def __init__(self, n_clusters, reg_cov: float = 1e-06): + self.cluNum = n_clusters + self.max_iter = 200 + self.reg_cov = reg_cov + self.alpha = (np.ones(n_clusters) / n_clusters) + self.sigma2 = (np.ones(n_clusters)) + + def fit(self, train_data): + sampleN, sample_fea = train_data.shape + if sample_fea == 1: + train_data = self.normalize(train_data) + print(train_data) + self.gamma = np.ones((train_data.shape[0], self.cluNum)) / self.cluNum + self.mu = (np.arange(self.cluNum) - self.cluNum // 2) * (train_data.max() - train_data.min()) / self.cluNum + sigma2_ = self.sigma2 + mu_ = self.mu + while True: + # gamma.shape(N, K) + self.gamma = (0.1 * self.gamma + 0.9 * self.phi(train_data, self.mu).T * self.alpha / ( + self.phi(train_data, self.mu).T * self.alpha).sum( + axis=1).reshape(train_data.shape[0], 1)) + # mu.shape(1, K) + self.mu = (0.1 * self.mu + 0.9 * np.matmul(train_data, self.gamma) / self.gamma.sum(axis=0)) + # sigma2.shape(1,K) + self.sigma2 = (0.1 * self.sigma2 + 0.9 * ( + self.gamma * (train_data.reshape(train_data.shape[0], 1) - self.mu) ** 2).sum( + axis=0) / self.gamma.sum(axis=0)) + # alpha.shape(1, K) + self.alpha = (0.1 * self.alpha + 0.9 * self.gamma.sum(axis=0) / train_data.shape[0]) + if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1: + break + mu_ = self.mu + sigma2_ = self.sigma2 + # # reg covariance depend on dimension of the features + elif sample_fea == 2: + self.reg_cov = self.reg_cov * np.identity(sample_fea) + self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) + # there should be n_clusters covariance and each one's size depend on feature + self.covariance = np.zeros((self.cluNum, sample_fea, sample_fea)) + for k in range(self.cluNum): + # make the variance equals to 1 as diagonal + np.fill_diagonal(self.covariance[k], 1) + self.weight = np.ones(self.cluNum) / self.cluNum + p_mat = np.zeros((sampleN, self.cluNum)) + for i in range(self.max_iter): + for j in range(self.cluNum): + self.covariance += self.reg_cov + g = multivariate_normal(mean=self.means[j], cov=self.covariance[j]) + p_mat[:, j] = self.weight[j] * g.pdf(train_data) + total_n = p_mat.sum(axis=1) + total_n[total_n == 0] = self.cluNum + p_mat /= total_n.reshape(-1, 1) + if sample_fea == 2: + for j in range(self.cluNum): + N_k = np.sum(p_mat[:, j], axis=0) + self.means[j] = (1 / N_k) * np.sum(train_data * p_mat[:, j].reshape(-1, 1), axis=0) + + self.covariance[j] = (1 / N_k) * np.dot( + (p_mat[:, j].reshape(-1, 1) * (train_data - self.means[j])).T, + (train_data - self.means[j])) + self.reg_cov + self.weight[j] = N_k / sampleN + else: + print("one and two dimension data is accepted") + + def predict(self, test_data): + sampleN, sample_fea = test_data.shape + if sample_fea == 1: + test_data = self.normalize(test_data) + gamma = (self.phi(test_data, self.mu).T * self.alpha / (self.phi(test_data, self.mu).T * self.alpha).sum( + axis=1).reshape(test_data.shape[0], 1)) + return gamma.argmax(axis=1) + elif sample_fea == 2: + p_mat = np.zeros((test_data.shape[0], self.cluNum)) + for j in range(self.cluNum): + # self.covariance += self.reg_cov + g = multivariate_normal(mean=self.means[j], cov=self.covariance[j]) + p_mat[:, j] = self.weight[j] * g.pdf(test_data) + + total_n = p_mat.sum(axis=1) + total_n[total_n == 0] = self.cluNum + p_mat /= total_n.reshape(-1, 1) + return np.argmax(p_mat, axis=1) + else: + print("one and two dimension data is accepted") + + def normalize(self, data): + flat_data = data.flatten() + nor_data = (flat_data - flat_data.mean()) / np.sqrt(flat_data.var()) + return nor_data + + def phi(self, data, mu): + # phi.shape(K, N) + mu = (np.arange(self.cluNum) - self.cluNum // 2) * (data.max() - data.min()) / self.K + phi = (1 / np.sqrt(2 * np.pi * self.sigma2.reshape(self.cluNum, 1)) * np.exp( + - (data - mu.reshape(self.cluNum, 1)) ** 2 / (2 * self.sigma2.reshape(self.cluNum, 1)))) + return phi -- Gitee From 0d8b4a41945eaee4951ee4d40325dcaaad7706d3 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:24:27 +0800 Subject: [PATCH 04/80] add assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) create mode 100644 assignment-3/submission/19210680053/README.md diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md new file mode 100644 index 0000000..2d21e48 --- /dev/null +++ b/assignment-3/submission/19210680053/README.md @@ -0,0 +1,12 @@ +# Assignment 3 + +## 1.KMeans 模型结构 +本次实验首先对KMeans模型进行实现 +### 类中心点的初始化 +在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 +初始化数据中心 +$$ +{C_1,C_2,...,C_cluNum} +$$ +### 数据到中心的距离以及分类 + -- Gitee From 48cb43f71555346268ade0827d82d9dd888d933e Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:27:31 +0800 Subject: [PATCH 05/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 2d21e48..d012866 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -6,7 +6,7 @@ 在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 初始化数据中心 $$ -{C_1,C_2,...,C_cluNum} +{{C_1,C_2,...,C_(cluNum)}} $$ ### 数据到中心的距离以及分类 -- Gitee From 2dc595b4d2a7d4b37241bf6d508732a4b0bd8cce Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:27:59 +0800 Subject: [PATCH 06/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index d012866..41af81b 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -6,7 +6,7 @@ 在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 初始化数据中心 $$ -{{C_1,C_2,...,C_(cluNum)}} +{C_1,C_2,...,C_(cluNum)} $$ ### 数据到中心的距离以及分类 -- Gitee From a849bc5586cebb354b3e4e996f034d80decaaed5 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:28:48 +0800 Subject: [PATCH 07/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 41af81b..a63ef4f 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -6,7 +6,7 @@ 在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 初始化数据中心 $$ -{C_1,C_2,...,C_(cluNum)} +{{C_1,C_2,...,C_{cluNum}}} $$ ### 数据到中心的距离以及分类 -- Gitee From cd60eea23e55fce3a673f190e076a7b86ec0fdcc Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:30:19 +0800 Subject: [PATCH 08/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index a63ef4f..c3dc872 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -6,7 +6,7 @@ 在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 初始化数据中心 $$ -{{C_1,C_2,...,C_{cluNum}}} +{{{C_1,C_2,...,C_{cluNum}}}} $$ ### 数据到中心的距离以及分类 -- Gitee From df104ce56c77331b36ec71d3005ab8bc3e9b5545 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:31:18 +0800 Subject: [PATCH 09/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index c3dc872..081f81a 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -4,9 +4,11 @@ 本次实验首先对KMeans模型进行实现 ### 类中心点的初始化 在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 + + 初始化数据中心 $$ -{{{C_1,C_2,...,C_{cluNum}}}} +\begin{{{C_1,C_2,...,C_{cluNum}}}}\end $$ ### 数据到中心的距离以及分类 -- Gitee From 214d181d6b8c1167b3f3bb8a0615d9d62862b870 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:32:24 +0800 Subject: [PATCH 10/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 081f81a..0e2a57f 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -8,7 +8,7 @@ 初始化数据中心 $$ -\begin{{{C_1,C_2,...,C_{cluNum}}}}\end +{{{C_1,C_2,...,C_{cluNum}}}} $$ ### 数据到中心的距离以及分类 -- Gitee From e831f8b701dd55b373824118f91fe61d1d80525d Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:36:51 +0800 Subject: [PATCH 11/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 0e2a57f..e4f4499 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -5,10 +5,12 @@ ### 类中心点的初始化 在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 - -初始化数据中心 +得到如下初始化数据中心 $$ {{{C_1,C_2,...,C_{cluNum}}}} $$ ### 数据到中心的距离以及分类 +接着计算训练集中每个对象到各个中心的欧式距离， +$$ +euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})**2}} -- Gitee From 3c50a18ca62cb13003d0a2d262dbc9ed42be7741 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:37:07 +0800 Subject: [PATCH 12/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index e4f4499..b98f490 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -13,4 +13,4 @@ $$ 接着计算训练集中每个对象到各个中心的欧式距离， $$ euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})**2}} - +$$ -- Gitee From 7cdf59554a24876e12aedc298e587cf6fbe2bab6 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:40:08 +0800 Subject: [PATCH 13/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index b98f490..3a5adce 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -6,11 +6,11 @@ 在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 得到如下初始化数据中心 -$$ -{{{C_1,C_2,...,C_{cluNum}}}} +$$\begin{Bmatrix} +{{{C_1,C_2,...,C_{cluNum}}}}\end{Bmatrix} $$ ### 数据到中心的距离以及分类 接着计算训练集中每个对象到各个中心的欧式距离， $$ -euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})**2}} +euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} $$ -- Gitee From ddf8f9b12992a1b57ee5819425155495f7faa96c Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 21:52:15 +0800 Subject: [PATCH 14/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 3a5adce..725e930 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -3,7 +3,7 @@ ## 1.KMeans 模型结构 本次实验首先对KMeans模型进行实现 ### 类中心点的初始化 -在给定类簇数目（cluNum)以及数据维度(dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 +在给定类簇数目（cluNum)以及数据维度(N*dim)之后，首先随机从数据集中选取cluNum行数据，作为若干个类的中心点 得到如下初始化数据中心 $$\begin{Bmatrix} @@ -14,3 +14,6 @@ $$ $$ euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} $$ +对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 +### 中心点更新 +根据clusterAssment的第一列数据，分别得到距离每个C_k,1= Date: Sun, 13 Jun 2021 21:52:37 +0800 Subject: [PATCH 15/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 725e930..6e27273 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,4 +16,4 @@ euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个C_k,1= Date: Sun, 13 Jun 2021 21:53:34 +0800 Subject: [PATCH 16/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 6e27273..258464f 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,4 +16,4 @@ euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个$$C_k,1= Date: Sun, 13 Jun 2021 21:54:15 +0800 Subject: [PATCH 17/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 258464f..f207f22 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,4 +16,4 @@ euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个{C_k},{1= Date: Sun, 13 Jun 2021 21:54:44 +0800 Subject: [PATCH 18/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index f207f22..d45b7b7 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,4 +16,4 @@ euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个${C_k},{1= Date: Sun, 13 Jun 2021 22:01:42 +0800 Subject: [PATCH 19/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index d45b7b7..40e3f6c 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,4 +16,6 @@ euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1= Date: Sun, 13 Jun 2021 22:03:05 +0800 Subject: [PATCH 20/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 40e3f6c..b460c8e 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -18,4 +18,9 @@ $$ ### 中心点更新 根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1= Date: Sun, 13 Jun 2021 22:05:24 +0800 Subject: [PATCH 21/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index b460c8e..3c59bc6 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -23,4 +23,8 @@ $$ if clusterAssment[i, 0] != minIndex: clusterChanged = True clusterAssment[i, :] = minIndex, minDist ** 2 -``` \ No newline at end of file +``` +此时输出cluNum个中心点作为模型训练结果 +$$\begin{Bmatrix} +C_1,C_2,C_3,...C_{cluNum}\end{Bmatrix} +$$ \ No newline at end of file -- Gitee From 5f7516740c9efb057649869373d79ed97c9d84f7 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 22:06:36 +0800 Subject: [PATCH 22/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 3c59bc6..81d5a5f 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -12,7 +12,7 @@ $$ ### 数据到中心的距离以及分类 接着计算训练集中每个对象到各个中心的欧式距离， $$ -euclDistance={\sqrt {\sum_{n=1}^{dim} (X_{it}-C_{it})^2}} +euclDistance_i={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -- Gitee From 3653891a15ea25da9f1ef103036761aa83f1f13c Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Sun, 13 Jun 2021 22:07:01 +0800 Subject: [PATCH 23/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 81d5a5f..2e7d3c9 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -12,7 +12,7 @@ $$ ### 数据到中心的距离以及分类 接着计算训练集中每个对象到各个中心的欧式距离， $$ -euclDistance_i={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} +euclDistance_{i,j}={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -- Gitee From d341f7e75fb3b0c2bbbddbfa2ca4cae653bdda0a Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 08:55:42 +0800 Subject: [PATCH 24/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 20 ++++++++++++++++--- 1 file changed, 17 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 2e7d3c9..46b72ac 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,9 +16,9 @@ euclDistance_{i,j}={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1= Date: Mon, 14 Jun 2021 08:56:25 +0800 Subject: [PATCH 25/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 46b72ac..6b12e3b 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,7 +16,7 @@ euclDistance_{i,j}={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1\geqk\leqcluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ +根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1$\geqk\$leqcluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ ### 循环停止条件 设置clusterchanged作为循环标志，即对于所有点的clusterAssment中距离最近中心点$C_k$的下标k不再发生改变，则循环结束 ```python @@ -29,7 +29,7 @@ $$\begin{Bmatrix} C_1,C_2,C_3,...C_{cluNum}\end{Bmatrix} $$ ### 模型预测 -'''python +```python def predict(self, test_data): self.test_data = test_data numSamples, dim = self.test_data.shape @@ -39,6 +39,6 @@ $$ clus_type = distance.index(min(distance)) m_res.append(clus_type) return np.array(m_res) -''' +``` 通过计算测试集每个对象距离所有中心点的欧式距离，每个点会被归类到距其最近的中心点所属类中 . -- Gitee From ae36d9b808046158e50f3ecaa2967b608b32a927 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 08:57:01 +0800 Subject: [PATCH 26/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 6b12e3b..b46e21a 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,7 +16,7 @@ euclDistance_{i,j}={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1$\geqk\$leqcluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ +根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1\geq k\leq cluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ ### 循环停止条件 设置clusterchanged作为循环标志，即对于所有点的clusterAssment中距离最近中心点$C_k$的下标k不再发生改变，则循环结束 ```python -- Gitee From 75dac6190348e2160814d35c8fd578e55d84c347 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 08:57:18 +0800 Subject: [PATCH 27/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index b46e21a..bf8fb85 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -16,7 +16,7 @@ euclDistance_{i,j}={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ 对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 -根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1\geq k\leq cluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ +根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1\leq k\leq cluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ ### 循环停止条件 设置clusterchanged作为循环标志，即对于所有点的clusterAssment中距离最近中心点$C_k$的下标k不再发生改变，则循环结束 ```python -- Gitee From 466e28b5f390c215df449ea2bc90d7a38ac58f5e Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:17:42 +0800 Subject: [PATCH 28/80] =?UTF-8?q?=E6=96=B0=E5=BB=BA=20img?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-3/submission/19210680053/img/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-3/submission/19210680053/img/.keep diff --git a/assignment-3/submission/19210680053/img/.keep b/assignment-3/submission/19210680053/img/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From a1a3f5ec6b9f8cb2a5d2cbd2f0663f6b8e5effe5 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:21:03 +0800 Subject: [PATCH 29/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 13 +++++++++++-- 1 file changed, 11 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index bf8fb85..61540b0 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -40,5 +40,14 @@ $$ m_res.append(clus_type) return np.array(m_res) ``` -通过计算测试集每个对象距离所有中心点的欧式距离，每个点会被归类到距其最近的中心点所属类中 -. +通过计算测试集每个对象距离所有中心点的欧式距离，每个点会被归类到距其最近的中心点所属类中。 + +## 2.GaussianMixture 模型结构 +本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 +###1维数据 +###2维数据 +####进行每个聚类的均值以及协方差矩阵初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$\begin{Mmatrix}Minimum value/2,Maximum value/2\end{Mmatrix}$之间生成随机数 +```python +self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) + +``` \ No newline at end of file -- Gitee From 4067bf98659580f7feb5bfbb0a7480ba6cccbb5a Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:21:45 +0800 Subject: [PATCH 30/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 61540b0..a1cd457 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -46,7 +46,7 @@ $$ 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 ###1维数据 ###2维数据 -####进行每个聚类的均值以及协方差矩阵初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$\begin{Mmatrix}Minimum value/2,Maximum value/2\end{Mmatrix}$之间生成随机数 +####进行每个聚类的均值以及协方差矩阵初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[Minimum value/2,Maximum value/2]$之间生成随机数 ```python self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) -- Gitee From fbe913a90b26ebb52c612e5d8a032657cb5ced06 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:22:23 +0800 Subject: [PATCH 31/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index a1cd457..6589846 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -46,7 +46,7 @@ $$ 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 ###1维数据 ###2维数据 -####进行每个聚类的均值以及协方差矩阵初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[Minimum value/2,Maximum value/2]$之间生成随机数 +####进行每个聚类的均值以及协方差矩阵初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 ```python self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) -- Gitee From f32b761bb9569551cf73ca771bd3ffbb332e09ac Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:29:16 +0800 Subject: [PATCH 32/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 13 +++++++++++-- 1 file changed, 11 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 6589846..d68d610 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -46,8 +46,17 @@ $$ 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 ###1维数据 ###2维数据 -####进行每个聚类的均值以及协方差矩阵初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 +####进行每个聚类的均值、协方差矩阵以及对应权重初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 ```python self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) -``` \ No newline at end of file +``` +每个协方差矩阵令其矩阵对角线取值为1，非对角线取值为0 +每个聚类具有等权重 +```python + self.weight = np.ones(self.cluNum) / self.cluNum +``` +#### E step +$$ +\gamma_k^(i)= \pi_kN(x^(i)|\Miu_k,\Sum_k)/\Sum_{k=1}^ +$$ \ No newline at end of file -- Gitee From e39c271669fe27a31ce0c07355cec2ffa4140c86 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:29:39 +0800 Subject: [PATCH 33/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index d68d610..7737cb0 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,5 +58,5 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step $$ -\gamma_k^(i)= \pi_kN(x^(i)|\Miu_k,\Sum_k)/\Sum_{k=1}^ +\Gamma_k^i= \pi_kN(x^(i)|\Miu_k,\Sum_k)/\Sum_{k=1}^ $$ \ No newline at end of file -- Gitee From 92cd5be5a8db203b29150ea922b73f631f76ae49 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:30:13 +0800 Subject: [PATCH 34/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 7737cb0..c4ecfa9 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,5 +58,6 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step $$ -\Gamma_k^i= \pi_kN(x^(i)|\Miu_k,\Sum_k)/\Sum_{k=1}^ +\Gamma_k^{i}= \pi_kN(x^(i)|\Miu_k,\Sum_k)/\Sum_{k=1}^ + $$ \ No newline at end of file -- Gitee From cc03857d1ab48cb15c870e24f87be4c7997655d3 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:30:27 +0800 Subject: [PATCH 35/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index c4ecfa9..77a0c2d 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,6 +58,6 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step $$ -\Gamma_k^{i}= \pi_kN(x^(i)|\Miu_k,\Sum_k)/\Sum_{k=1}^ +\Gamma_k^{i} $$ \ No newline at end of file -- Gitee From fcb70890914928a68b7fb4f0e98307c47c0f702c Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:30:52 +0800 Subject: [PATCH 36/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 77a0c2d..fa34f58 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,6 +58,6 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step $$ -\Gamma_k^{i} +\Gamma_k $$ \ No newline at end of file -- Gitee From e4c329772749562a9aef253f77809aa8dbf675e2 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:31:10 +0800 Subject: [PATCH 37/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index fa34f58..6d69a75 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,6 +58,7 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step $$ -\Gamma_k + +\Gamma_{k} $$ \ No newline at end of file -- Gitee From 20e92e11518b0e070462683c3ee6669c29f25091 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:31:50 +0800 Subject: [PATCH 38/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 6d69a75..184cd25 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -59,6 +59,6 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= #### E step $$ -\Gamma_{k} +\gamma_{k}= \pi_kN(x^(i)|\miu_k,\sum_k)/\Sum_{k=1}^ $$ \ No newline at end of file -- Gitee From e107aff4ed0c90864bb5af45bf6b5efcebca8c1a Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:32:15 +0800 Subject: [PATCH 39/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 184cd25..a5eee75 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -59,6 +59,6 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= #### E step $$ -\gamma_{k}= \pi_kN(x^(i)|\miu_k,\sum_k)/\Sum_{k=1}^ +\gamma_k $$ \ No newline at end of file -- Gitee From 976cb340d6091a473ba9fab5d0e02675e26b0e02 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:33:47 +0800 Subject: [PATCH 40/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index a5eee75..b98099c 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -59,6 +59,6 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= #### E step $$ -\gamma_k +$$\gamma_{Relu}(t) = \text{ReLU}(t + 0.5) - \text{ReLU}(t - 0.5).$$ $$ \ No newline at end of file -- Gitee From 9038fe6bf0cfa1c53d90fb0d515a621fed2d8ee3 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:36:30 +0800 Subject: [PATCH 41/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index b98099c..c0f9758 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -59,6 +59,6 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= #### E step $$ -$$\gamma_{Relu}(t) = \text{ReLU}(t + 0.5) - \text{ReLU}(t - 0.5).$$ +$$\gamma_{k}^(i) = \pi_{k}N(x^(i),\sum_{k})/\sum_{k=1}^{K}N(x^{(i)}|\miu_{k},\sum_k}- \text{ReLU}(t - 0.5).$$ $$ \ No newline at end of file -- Gitee From 6438c2b3119dd84ccb3cb6d672e9a527cd12d739 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:37:43 +0800 Subject: [PATCH 42/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index c0f9758..3fc199c 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -57,8 +57,5 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= self.weight = np.ones(self.cluNum) / self.cluNum ``` #### E step -$$ - -$$\gamma_{k}^(i) = \pi_{k}N(x^(i),\sum_{k})/\sum_{k=1}^{K}N(x^{(i)}|\miu_{k},\sum_k}- \text{ReLU}(t - 0.5).$$ -$$ \ No newline at end of file +$$\gamma_{k}^(i) = $$ -- Gitee From 79252ba467d90fd83e9e1bc979ddc62cb37589ea Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:38:13 +0800 Subject: [PATCH 43/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 3fc199c..41db74c 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,4 +58,4 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step -$$\gamma_{k}^(i) = $$ +$$\gamma_{k}^{(i)} = $$\pi_{k}N(x^(i),\sum_{k})$$ -- Gitee From 5701d70982501194653f63e1e1126b55694122fd Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:38:39 +0800 Subject: [PATCH 44/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 41db74c..4ecf08f 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,4 +58,4 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step -$$\gamma_{k}^{(i)} = $$\pi_{k}N(x^(i),\sum_{k})$$ +$$\gamma_{k}^{(i)} = \pi_{k}N(x^(i),\sum_{k})$$ -- Gitee From ebc12701b4b3ac8b25421d87415ad9ce27524e6a Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:39:52 +0800 Subject: [PATCH 45/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 4ecf08f..d45594d 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,4 +58,4 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step -$$\gamma_{k}^{(i)} = \pi_{k}N(x^(i),\sum_{k})$$ +$$\gamma_{k}^{(i)} = \pi_{k}N(x^{(i)}|\mu_{k},\sum_{k})$$ -- Gitee From 2a001f88d5eb088df8f4ea36df0089e86927ef75 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:40:29 +0800 Subject: [PATCH 46/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index d45594d..771543a 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,4 +58,4 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step -$$\gamma_{k}^{(i)} = \pi_{k}N(x^{(i)}|\mu_{k},\sum_{k})$$ +$$\gamma_{k}^{(i)} = \pi_{k}N(x^{(i)}|\mu_{k},\sum{k})$$ -- Gitee From 71cd8dda2b3fe4f0f610bdaf84c4576793cf8b4d Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:42:43 +0800 Subject: [PATCH 47/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 771543a..a2850f0 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,4 +58,4 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step -$$\gamma_{k}^{(i)} = \pi_{k}N(x^{(i)}|\mu_{k},\sum{k})$$ +$$\gamma_{k}^{(i)} = \pi_{k}N(x^{(i)}|\mu_{k},\Sigma{k})/\sum_{k=1}^{K}N(x^{(i)}|\mu_{k},\Sigma{k})$$ -- Gitee From 17b5ed43158f00541fdf01fda689e92827914b9c Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:44:05 +0800 Subject: [PATCH 48/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index a2850f0..f652b99 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,4 +58,4 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step -$$\gamma_{k}^{(i)} = \pi_{k}N(x^{(i)}|\mu_{k},\Sigma{k})/\sum_{k=1}^{K}N(x^{(i)}|\mu_{k},\Sigma{k})$$ +$$\gamma_{k}^{(i)} = \frac{\pi_{k}N(x^{(i)}|\mu_{k},\Sigma{k})}{\sum_{k=1}^{K}N(x^{(i)}|\mu_{k},\Sigma{k})}$$ -- Gitee From a98d66dc875c610d6995cafc02cb1dc034bc171a Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 09:59:33 +0800 Subject: [PATCH 49/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index f652b99..10dfe26 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -58,4 +58,12 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= ``` #### E step -$$\gamma_{k}^{(i)} = \frac{\pi_{k}N(x^{(i)}|\mu_{k},\Sigma{k})}{\sum_{k=1}^{K}N(x^{(i)}|\mu_{k},\Sigma{k})}$$ +$$\gamma_{k}^{(i)} = \frac{\pi_{k}N(x^{(i)}|\mu_{k},\Sigma_{k})}{\sum_{k=1}^{K}N(x^{(i)}|\mu_{k},\Sigma_{k})}$$ +$N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$pi_{k}$每个cluster对应weight,通过上式计算得到第i个数据样本点落在第k个聚类中的概率 +#### M step +通过计算cluster k 中的样本数来进行权重更新$\pi_{k}$ +$$\N_{k}=\sum_{i=1}^{n}\gamma_{k}^{(i)}$$ +$$\pi_{k}=\frac{N_{k}}{N} +并对每个cluster的均值以及协方差matrix进行更新 +$$\mu_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^(i)x^{(i)}}{N_{k}}$$ +$$\Sigma_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^(i)(x^{(i)}-\mu_{k})(x^{(i)}-\mu_{k})^{T}}{N_{k}}$$ \ No newline at end of file -- Gitee From 27a9b7e88066f363da6021bb8d3de9456172ff97 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:00:43 +0800 Subject: [PATCH 50/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 10dfe26..4b965b1 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -63,7 +63,7 @@ $N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$ #### M step 通过计算cluster k 中的样本数来进行权重更新$\pi_{k}$ $$\N_{k}=\sum_{i=1}^{n}\gamma_{k}^{(i)}$$ -$$\pi_{k}=\frac{N_{k}}{N} +$$\pi_{k}=\frac{N_{k}}{N}$$ 并对每个cluster的均值以及协方差matrix进行更新 $$\mu_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^(i)x^{(i)}}{N_{k}}$$ $$\Sigma_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^(i)(x^{(i)}-\mu_{k})(x^{(i)}-\mu_{k})^{T}}{N_{k}}$$ \ No newline at end of file -- Gitee From 1e8debc773db75788c677bc827d088ba62e1e707 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:02:55 +0800 Subject: [PATCH 51/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 16 +++++++++++++--- 1 file changed, 13 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 4b965b1..5ccd9c9 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -63,7 +63,17 @@ $N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$ #### M step 通过计算cluster k 中的样本数来进行权重更新$\pi_{k}$ $$\N_{k}=\sum_{i=1}^{n}\gamma_{k}^{(i)}$$ -$$\pi_{k}=\frac{N_{k}}{N}$$ +$$Weight_{k}=\frac{N_{k}}{N}$$ 并对每个cluster的均值以及协方差matrix进行更新 -$$\mu_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^(i)x^{(i)}}{N_{k}}$$ -$$\Sigma_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^(i)(x^{(i)}-\mu_{k})(x^{(i)}-\mu_{k})^{T}}{N_{k}}$$ \ No newline at end of file +$$\mu_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^{(i)}x^{(i)}}{N_{k}}$$ +$$\Sigma_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^{(i)}(x^{(i)}-\mu_{k})(x^{(i)}-\mu_{k})^{T}}{N_{k}}$$ + +```python +N_k = np.sum(p_mat[:, j], axis=0) +self.weight[j] = N_k / sampleN +self.means[j] = (1 / N_k) * np.sum(train_data * p_mat[:, j].reshape(-1, 1), axis=0) + +self.covariance[j] = (1 / N_k) * np.dot( + (p_mat[:, j].reshape(-1, 1) * (train_data - self.means[j])).T, + (train_data - self.means[j])) + self.reg_cov +``` \ No newline at end of file -- Gitee From ac5209a22f49bc1e43829725b02627eb4962d503 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:39:42 +0800 Subject: [PATCH 52/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 40 +++++++++++++++++-- 1 file changed, 37 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 5ccd9c9..541e58e 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -45,6 +45,34 @@ $$ ## 2.GaussianMixture 模型结构 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 ###1维数据 +####数据正则化 +对于一维数据，首先进行数据正则化处理,以及形式上转化为一维数据 +```python + def normalize(self, data): + flat_data = data.flatten() + nor_data = (flat_data - flat_data.mean()) / np.sqrt(flat_data.var()) + return nor_data +``` +####进行数据的每个聚类均值、方差（而非协方差矩阵）以及对应权重初始化 +对于一维数据均值初始化，采用方式是：生成关于0对称array * 训练集中均值 +```python +self.mu = (np.arange(self.cluNum) - self.cluNum // 2) * (train_data.max() - train_data.min()) / self.cluNum +``` +对于方差初始化，cluNum个聚类全部取值为1； +对于权重，赋予每个聚类等权重 +#### E step and M step +E step与M step同2D数据思想相同 +但在M step中进行每个cluster均值与方差更新时，会赋予旧均值、旧方差0.1的权重；新均值方差0.9的权重，进行迭代更新 +####迭代停止条件 +模型通过设置阈值，使得$\begin{Bmatrix}\Sigma_{k},\pi_{k},\mu_{k}\end{Bmatrix}$均收敛来作为停止条件 +```python + if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1e-3: + break +``` +####模型预测 +$$ +由train_data得到每个聚类的均值、方差以及对应权重，同样进行$frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}{\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ +数据会被归至该类。 ###2维数据 ####进行每个聚类的均值、协方差矩阵以及对应权重初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 ```python @@ -62,8 +90,8 @@ $$\gamma_{k}^{(i)} = \frac{\pi_{k}N(x^{(i)}|\mu_{k},\Sigma_{k})}{\sum_{k=1}^{K}N $N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$pi_{k}$每个cluster对应weight,通过上式计算得到第i个数据样本点落在第k个聚类中的概率 #### M step 通过计算cluster k 中的样本数来进行权重更新$\pi_{k}$ -$$\N_{k}=\sum_{i=1}^{n}\gamma_{k}^{(i)}$$ -$$Weight_{k}=\frac{N_{k}}{N}$$ +$$N_{k}=\sum_{i=1}^{n}\gamma_{k}^{(i)}$$ +$$\pi_{k}=\frac{N_{k}}{N}$$ 并对每个cluster的均值以及协方差matrix进行更新 $$\mu_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^{(i)}x^{(i)}}{N_{k}}$$ $$\Sigma_{k}=\frac{\sum_{i=1}^{cluNum}\gamma_{k}^{(i)}(x^{(i)}-\mu_{k})(x^{(i)}-\mu_{k})^{T}}{N_{k}}$$ @@ -76,4 +104,10 @@ self.means[j] = (1 / N_k) * np.sum(train_data * p_mat[:, j].reshape(-1, 1), axis self.covariance[j] = (1 / N_k) * np.dot( (p_mat[:, j].reshape(-1, 1) * (train_data - self.means[j])).T, (train_data - self.means[j])) + self.reg_cov -``` \ No newline at end of file +``` +####迭代条件 +模型可通过使得$\begin{Bmatrix}\Sigma_{k},\pi_{k},\mu_{k}\end{Bmatrix}$均收敛来作为停止条件，此处进行最大训练次数来作为模型训练的终止条件。 +####模型预测 +由train_data得到每个聚类的均值、协方差矩阵以及对应权重 +$prob_{k,i}=\pi_{k}N(x^{(i)}|\mu_{k},\Sigma_{k})$ +对于训练集中数据点i,寻求在所有中心点中令上式最大化的中心点k，数据会被归至该类。 \ No newline at end of file -- Gitee From 69fe7ef0a3a4ec2722bb9a0911710c9af3d584f7 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:40:39 +0800 Subject: [PATCH 53/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 541e58e..4d19b17 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -44,8 +44,8 @@ $$ ## 2.GaussianMixture 模型结构 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 -###1维数据 -####数据正则化 +### 1维数据 +#### 数据正则化 对于一维数据，首先进行数据正则化处理,以及形式上转化为一维数据 ```python def normalize(self, data): @@ -53,7 +53,7 @@ $$ nor_data = (flat_data - flat_data.mean()) / np.sqrt(flat_data.var()) return nor_data ``` -####进行数据的每个聚类均值、方差（而非协方差矩阵）以及对应权重初始化 +#### 进行数据的每个聚类均值、方差（而非协方差矩阵）以及对应权重初始化 对于一维数据均值初始化，采用方式是：生成关于0对称array * 训练集中均值 ```python self.mu = (np.arange(self.cluNum) - self.cluNum // 2) * (train_data.max() - train_data.min()) / self.cluNum @@ -63,13 +63,13 @@ self.mu = (np.arange(self.cluNum) - self.cluNum // 2) * (train_data.max() - trai #### E step and M step E step与M step同2D数据思想相同 但在M step中进行每个cluster均值与方差更新时，会赋予旧均值、旧方差0.1的权重；新均值方差0.9的权重，进行迭代更新 -####迭代停止条件 +#### 迭代停止条件 模型通过设置阈值，使得$\begin{Bmatrix}\Sigma_{k},\pi_{k},\mu_{k}\end{Bmatrix}$均收敛来作为停止条件 ```python if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1e-3: break ``` -####模型预测 +#### 模型预测 $$ 由train_data得到每个聚类的均值、方差以及对应权重，同样进行$frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}{\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ 数据会被归至该类。 @@ -105,9 +105,9 @@ self.covariance[j] = (1 / N_k) * np.dot( (p_mat[:, j].reshape(-1, 1) * (train_data - self.means[j])).T, (train_data - self.means[j])) + self.reg_cov ``` -####迭代条件 +#### 迭代条件 模型可通过使得$\begin{Bmatrix}\Sigma_{k},\pi_{k},\mu_{k}\end{Bmatrix}$均收敛来作为停止条件，此处进行最大训练次数来作为模型训练的终止条件。 -####模型预测 +#### 模型预测 由train_data得到每个聚类的均值、协方差矩阵以及对应权重 $prob_{k,i}=\pi_{k}N(x^{(i)}|\mu_{k},\Sigma_{k})$ 对于训练集中数据点i,寻求在所有中心点中令上式最大化的中心点k，数据会被归至该类。 \ No newline at end of file -- Gitee From f02dcfa48b2229deeaf5a467bdfb73a4d0c9f4b3 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:41:25 +0800 Subject: [PATCH 54/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 4d19b17..51d27ec 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -70,8 +70,9 @@ E step与M step同2D数据思想相同 break ``` #### 模型预测 -$$ -由train_data得到每个聚类的均值、方差以及对应权重，同样进行$frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}{\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ + +由train_data得到每个聚类的均值、方差以及对应权重，同样进行$frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k} +{\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ 数据会被归至该类。 ###2维数据 ####进行每个聚类的均值、协方差矩阵以及对应权重初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 -- Gitee From cf92556def9358db3b20e8da2aac5c18d814fdf7 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:42:45 +0800 Subject: [PATCH 55/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 51d27ec..3417591 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -71,11 +71,12 @@ E step与M step同2D数据思想相同 ``` #### 模型预测 -由train_data得到每个聚类的均值、方差以及对应权重，同样进行$frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k} +由train_data得到每个聚类的均值、方差以及对应权重，同样进行 +$frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}} {\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ 数据会被归至该类。 -###2维数据 -####进行每个聚类的均值、协方差矩阵以及对应权重初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 +### 2维数据 +#### 进行每个聚类的均值、协方差矩阵以及对应权重初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 ```python self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) -- Gitee From 9adbf8f3f5c1494382cc28ea3ad3f005a9d94d77 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:43:35 +0800 Subject: [PATCH 56/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 3417591..aeb4210 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -72,7 +72,7 @@ E step与M step同2D数据思想相同 #### 模型预测 由train_data得到每个聚类的均值、方差以及对应权重，同样进行 -$frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}} +$\frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}} {\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ 数据会被归至该类。 ### 2维数据 -- Gitee From eacf990fc944127658648039b1d078353918fe1c Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:45:00 +0800 Subject: [PATCH 57/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 64 +++++++++---------- 1 file changed, 32 insertions(+), 32 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index aeb4210..e891314 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -44,37 +44,6 @@ $$ ## 2.GaussianMixture 模型结构 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 -### 1维数据 -#### 数据正则化 -对于一维数据，首先进行数据正则化处理,以及形式上转化为一维数据 -```python - def normalize(self, data): - flat_data = data.flatten() - nor_data = (flat_data - flat_data.mean()) / np.sqrt(flat_data.var()) - return nor_data -``` -#### 进行数据的每个聚类均值、方差（而非协方差矩阵）以及对应权重初始化 -对于一维数据均值初始化，采用方式是：生成关于0对称array * 训练集中均值 -```python -self.mu = (np.arange(self.cluNum) - self.cluNum // 2) * (train_data.max() - train_data.min()) / self.cluNum -``` -对于方差初始化，cluNum个聚类全部取值为1； -对于权重，赋予每个聚类等权重 -#### E step and M step -E step与M step同2D数据思想相同 -但在M step中进行每个cluster均值与方差更新时，会赋予旧均值、旧方差0.1的权重；新均值方差0.9的权重，进行迭代更新 -#### 迭代停止条件 -模型通过设置阈值，使得$\begin{Bmatrix}\Sigma_{k},\pi_{k},\mu_{k}\end{Bmatrix}$均收敛来作为停止条件 -```python - if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1e-3: - break -``` -#### 模型预测 - -由train_data得到每个聚类的均值、方差以及对应权重，同样进行 -$\frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}} -{\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ -数据会被归至该类。 ### 2维数据 #### 进行每个聚类的均值、协方差矩阵以及对应权重初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 ```python @@ -112,4 +81,35 @@ self.covariance[j] = (1 / N_k) * np.dot( #### 模型预测 由train_data得到每个聚类的均值、协方差矩阵以及对应权重 $prob_{k,i}=\pi_{k}N(x^{(i)}|\mu_{k},\Sigma_{k})$ -对于训练集中数据点i,寻求在所有中心点中令上式最大化的中心点k，数据会被归至该类。 \ No newline at end of file +对于训练集中数据点i,寻求在所有中心点中令上式最大化的中心点k，数据会被归至该类。 +### 1维数据 +#### 数据正则化 +对于一维数据，首先进行数据正则化处理,以及形式上转化为一维数据 +```python + def normalize(self, data): + flat_data = data.flatten() + nor_data = (flat_data - flat_data.mean()) / np.sqrt(flat_data.var()) + return nor_data +``` +#### 进行数据的每个聚类均值、方差（而非协方差矩阵）以及对应权重初始化 +对于一维数据均值初始化，采用方式是：生成关于0对称array * 训练集中均值 +```python +self.mu = (np.arange(self.cluNum) - self.cluNum // 2) * (train_data.max() - train_data.min()) / self.cluNum +``` +对于方差初始化，cluNum个聚类全部取值为1； +对于权重，赋予每个聚类等权重 +#### E step and M step +E step与M step同2D数据思想相同 +但在M step中进行每个cluster均值与方差更新时，会赋予旧均值、旧方差0.1的权重；新均值方差0.9的权重，进行迭代更新 +#### 迭代停止条件 +模型通过设置阈值，使得$\begin{Bmatrix}\Sigma_{k},\pi_{k},\mu_{k}\end{Bmatrix}$均收敛来作为停止条件 +```python + if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1e-3: + break +``` +#### 模型预测 + +由train_data得到每个聚类的均值、方差以及对应权重，同样进行 +$argmax\frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}} +{\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ +的计算，此时数据点i会被归至第k类 -- Gitee From de1d34616dbf9c489b903595293b9f91cc1872f1 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:46:34 +0800 Subject: [PATCH 58/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index e891314..706db2a 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -45,7 +45,8 @@ $$ ## 2.GaussianMixture 模型结构 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 ### 2维数据 -#### 进行每个聚类的均值、协方差矩阵以及对应权重初始化,由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum value)/2,(Maximum value)/2]$之间生成随机数 +#### 进行每个聚类的均值、协方差矩阵以及对应权重初始化 +由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum\quadvalue)/2,(Maximum\quadvalue)/2]$之间生成随机数 ```python self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) @@ -58,7 +59,7 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= #### E step $$\gamma_{k}^{(i)} = \frac{\pi_{k}N(x^{(i)}|\mu_{k},\Sigma_{k})}{\sum_{k=1}^{K}N(x^{(i)}|\mu_{k},\Sigma_{k})}$$ -$N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$pi_{k}$每个cluster对应weight,通过上式计算得到第i个数据样本点落在第k个聚类中的概率 +$N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$/pi_{k}$每个cluster对应weight,通过上式计算得到第i个数据样本点落在第k个聚类中的概率 #### M step 通过计算cluster k 中的样本数来进行权重更新$\pi_{k}$ $$N_{k}=\sum_{i=1}^{n}\gamma_{k}^{(i)}$$ -- Gitee From 8672646788b4939127d687de1f4d8a5a461dda32 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:47:39 +0800 Subject: [PATCH 59/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 706db2a..6096a20 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -46,7 +46,7 @@ $$ 本次实验要求对1-D 与2-D 数据进行GaussianMixture的实现,所以分别对两种类型数据进行实现 ### 2维数据 #### 进行每个聚类的均值、协方差矩阵以及对应权重初始化 -由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum\quadvalue)/2,(Maximum\quadvalue)/2]$之间生成随机数 +由于初值选择会影响分类效果，因此均值采用介于训练集数据$[(Minimum \quad value)/2,(Maximum \quad value)/2]$之间生成随机数 ```python self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) -- Gitee From edc69dec30a7c07374c290e6aacf887ccda2d9ff Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 10:48:04 +0800 Subject: [PATCH 60/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 6096a20..873aa6c 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -59,7 +59,7 @@ self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size= #### E step $$\gamma_{k}^{(i)} = \frac{\pi_{k}N(x^{(i)}|\mu_{k},\Sigma_{k})}{\sum_{k=1}^{K}N(x^{(i)}|\mu_{k},\Sigma_{k})}$$ -$N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$/pi_{k}$每个cluster对应weight,通过上式计算得到第i个数据样本点落在第k个聚类中的概率 +$N(x^{(i)}|\mu_{k},\Sigma_{k})$采用二维高斯分布进行拟合，再乘以$\pi_{k}$每个cluster对应weight,通过上式计算得到第i个数据样本点落在第k个聚类中的概率 #### M step 通过计算cluster k 中的样本数来进行权重更新$\pi_{k}$ $$N_{k}=\sum_{i=1}^{n}\gamma_{k}^{(i)}$$ -- Gitee From 3e92df86b840888a984d9889cee67d961af596d6 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 11:06:53 +0800 Subject: [PATCH 61/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 55 +++++++++++++++++++ 1 file changed, 55 insertions(+) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 873aa6c..a524338 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -114,3 +114,58 @@ E step与M step同2D数据思想相同 $argmax\frac{N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}} {\sum_{k=1}^{cluNum}N(X_{k}|\mu_{k},\Sigma_{k})Weight_{k}}$ 的计算，此时数据点i会被归至第k类 +## 3.基础实验 +### 3.1数据可视化 +在test_demo.py中进行数据可视化实现 +```python +def pltshow(test_data, res, n_clu): + mark = [[np.random.randint(0, 256) for i in range(3)] for j in range(n_clu)] + marklist = ["#{:02x}{:02x}{:02x}".format(mark[i][0], mark[i][1], mark[i][2]) for i in range(n_clu)] + colorlist = [marklist[i] for i in res] + pyplot.scatter(test[:, 0], test[:, 1], c=colorlist) + pyplot.show() +``` +### 3.2随机二维数据集生成 +通过生成不同均值、方差（协方差矩阵）、以及不同数目高斯分布作为训练集与数据集的二维数据对模型效果进行检验 +当数据分散时，分类效果较准确 ++ 第一类数据，数量为800个，标签为0： + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +3 & 0 \\\\ +0 & 2 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +1 & 2 +\end{array}\right] +\end{array} +$$ + ++ 第二类数据，数量为200个，标签为1： + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +2 & 0 \\\\ +0 & 2 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +26 & 28 +\end{array}\right] +\end{array} +$$ + ++ 第三类数据，数量为1000个，标签为2： + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +10 & 5 \\\\ +5 & 10 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +-25 & -23 +\end{array}\right] +\end{array} +$$ -- Gitee From 34264463e0e1b5151057f7b2cb9c9c2c2d98d5ae Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: 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zFMkVM%6)ZF}bm#DUmnb|cVVd1qvzXk}XFWR)pXtKzc*G21|1_cBNm`rYF=V!aN zW7^3Dz+LU9fjik#FJ8P@2JD8j+J-4nzJ}4|qEaGvJ9le0uulDvx76guW3F3I#G Date: Mon, 14 Jun 2021 13:56:17 +0800 Subject: [PATCH 63/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 35 +++++++++++++++++++ 1 file changed, 35 insertions(+) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index a524338..693e66a 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -169,3 +169,38 @@ $$ \end{array}\right] \end{array} $$ + +随机打乱数据集后，前80%作为训练集，后20%作为测试集 +生成训练集如下所示 +Training dataset with 3 Gaussian Distribution +测试集如下所示 +Testing dataset with 3 Gaussian Distribution +Kmeans分类结果如下所示： +Kmeans Classification with 3 Gaussian Distribution +Gmm分类结果如下所示： + + +此时，加大分类难度，再增加一类数据集： + +第四类数据集，数量为1000，标签为3： +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +4 & 3 \\\\ +3 & 4 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +-20 & -21 +\end{array}\right] +\end{array} +$$ + +随机打乱新数据集后，前80%作为训练集，后20%作为测试集 +生成训练集如下所示 + +测试集如下所示 + +Kmeans分类结果如下所示： + + +Gmm分类结果如下所示： \ No newline at end of file -- Gitee From 402e3096fc459b665add92c7c5000fb5a162b850 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 14:05:43 +0800 Subject: [PATCH 64/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 29 ++++++++++++++----- 1 file changed, 22 insertions(+), 7 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 693e66a..f5ba69f 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -171,16 +171,23 @@ $$ $$ 随机打乱数据集后，前80%作为训练集，后20%作为测试集 -生成训练集如下所示 +生成训练集如下所示: + Training dataset with 3 Gaussian Distribution -测试集如下所示 + +测试集如下所示: + Testing dataset with 3 Gaussian Distribution + Kmeans分类结果如下所示： -Kmeans Classification with 3 Gaussian Distribution + +Kmeans Classification with 3 Gaussian Distribution + Gmm分类结果如下所示： +Kmeans Classification with 3 Gaussian Distribution -此时，加大分类难度，再增加一类数据集： +此时，加大分类难度，再增加一类与已有较为接近数据集： 第四类数据集，数量为1000，标签为3： $$ @@ -196,11 +203,19 @@ $$ $$ 随机打乱新数据集后，前80%作为训练集，后20%作为测试集 -生成训练集如下所示 -测试集如下所示 +生成训练集如下所示： + +Kmeans Classification with 4 Gaussian Distribution + +测试集如下所示： + +Kmeans Classification with 4 Gaussian Distribution Kmeans分类结果如下所示： +Kmeans Classification with 3 Gaussian Distribution + +Gmm分类结果如下所示： -Gmm分类结果如下所示： \ No newline at end of file +Kmeans Classification with 3 Gaussian Distribution \ No newline at end of file -- Gitee From 95ec37a03700d753dc586d16b31012fc226fb89c Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 14:06:43 +0800 Subject: [PATCH 65/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index f5ba69f..75e3abe 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -218,4 +218,4 @@ Kmeans分类结果如下所示： Gmm分类结果如下所示： -Kmeans Classification with 3 Gaussian Distribution \ No newline at end of file +Kmeans Classification with 3 Gaussian Distribution \ No newline at end of file -- Gitee From b9f7a87dbc9e5ee4117243cfb8b6d52bf30e1c85 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 14:07:35 +0800 Subject: [PATCH 66/80] kmeans --- .../submission/19210680053/img/KMeans2.png | Bin 0 -> 19815 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-3/submission/19210680053/img/KMeans2.png diff --git 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a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 75e3abe..17bb221 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -173,19 +173,19 @@ $$ 随机打乱数据集后，前80%作为训练集，后20%作为测试集 生成训练集如下所示: -Training dataset with 3 Gaussian Distribution +Training dataset with 3 Gaussian Distribution 测试集如下所示: -Testing dataset with 3 Gaussian Distribution +Testing dataset with 3 Gaussian Distribution Kmeans分类结果如下所示： -Kmeans Classification with 3 Gaussian Distribution +Kmeans Classification with 3 Gaussian Distribution Gmm分类结果如下所示： -Kmeans Classification with 3 Gaussian Distribution +Kmeans Classification with 3 Gaussian Distribution 此时，加大分类难度，再增加一类与已有较为接近数据集： @@ -206,16 +206,25 @@ $$ 生成训练集如下所示： -Kmeans Classification with 4 Gaussian Distribution +Kmeans Classification with 4 Gaussian Distribution 测试集如下所示： -Kmeans Classification with 4 Gaussian Distribution +Kmeans Classification with 4 Gaussian Distribution Kmeans分类结果如下所示： -Kmeans Classification with 3 Gaussian Distribution +Kmeans Classification with 3 Gaussian Distribution -Gmm分类结果如下所示： +GMM分类结果如下所示： + +Kmeans Classification with 3 Gaussian Distribution + +此时，GMM分类结果优于KMeans，原因是给出数据本身服从二维高斯分布。 + +KMeans的迭代停止条件是计算欧氏距离，直至每一cluster中心点不再发生变化，当存在两类数据中心点较为接近时，即便迭代停止，也无法对数据点进行有效区分； + +而在给定数据服从二维高斯分布，符合GMM也是假定数据服从高斯分布假设，此时分类效果更好。 + +## 4.类簇选择 -Kmeans Classification with 3 Gaussian Distribution \ No newline at end of file -- Gitee From 9c843d9fc4f7bce742f1fbc405a5e381d1740667 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 15:56:53 +0800 Subject: [PATCH 68/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 17bb221..93f619c 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -183,7 +183,7 @@ Kmeans分类结果如下所示： Kmeans Classification with 3 Gaussian Distribution -Gmm分类结果如下所示： +GaussianMixture分类结果如下所示： Kmeans Classification with 3 Gaussian Distribution @@ -228,3 +228,11 @@ KMeans的迭代停止条件是计算欧氏距离，直至每一cluster中心点 ## 4.类簇选择 +##Elbow Method 进行优化 + +算法原理是在K 值相对较小的情况下，当选择的k值小于真正的n_clusters时，k每增加1，代价值就会大幅的减小；当选择的k值大于真正的n_cluster时， k每增加1，cost值的变化就不会那么明显。此时，正确的k值就会在这个转折点，类似肘部的地方。 + +对于代价值定义： +$$ +cost = \sum_{k=1}^{n_cluster}\sum_{i=1}^{n}(X_{i,k}-C_{k})^2 +$$ \ No newline at end of file -- Gitee From 4af92564956ae2b92be3f38f1bffff7c2bc11c82 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 16:47:39 +0800 Subject: [PATCH 69/80] elbow --- .../submission/19210680053/img/elbowres1.png | Bin 0 -> 22952 bytes .../submission/19210680053/img/elbowres2.png | Bin 0 -> 24114 bytes 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zhA@Ei0dzrPKoesOl}KO>HL=!m^Ydqheg867dU3WrLB<5gkU%;w4cYQ`!^~uF8Wf9q z5g6wkG+=J`+nI(oHX=hM4hi?AgA@Zo*x%REw0&@5!9!%oR%G?{rGUZM4sB5G#voF8 zZZ3C8-HLfiFr^mF)2sJQ0381wbeUygtxV|QKk17^Fcw|o=3;tiqBSHiloEg-Yc@lW z+Ci)N?$lC4`LmgdTU%QLLqkyRj4&_&Daq@zg9R&}U9&nN6FCe9D0ghSqX@{pKTu)z z#M^{DaDOC|L!c51E`g_z^jNXD!J#0?tb?cOtjwbpWn&@zu~mKCmzg= z*4kbT_`=(-eg;~I3Wo}lq+nt7(d&bsRa9I!ckWy(Yt7u#v$!im%L;^1P7PnYc(D_5 z-aj=pFTtlA&ub#i@Bl$!KLQ(O|NbjsR^7EHQwd*ro7v_lIrM&|P4ZR;^y%L*mph8c zbP4XZ6z?e867x1Buv8HL z=Slws+E_!G?CGeE!GiOVU##wGl%I~aKY5G@Ws(PcdOh6mJPvt_^BKVD(0wNayv_eN dUZ(x#-{m#pu-A^~At>)6%#6;Wi%&V;`8V*^W_bVr literal 0 HcmV?d00001 -- Gitee From 6e2b5ec95408669c0c0ad7ecd5504061e809e302 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 16:49:00 +0800 Subject: [PATCH 70/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 32 +++++++++++++++++-- 1 file changed, 29 insertions(+), 3 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index 93f619c..a47e954 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -14,7 +14,7 @@ $$ $$ euclDistance_{i,j}={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ -对于每个对象，分别保留其相距最近中心点下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 +对于每个对象，分别保留其相距__最近中心点__下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1\leq k\leq cluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ ### 循环停止条件 @@ -234,5 +234,31 @@ KMeans的迭代停止条件是计算欧氏距离，直至每一cluster中心点 对于代价值定义： $$ -cost = \sum_{k=1}^{n_cluster}\sum_{i=1}^{n}(X_{i,k}-C_{k})^2 -$$ \ No newline at end of file +cost = \sum_{k=1}^{(n_cluster)}\sum_{i=1}^{n}(X_{i,k}-C_{k})^2 +$$ +即对于训练集中每个点，计算它到所属类别中心的欧式距离并进行加总，作为总代价值 + +## 最优类簇数目选择 +$$ +cost chg_{k} = cost_{k} / cost_{k-1}-1 +$$ +选取$cost chg_{k}$最小的k值作为最优分类下的类簇数目进行拟合，分别使用test_demo_elbow中由三个高斯分布和四个高斯分布组合的数据集进行求解， +# 三个高斯分布 + +训练集的实际分布情况 +Elbow Kmeans Classification with 3 Gaussian Distribution + +模型预测 + +Elbow Kmeans Classification with 3 Gaussian Distribution + +# 四个高斯分布 + +训练集的实际分布情况 + +Kmeans Classification with 3 Gaussian Distribution + +模型预测 + +Kmeans Classification with 3 Gaussian Distribution + -- Gitee From 315c44381c18c4f928c99fde201d30aa65a5a4cf Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 17:31:01 +0800 Subject: [PATCH 71/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 19 +++++++++++++++---- 1 file changed, 15 insertions(+), 4 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index a47e954..ca53159 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -228,7 +228,7 @@ KMeans的迭代停止条件是计算欧氏距离，直至每一cluster中心点 ## 4.类簇选择 -##Elbow Method 进行优化 +### Elbow Method 进行优化 算法原理是在K 值相对较小的情况下，当选择的k值小于真正的n_clusters时，k每增加1，代价值就会大幅的减小；当选择的k值大于真正的n_cluster时， k每增加1，cost值的变化就不会那么明显。此时，正确的k值就会在这个转折点，类似肘部的地方。 @@ -236,13 +236,23 @@ KMeans的迭代停止条件是计算欧氏距离，直至每一cluster中心点 $$ cost = \sum_{k=1}^{(n_cluster)}\sum_{i=1}^{n}(X_{i,k}-C_{k})^2 $$ -即对于训练集中每个点，计算它到所属类别中心的欧式距离并进行加总，作为总代价值 +即对于训练集中每个点，计算它到所属类别中心的欧式距离平方进行加总，作为总代价值 ## 最优类簇数目选择 + +首先进行总代价变化率： $$ cost chg_{k} = cost_{k} / cost_{k-1}-1 $$ -选取$cost chg_{k}$最小的k值作为最优分类下的类簇数目进行拟合，分别使用test_demo_elbow中由三个高斯分布和四个高斯分布组合的数据集进行求解， +接着计算变化率的变动情况(即凸性） +$$ +cost convex \quad chg_{k} = cost chg_{k} - cost chg_{k-1} +$$ +选取$cost convex \quad chg_{k}$最大的k值作为最优分类下的类簇数目进行拟合，即分类数目为$k-1$到k下降陡峭，分类数目为k到$k+1下降平缓。 + +分别使用test_demo_elbow中由三个高斯分布和四个高斯分布组合的数据集进行求解： + + # 三个高斯分布 训练集的实际分布情况 @@ -250,7 +260,7 @@ $$ 模型预测 -Elbow Kmeans Classification with 3 Gaussian Distribution +Elbow Kmeans Classification with 3 Gaussian Distribution # 四个高斯分布 @@ -262,3 +272,4 @@ $$ Kmeans Classification with 3 Gaussian Distribution +Elbow test的局限性在于其一般适用于k值较小的情况，因此生成二维高斯数据集数目较少。 -- Gitee From b2359613a7920a35a1bdfa9d140b3b9a9efb6d61 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 17:33:06 +0800 Subject: [PATCH 72/80] update assignment-3/submission/19210680053/source.py. --- assignment-3/submission/19210680053/source.py | 44 ++++++++++++++++--- 1 file changed, 39 insertions(+), 5 deletions(-) diff --git a/assignment-3/submission/19210680053/source.py b/assignment-3/submission/19210680053/source.py index 4155b56..eb8b9e1 100644 --- a/assignment-3/submission/19210680053/source.py +++ b/assignment-3/submission/19210680053/source.py @@ -5,6 +5,7 @@ from scipy.stats import multivariate_normal class KMeans(object): def __init__(self, n_clusters): self.cluNum = n_clusters + self.distance = 0 def fit(self, train_data): # first set the initial centers by random selection @@ -41,6 +42,9 @@ class KMeans(object): if len(pointsInCluster) != 0: self.centroids[j, :] = np.mean(pointsInCluster, axis=0) + for i in range(len(clusterAssment)): + self.distance += clusterAssment[i, 1] + return self.centroids, clusterAssment, self.distance def predict(self, test_data): self.test_data = test_data @@ -52,16 +56,18 @@ class KMeans(object): m_res.append(clus_type) return np.array(m_res) + def euclDistance(self, vector1, vector2): return np.sqrt(sum(np.power(vector2 - vector1, 2))) + class GaussianMixture: # covariance: ndarray def __init__(self, n_clusters, reg_cov: float = 1e-06): self.cluNum = n_clusters - self.max_iter = 200 + self.max_iter = 1200 self.reg_cov = reg_cov self.alpha = (np.ones(n_clusters) / n_clusters) self.sigma2 = (np.ones(n_clusters)) @@ -88,7 +94,7 @@ class GaussianMixture: axis=0) / self.gamma.sum(axis=0)) # alpha.shape(1, K) self.alpha = (0.1 * self.alpha + 0.9 * self.gamma.sum(axis=0) / train_data.shape[0]) - if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1: + if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1e-3: break mu_ = self.mu sigma2_ = self.sigma2 @@ -102,6 +108,7 @@ class GaussianMixture: # make the variance equals to 1 as diagonal np.fill_diagonal(self.covariance[k], 1) self.weight = np.ones(self.cluNum) / self.cluNum + p_mat = np.zeros((sampleN, self.cluNum)) for i in range(self.max_iter): for j in range(self.cluNum): @@ -111,17 +118,18 @@ class GaussianMixture: total_n = p_mat.sum(axis=1) total_n[total_n == 0] = self.cluNum p_mat /= total_n.reshape(-1, 1) - if sample_fea == 2: + if sample_fea != 1: for j in range(self.cluNum): N_k = np.sum(p_mat[:, j], axis=0) + self.means[j] = (1 / N_k) * np.sum(train_data * p_mat[:, j].reshape(-1, 1), axis=0) self.covariance[j] = (1 / N_k) * np.dot( (p_mat[:, j].reshape(-1, 1) * (train_data - self.means[j])).T, (train_data - self.means[j])) + self.reg_cov self.weight[j] = N_k / sampleN - else: - print("one and two dimension data is accepted") + else: + print("sorry, the model is only designed for 1-D and 2-D data") def predict(self, test_data): sampleN, sample_fea = test_data.shape @@ -155,3 +163,29 @@ class GaussianMixture: phi = (1 / np.sqrt(2 * np.pi * self.sigma2.reshape(self.cluNum, 1)) * np.exp( - (data - mu.reshape(self.cluNum, 1)) ** 2 / (2 * self.sigma2.reshape(self.cluNum, 1)))) return phi + + +class ClusteringAlgorithm: + + def __init__(self): + self.elbow_dict = {} + self.elbow_chg = [] + self.elbow_chg_next = [] + self.bestCluNum = 0 + + def fit(self, train_data): + for i in range(2, 6): + self.km = KMeans(i) + self.elbow_dict[i] = self.km.fit(train_data)[2] + elbow_dist = list(self.elbow_dict.values()) + self.elbow_chg = [(elbow_dist[i] / elbow_dist[i - 1]) - 1 for i in range(1, len(elbow_dist))] + self.elbow_chg_next = [(self.elbow_chg[i] - self.elbow_chg[i - 1]) for i in range(1, len(self.elbow_chg))] + self.bestCluNum = self.elbow_chg.index(max(self.elbow_chg)) + 3 + self.km = KMeans(self.bestCluNum) + self.km.fit(train_data) + return elbow_dist, self.bestCluNum + + def predict(self, test_data): + res = self.km.predict(test_data) + return res + -- Gitee From b3cc172f5cdc5fab2ac08574164f698389006d2e Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 17:35:37 +0800 Subject: [PATCH 73/80] update assignment-3/submission/19210680053/source.py. --- assignment-3/submission/19210680053/source.py | 21 +++++++++++-------- 1 file changed, 12 insertions(+), 9 deletions(-) diff --git a/assignment-3/submission/19210680053/source.py b/assignment-3/submission/19210680053/source.py index eb8b9e1..ce8488b 100644 --- a/assignment-3/submission/19210680053/source.py +++ b/assignment-3/submission/19210680053/source.py @@ -74,6 +74,12 @@ class GaussianMixture: def fit(self, train_data): sampleN, sample_fea = train_data.shape + ''' + gamma.shape(N, K) + mu.shape(1, K) + sigma2.shape(1,K) + alpha.shape(1, K) + ''' if sample_fea == 1: train_data = self.normalize(train_data) print(train_data) @@ -82,30 +88,27 @@ class GaussianMixture: sigma2_ = self.sigma2 mu_ = self.mu while True: - # gamma.shape(N, K) + self.gamma = (0.1 * self.gamma + 0.9 * self.phi(train_data, self.mu).T * self.alpha / ( self.phi(train_data, self.mu).T * self.alpha).sum( axis=1).reshape(train_data.shape[0], 1)) - # mu.shape(1, K) + self.mu = (0.1 * self.mu + 0.9 * np.matmul(train_data, self.gamma) / self.gamma.sum(axis=0)) - # sigma2.shape(1,K) + self.sigma2 = (0.1 * self.sigma2 + 0.9 * ( self.gamma * (train_data.reshape(train_data.shape[0], 1) - self.mu) ** 2).sum( axis=0) / self.gamma.sum(axis=0)) - # alpha.shape(1, K) + self.alpha = (0.1 * self.alpha + 0.9 * self.gamma.sum(axis=0) / train_data.shape[0]) if (np.sum((self.mu - mu_) ** 2) + np.abs(self.sigma2 - sigma2_).sum()) < 1e-3: break mu_ = self.mu sigma2_ = self.sigma2 - # # reg covariance depend on dimension of the features elif sample_fea == 2: self.reg_cov = self.reg_cov * np.identity(sample_fea) self.means = np.random.randint(train_data.min() / 2, train_data.max() / 2, size=(self.cluNum, sample_fea)) - # there should be n_clusters covariance and each one's size depend on feature self.covariance = np.zeros((self.cluNum, sample_fea, sample_fea)) for k in range(self.cluNum): - # make the variance equals to 1 as diagonal np.fill_diagonal(self.covariance[k], 1) self.weight = np.ones(self.cluNum) / self.cluNum @@ -141,7 +144,7 @@ class GaussianMixture: elif sample_fea == 2: p_mat = np.zeros((test_data.shape[0], self.cluNum)) for j in range(self.cluNum): - # self.covariance += self.reg_cov + self.covariance += self.reg_cov g = multivariate_normal(mean=self.means[j], cov=self.covariance[j]) p_mat[:, j] = self.weight[j] * g.pdf(test_data) @@ -158,7 +161,7 @@ class GaussianMixture: return nor_data def phi(self, data, mu): - # phi.shape(K, N) + '''phi.shape(K, N)''' mu = (np.arange(self.cluNum) - self.cluNum // 2) * (data.max() - data.min()) / self.K phi = (1 / np.sqrt(2 * np.pi * self.sigma2.reshape(self.cluNum, 1)) * np.exp( - (data - mu.reshape(self.cluNum, 1)) ** 2 / (2 * self.sigma2.reshape(self.cluNum, 1)))) -- Gitee From 0557651654195e78e312c70d1efffcae26547e4c Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 18:34:19 +0800 Subject: [PATCH 74/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index ca53159..a0b8c66 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -14,7 +14,7 @@ $$ $$ euclDistance_{i,j}={\sqrt {\sum_{t=1}^{dim} (X_{it}-C_{jt})^2}} $$ -对于每个对象，分别保留其相距__最近中心点__下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 +对于每个对象，分别保留其相距 __最近中心点__ 下标以及对应距离平方，存储在clusterAssment中（shape: N*2)的第一列与第二列 ### 中心点更新 根据clusterAssment的第一列数据，分别得到距离每个$C_k$,$1\leq k\leq cluNum$最近的一系列点坐标,因此对于k类数据点求取均值，得到其作为新的$C_k$ ### 循环停止条件 -- Gitee From d667176676629fabfa6d3f24a04cd64a96aef054 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 18:35:21 +0800 Subject: [PATCH 75/80] update assignment-3/submission/19210680053/README.md. --- assignment-3/submission/19210680053/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/README.md b/assignment-3/submission/19210680053/README.md index a0b8c66..6f59e45 100644 --- a/assignment-3/submission/19210680053/README.md +++ b/assignment-3/submission/19210680053/README.md @@ -253,7 +253,7 @@ $$ 分别使用test_demo_elbow中由三个高斯分布和四个高斯分布组合的数据集进行求解： -# 三个高斯分布 +#### 三个高斯分布 训练集的实际分布情况 Elbow Kmeans Classification with 3 Gaussian Distribution @@ -262,7 +262,7 @@ $$ Elbow Kmeans Classification with 3 Gaussian Distribution -# 四个高斯分布 +#### 四个高斯分布 训练集的实际分布情况 -- Gitee From 562fdcce74ffb22f665c64368fc1fca51a492231 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 18:40:25 +0800 Subject: [PATCH 76/80] test demo update --- .../submission/19210680053/test_demo.py | 182 ++++++++++++++++++ .../submission/19210680053/test_demo_elbow.py | 70 +++++++ 2 files changed, 252 insertions(+) create mode 100644 assignment-3/submission/19210680053/test_demo.py create mode 100644 assignment-3/submission/19210680053/test_demo_elbow.py diff --git a/assignment-3/submission/19210680053/test_demo.py b/assignment-3/submission/19210680053/test_demo.py new file mode 100644 index 0000000..f04f54c --- /dev/null +++ b/assignment-3/submission/19210680053/test_demo.py @@ -0,0 +1,182 @@ +import numpy as np +import sys +from source import GaussianMixture, KMeans, ClusteringAlgorithm +from ondGMM import GMM +from matplotlib import pyplot + + +def shuffle(*datas): + data = np.concatenate(datas) + label = np.concatenate([ + np.ones((d.shape[0],), dtype=int) * i + for (i, d) in enumerate(datas)]) + N = data.shape[0] + # idx = np.random.permutation(np.arange(N)) + idx = np.arange(N) + np.random.shuffle(idx) + # random_index = np.random.permutation(N) + # for i in range(N): + # datashu[i,:] = data[idx[i],:] + # labelshu[i] = label[idx[i]] + data = data[idx] + label = label[idx] + return data, label + + +def data_1(): + mean = (1, 2) + cov = np.array([[73, 0], [0, 22]]) + x = np.random.multivariate_normal(mean, cov, (800,)) + + mean = (16, -5) + cov = np.array([[21.2, 0], [0, 32.1]]) + y = np.random.multivariate_normal(mean, cov, (200,)) + + mean = (10, 22) + cov = np.array([[10, 5], [5, 10]]) + z = np.random.multivariate_normal(mean, cov, (1000,)) + + data, _ = shuffle(x, y, z) + return (data, data), 3 + + +def data_test(input=3): + mean = (1, 2) + cov = np.array([[3, 0], [0, 2]]) + x = np.random.multivariate_normal(mean, cov, (800,)) + + mean = (26, 28) + cov = np.array([[2, 0], [0, 2]]) + y = np.random.multivariate_normal(mean, cov, (200,)) + + mean = (-25, -23) + cov = np.array([[10, 5], [5, 10]]) + z = np.random.multivariate_normal(mean, cov, (1000,)) + + mean = (11, 13) + cov = np.array([[4, 3], [3, 4]]) + q = np.random.multivariate_normal(mean, cov, (1000,)) + if input == 3: + data, label = shuffle(x, y, z) + elif input == 4: + data, label = shuffle(x, y, z, q) + else: + print("only 3 and 4 is accepted") + num = len(data) + train_data, test_data = data[:int(0.8 * num)], data[int(0.8 * num):num] + train_label, test_label = label[:int(0.8 * num)], label[int(0.8 * num):num] + return train_data, test_data, train_label, test_label + + +def data_2(): + train_data = np.array([ + [23, 12, 173, 2134], + [99, -12, -126, -31], + [55, -145, -123, -342], + ]) + return (train_data, train_data), 2 + + +def data_3(): + train_data = np.array([ + [23], + [-2999], + [-2955], + ]) + # train_data = np.array([1.4140995 , -0.72260484, -0.69149465]) + return (train_data, train_data), 2 + + +def test_with_n_clusters(data_fuction, algorithm_class): + (train_data, test_data), n_clusters = data_fuction()[0], data_fuction()[1] + model = algorithm_class(n_clusters) + model.fit(train_data) + res = model.predict(test_data) + assert len( + res.shape) == 1 and res.shape[0] == test_data.shape[0], "shape of result is wrong" + return res + + +def testcase_1_1(): + test_with_n_clusters(data_1, KMeans) + return True + + +def testcase_1_2(): + res = test_with_n_clusters(data_2, KMeans) + return res[0] != res[1] and res[1] == res[2] + + +def testcase_2_1(): + test_with_n_clusters(data_1, GaussianMixture) + return True + + +def testcase_2_2(): + res = test_with_n_clusters(data_3, GMM) + return res[0] != res[1] and res[1] == res[2] + + +def test_all(err_report=False): + testcases = [ + ["KMeans-1", testcase_1_1, 4], + ["KMeans-2", testcase_1_2, 4], + # ["KMeans-3", testcase_1_3, 4], + # ["KMeans-4", testcase_1_4, 4], + # ["KMeans-5", testcase_1_5, 4], + ["GMM-1", testcase_2_1, 4], + ["GMM-2", testcase_2_2, 4], + # ["GMM-3", testcase_2_3, 4], + # ["GMM-4", testcase_2_4, 4], + # ["GMM-5", testcase_2_5, 4], + ] + sum_score = sum([case[2] for case in testcases]) + score = 0 + for case in testcases: + try: + res = case[2] if case[1]() else 0 + except Exception as e: + if err_report: + print("Error [{}] occurs in {}".format(str(e), case[0])) + res = 0 + score += res + print("+ {:14} {}/{}".format(case[0], res, case[2])) + print("{:16} {}/{}".format("FINAL SCORE", score, sum_score)) + + +def pltshow(data, res, n_clu): + mark = [[np.random.randint(0, 256) for i in range(3)] for j in range(n_clu)] + marklist = ["#{:02x}{:02x}{:02x}".format(mark[i][0], mark[i][1], mark[i][2]) for i in range(n_clu)] + colorlist = [marklist[i] for i in res] + pyplot.scatter(data[:, 0], data[:, 1], c=colorlist) + pyplot.show() + + +# def display(data, label, name, labelNum): +# datas = [[] for i in range(labelNum)] +# for i in range(len(data)): +# datas[label[i]].append(data[i]) + +# for each in datas: +# each = np.array(each) +# pyplot.scatter(each[:, 0], each[:, 1]) + +if __name__ == "__main__": + if len(sys.argv) > 1 and sys.argv[1] == "--report": + test_all(True) + else: + test_all() + + final = data_test(3)#input = 3 or 4 + train, test, train_label, test_label = final[0], final[1], final[2], final[3] + cluster_num = 3 + km = KMeans(cluster_num) + km.fit(train) + kmeans_res = km.predict(test) + gmm = GaussianMixture(cluster_num) + gmm.fit(train) + gmm_res = gmm.predict(test) + # pltshow(train, train_label, cluster_num) + # pltshow(test, test_label, cluster_num) + # pltshow(test, kmeans_res, cluster_num) + # pltshow(test, gmm_res, cluster_num) diff --git a/assignment-3/submission/19210680053/test_demo_elbow.py b/assignment-3/submission/19210680053/test_demo_elbow.py new file mode 100644 index 0000000..b24efe5 --- /dev/null +++ b/assignment-3/submission/19210680053/test_demo_elbow.py @@ -0,0 +1,70 @@ +import numpy as np +from source import KMeans, ClusteringAlgorithm +from matplotlib import pyplot + + +def shuffle(*datas): + data = np.concatenate(datas) + label = np.concatenate([ + np.ones((d.shape[0],), dtype=int) * i + for (i, d) in enumerate(datas)]) + N = data.shape[0] + idx = np.arange(N) + np.random.shuffle(idx) + data = data[idx] + label = label[idx] + return data, label + + +def data_test(input=3): + mean = (1, 2) + cov = np.array([[3, 0], [0, 2]]) + x = np.random.multivariate_normal(mean, cov, (800,)) + + mean = (26, 28) + cov = np.array([[2, 0], [0, 2]]) + y = np.random.multivariate_normal(mean, cov, (200,)) + + mean = (-25, -23) + cov = np.array([[10, 5], [5, 10]]) + z = np.random.multivariate_normal(mean, cov, (1000,)) + + mean = (11, 13) + cov = np.array([[4, 3], [3, 4]]) + q = np.random.multivariate_normal(mean, cov, (1000,)) + if input == 3: + data, label = shuffle(x, y, z) + elif input == 4: + data, label = shuffle(x, y, z, q) + else: + print("only 3 and 4 is accepted") + num = len(data) + train_data, test_data = data[:int(0.8 * num)], data[int(0.8 * num):num] + train_label, test_label = label[:int(0.8 * num)], label[int(0.8 * num):num] + return train_data, test_data, train_label, test_label + + +def pltshow(data, res, n_clu): + mark = [[np.random.randint(0, 256) for i in range(3)] for j in range(n_clu)] + marklist = ["#{:02x}{:02x}{:02x}".format(mark[i][0], mark[i][1], mark[i][2]) for i in range(n_clu)] + # marklist = ['c', 'b', 'g', 'r', 'm', 'y', 'k', 'w'] + colorlist = [marklist[i] for i in res] + pyplot.scatter(data[:, 0], data[:, 1], c=colorlist) + pyplot.show() + + +if __name__ == "__main__": + input_ = 4 + final = data_test(input_) + train, test, train_label, test_label = final[0], final[1], final[2], final[3] + # cluster_num = 3 + clu_test = ClusteringAlgorithm() + elbow_dict, best_num = clu_test.fit(train) + clu_res = clu_test.predict(test) + + km = KMeans(input_) + km.fit(train) + res = km.predict(test) + + pltshow(test, res, input_) + pltshow(test, clu_res, best_num) -- Gitee From 82a6dc2310a619a76093fb21b93caed6d2de5ef6 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 18:42:06 +0800 Subject: [PATCH 77/80] update assignment-3/submission/19210680053/test_demo.py. shanchu unnecessary --- assignment-3/submission/19210680053/test_demo.py | 16 +--------------- 1 file changed, 1 insertion(+), 15 deletions(-) diff --git a/assignment-3/submission/19210680053/test_demo.py b/assignment-3/submission/19210680053/test_demo.py index f04f54c..1dbd114 100644 --- a/assignment-3/submission/19210680053/test_demo.py +++ b/assignment-3/submission/19210680053/test_demo.py @@ -11,13 +11,8 @@ def shuffle(*datas): np.ones((d.shape[0],), dtype=int) * i for (i, d) in enumerate(datas)]) N = data.shape[0] - # idx = np.random.permutation(np.arange(N)) idx = np.arange(N) np.random.shuffle(idx) - # random_index = np.random.permutation(N) - # for i in range(N): - # datashu[i,:] = data[idx[i],:] - # labelshu[i] = label[idx[i]] data = data[idx] label = label[idx] return data, label @@ -83,7 +78,7 @@ def data_3(): [-2999], [-2955], ]) - # train_data = np.array([1.4140995 , -0.72260484, -0.69149465]) + return (train_data, train_data), 2 @@ -152,15 +147,6 @@ def pltshow(data, res, n_clu): pyplot.show() -# def display(data, label, name, labelNum): -# datas = [[] for i in range(labelNum)] -# for i in range(len(data)): -# datas[label[i]].append(data[i]) - -# for each in datas: -# each = np.array(each) -# pyplot.scatter(each[:, 0], each[:, 1]) - if __name__ == "__main__": if len(sys.argv) > 1 and sys.argv[1] == "--report": test_all(True) -- Gitee From 2b0d149322b4252065226310afd9fb46b8f360a1 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 19:06:42 +0800 Subject: [PATCH 78/80] update assignment-3/submission/19210680053/source.py. --- assignment-3/submission/19210680053/source.py | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/source.py b/assignment-3/submission/19210680053/source.py index ce8488b..3fd5515 100644 --- a/assignment-3/submission/19210680053/source.py +++ b/assignment-3/submission/19210680053/source.py @@ -176,9 +176,15 @@ class ClusteringAlgorithm: self.elbow_chg_next = [] self.bestCluNum = 0 - def fit(self, train_data): + + def fit(self, train_data): for i in range(2, 6): - self.km = KMeans(i) + mini_loss = 1e8 + '''To guarantee robustness''' + for j in range(50): + self.km = KMeans(i) + if self.km.fit(train_data)[2] < mini_loss: + mini_loss = self.km.fit(train_data)[2] self.elbow_dict[i] = self.km.fit(train_data)[2] elbow_dist = list(self.elbow_dict.values()) self.elbow_chg = [(elbow_dist[i] / elbow_dist[i - 1]) - 1 for i in range(1, len(elbow_dist))] -- Gitee From d7162739e9ed2886d406fe1d73243d9bedb4a3f8 Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 19:07:36 +0800 Subject: [PATCH 79/80] update assignment-3/submission/19210680053/source.py. --- assignment-3/submission/19210680053/source.py | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/assignment-3/submission/19210680053/source.py b/assignment-3/submission/19210680053/source.py index 3fd5515..6da8cef 100644 --- a/assignment-3/submission/19210680053/source.py +++ b/assignment-3/submission/19210680053/source.py @@ -176,8 +176,7 @@ class ClusteringAlgorithm: self.elbow_chg_next = [] self.bestCluNum = 0 - - def fit(self, train_data): + def fit(self, train_data): for i in range(2, 6): mini_loss = 1e8 '''To guarantee robustness''' -- Gitee From 4423683f91900d479ef17098a3a5824d65f5966a Mon Sep 17 00:00:00 2001 From: Yantong He <8850706+yantong-he@user.noreply.gitee.com> Date: Mon, 14 Jun 2021 19:08:09 +0800 Subject: [PATCH 80/80] update assignment-3/submission/19210680053/source.py. --- assignment-3/submission/19210680053/source.py | 2 -- 1 file changed, 2 deletions(-) diff --git a/assignment-3/submission/19210680053/source.py b/assignment-3/submission/19210680053/source.py index 6da8cef..5bf9619 100644 --- a/assignment-3/submission/19210680053/source.py +++ b/assignment-3/submission/19210680053/source.py @@ -64,7 +64,6 @@ class KMeans(object): class GaussianMixture: # covariance: ndarray - def __init__(self, n_clusters, reg_cov: float = 1e-06): self.cluNum = n_clusters self.max_iter = 1200 @@ -169,7 +168,6 @@ class GaussianMixture: class ClusteringAlgorithm: - def __init__(self): self.elbow_dict = {} self.elbow_chg = [] -- Gitee