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+# 实验报告：ASS1-KNN分类器
+
+18307130341 黄韵澄
+
+[toc]
+
+### 1.1 实验概述
+
+​	本实验使用k近邻方法（KNN），实现了对二维带标签点集的分类。
+
+​	在**1.2**中生成了3组符合高斯分布的二维点集，并打上0~2共3种标签。初始数据集被划分为训练数据(train_data，80%)和测试数据(test_data，20%)，并将训练数据放进KNN模型中进行训练。
+
+​	**1.3**中是对KNN模型的实现部分，包括初始化、模型训练、预测分类三个部分。
+
+​	**1.4**中对KNN模型进行测试和实验探究。
+
+​	**1.5**中完成实验的自动测试部分。
+
+### 1.2 数据集生成
+
+​		数据集的生成在函数`data_generate`中实现。每种标签各生成了`num=200`个点集，通过设置其均值`mean`和协方差`cov`来生成符合高斯分布的二维数据集。生成数据集的参数如下：
+$$
+\mu_0 = [6, 4],\ \Sigma_0 = \begin{bmatrix}35&4\\4&11\\\end{bmatrix}\\
+\mu_1 = [11, 14],\ \Sigma_1 = \begin{bmatrix}21&6\\6&24	\\\end{bmatrix}\\
+\mu_2 = [22, 6],\ \Sigma_2 = \begin{bmatrix}25&5\\5&10\\\end{bmatrix}\\
+$$
+​	生成的数据集组成`data`，使用`shuffle`函数将其打乱，取前80%作为`train_data`，后20%作为`test_data`。	
+
+​	使用`matplotlib`绘图，测试集和训练集散点图如下：
+
+![train_data](img\train_data.png)
+
+<center>Fig 1:训练集</center>
+
+![test_data](D:\YC\study\大三下\模式识别与机器学习\pj1\prml-21-spring\assignment-1\submission\18307130341\img\test_data.png)
+
+<center>Fig 2: 测试集
+
+### 1.3 KNN模型的实现
+
+#### 1.3.1 KNN初始化
+
+​	`__init__`成员函数中初始化KNN模型。定义`data`、`label`作为k近邻的候选点集，`num`为点集规模，`k`为模型训练后选取的最优k值。
+
+#### 1.3.2 模型训练——fit函数
+
+​	将`train_data`再次划分为`train_set_data`和`dev_set_data`。`train_set_data`作为候选点集，`dev_set_data`作为开发集，实现对超参`k`的选取。
+
+​	超参`k`的选取范围设置为`1~15`。
+
+​	对每个候选k，对开发集进行类别预测。具体方式是在训练集中找到最近的k个点中出现中最多的类别作为预测类别。对每个k计算出其类别预测平均准确率acc，绘制成图如下：
+
+![k_acc](img\k_acc.png)
+
+<center> Fig 3：acc-k折线图
+
+​	在1%的波动范围内，选取准确度最高的最小k作为最终选取的超参`k`，此时模型训练完成。在上图的样例中，最终选取的超参`k`为6。
+
+#### 1.3.3 类别预测——predict函数
+
+​	对于每个需要预测的数据，找到训练集中距离最近的`k`个点，距离选取为欧几里得距离。
+
+​	最终每个点的预测类别为：`k`个最近邻的点中出现最多的类别。`k`为1.3.2中训练好的超参`k`。
+
+### 1.4 模型测试和实验探究
+
+#### 1.4.1 模型测试
+
+​	用`test_data`进行模型测试，输出模型的准确率。实验重复10次，结果如下：
+$$
+\begin{array}{c|l} {实验次数}&{1}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{10}\\ \hline {k}&{5}&{8}&{9}&{3}&{11}&{6}&{8}&{6}&{9}&{7}\\ {acc}&{0.83}&{0.88}&{0.8}&{0.83}&{0.87}&{0.85}&{0.88}&{0.88}&{0.86}&{0.88}\\ \end{array}
+$$
+
+<center>Table 1: 模型准确率
+
+​	平均超参`k`为`7~8`之间，平均准确率`acc`为`0.856`。
+
+#### 1.4.2 实验探究
+
+​	(1) 修改高斯分布距离，使得三种点集更加分散（重合部分更少）：
+
+![Fig4](img\Fig4.png)
+
+<center> Fig 4: 修改高斯分布距离后的点集
+
+​	该数据集测试出的模型准确率为92.92%。多次重复实验，增大点集的距离，得出结论：高斯分布距离越大，点集越分散，模型准确率越高。
+
+​	(2) 修改高斯分布距离，使得三种点集更加分散（重合部分更少）：
+
+![Fig5](img\Fig5.png)
+
+<center>Fig 5: 修改高斯分布方差后的点集
+
+​	该数据集测试出的模型准确率为97.5%。多次重复实验，减小点坐标方差（对角线的值），得出结论：高斯分布方差越小，点集内部更加集中，模型准确率更高。
+
+### 1.5 自动化测试
+
+​	程序只导入了`numpy`和`matplotlib`包。
+
+​	配置conda环境进行测试，可以通过测试。
+
+​	
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diff --git a/assignment-1/submission/18307130341/source.py b/assignment-1/submission/18307130341/source.py
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+import numpy as np
+import matplotlib.pyplot as plt
+
+class KNN:
+
+    def __init__(self):
+        self.data = []
+        self.label = []
+        self.num = 0
+        self.k = 1
+
+    def fit(self, train_data, train_label):
+        self.num, _ = train_data.shape
+
+        ratio = 0.8
+        idx = np.random.permutation(self.num)
+        train_data = train_data[idx]
+        train_label = train_label[idx]
+
+        train_set_num = (int)(ratio * self.num)
+        train_set_data = train_data[:train_set_num]
+        train_set_label = train_label[:train_set_num]
+        dev_set_data = train_data[train_set_num:]
+        dev_set_label = train_label[train_set_num:]
+
+        self.data = train_set_data
+        self.label = train_set_label
+        self.num = train_set_num
+        max_acc = -1
+        max_k = 15
+        
+        acc_k = []
+
+        for k in range(1,max_k):
+            self.k = k
+            predict_label = self.predict(dev_set_data)
+            acc = np.mean(np.equal(predict_label, dev_set_label))
+            acc_k.append(acc)
+            if acc >= max_acc + 0.01:
+                max_acc = acc
+                select_k = k
+        
+        # Graph_Plot(acc_k, "k_acc")
+
+        self.k = select_k
+        self.num , _ = train_data.shape
+        self.data = train_data
+        self.label = train_label
+
+    def predict(self, test_data):
+        predict_label = []
+        for x in test_data:
+            dis = np.array([np.sqrt(sum((x-y)**2)) for y in self.data])
+            knn = np.argsort(np.array(dis))[:self.k]
+            result = np.argmax(np.bincount(self.label[knn]))
+            predict_label.append(result)
+        return predict_label
+
+def data_generate(num):
+    mean = [(6,4), (11, 14), (22, 6)]
+    cov = [[35, 4], [4, 11]],[[21, 6], [6, 24]],[[25, 5], [5, 10]]
+    data0 = np.random.multivariate_normal(mean[0], cov[0], num)
+    data1 = np.random.multivariate_normal(mean[1], cov[1], num)
+    data2 = np.random.multivariate_normal(mean[2], cov[2], num)
+    data = np.concatenate([data0,data1,data2])
+    label = np.array([0]*num + [1]*num + [2]*num)
+    
+    idx = np.random.permutation(3*num)
+
+    data = data[idx]
+    label = label[idx]
+
+    return data, label
+
+def Graph_Plot(acc, name):
+    plt.plot(acc)
+    plt.xlabel('k')
+    plt.ylabel('acc')
+    plt.savefig(f'img/{name}')
+    plt.close()
+
+def Graph_Scatter(data, label, name):
+    points =[[],[],[]]
+    for i in range(len(data)):
+        points[label[i]].append(data[i])
+    for points_set in points:
+        points_set = np.array(points_set)
+        plt.scatter(points_set[:, 0], points_set[:, 1])
+    # plt.show()
+    plt.savefig(f'img/{name}')
+    plt.close()
+    
+
+if __name__ == "__main__":
+    num = 400
+    data, label = data_generate(num)
+    train_num = (int)(num* 3 * 0.8)
+    train_data = data[:train_num]
+    train_label = label[:train_num]
+    test_data = data[train_num:]
+    test_label = label[train_num:]
+
+    # Graph_Scatter(train_data, train_label, "train_data")
+    # Graph_Scatter(test_data, test_label,"test_data")
+
+    model = KNN()
+    model.fit(train_data, train_label)
+    test_predict = model.predict(test_data)
+    acc = np.mean(np.equal(test_predict, test_label))
+    print("k = ", model.k)
+    print("acc = ", acc)
+