From eb80cf9b370133f6c39de0686c8e5a1e6fda4da5 Mon Sep 17 00:00:00 2001 From: xny Date: Sat, 20 Mar 2021 16:43:15 +0800 Subject: [PATCH 001/103] add readme source --- assignment-1/submission/18300110042/README.md | 0 assignment-1/submission/18300110042/source.py | 0 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/18300110042/README.md create mode 100644 assignment-1/submission/18300110042/source.py diff --git a/assignment-1/submission/18300110042/README.md b/assignment-1/submission/18300110042/README.md new file mode 100644 index 0000000..e69de29 diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py new file mode 100644 index 0000000..e69de29 -- Gitee From fd9a819d4e23462a20b48fb25f71bc72944c92a3 Mon Sep 17 00:00:00 2001 From: xny Date: Sat, 20 Mar 2021 17:42:34 +0800 Subject: [PATCH 002/103] add README outline --- assignment-1/submission/18300110042/README.md | 56 +++++++++++++++++++ 1 file changed, 56 insertions(+) diff --git a/assignment-1/submission/18300110042/README.md b/assignment-1/submission/18300110042/README.md index e69de29..2e4d830 100644 --- a/assignment-1/submission/18300110042/README.md +++ b/assignment-1/submission/18300110042/README.md @@ -0,0 +1,56 @@ +# Introduction to KNN Classifier (maths) + supervised + MLE + + + +# Hyperparameter Tuning (Cross Validation) + k impact + odd number -- prevent equal (2 labels) + + decision boundary + non-linear + generalization + + as k grows larger, decision boundary smooth, stablity (rising), accuracy might decline + + -- cross validation + k-fold cross validation, increase stability + much data -- smaller k + leave-one-out cross validation + + KNN normally, select k from 1 + + + + + +# KD-Tree + (low dimension), backtracking + O(log N)~ O(N) + + +# Analysis +complexity (test not training, loop, number of samples), +feature encoding (categorical -- label/one-hot encoding), discretization(continuous ?) +distance Manhattan? Euclidean? +normalization, + Min-max normalization: (x - min) / (max - min) + Z-score normalization: (x - mean) / std(x) + +Nan (mean, deletion), + +weight + w(x, x_i) = exp(-\lambda |x - x_(i)|^(2)) + +low dimension (PCA, feature extraction), O(N) + distinctive, clustering + approximate KNN (https://www.cs.umd.edu/~mount/ANN/) + KD tree (low dimension), backtracking + + +# Summary + simple + low dimension (feature) data + training -- no time consumption + prediction, loop over all samples, complexity depends on number of samples linearly, bottleneck for big data \ No newline at end of file -- Gitee From 4c381c68bc5aa584a9c7f10067fe3e49f20f3a34 Mon Sep 17 00:00:00 2001 From: xny Date: Sat, 20 Mar 2021 23:55:20 +0800 Subject: [PATCH 003/103] brute-force & euc_dis finished --- assignment-1/submission/18300110042/README.md | 13 +- assignment-1/submission/18300110042/source.py | 174 ++++++++++++++++++ .../submission/18300110042/tester_demo.py | 24 +++ 3 files changed, 206 insertions(+), 5 deletions(-) create mode 100644 assignment-1/submission/18300110042/tester_demo.py diff --git a/assignment-1/submission/18300110042/README.md b/assignment-1/submission/18300110042/README.md index 2e4d830..d51fe63 100644 --- a/assignment-1/submission/18300110042/README.md +++ b/assignment-1/submission/18300110042/README.md @@ -17,11 +17,14 @@ -- cross validation k-fold cross validation, increase stability much data -- smaller k - leave-one-out cross validation - - KNN normally, select k from 1 + extreme case: leave-one-out cross validation + larger k, lower bias, higher variance + smaller k, higher bias, lower variance + KNN, normally, select k from 1 +# Distance + Manhattan? Euclidean? Mikn @@ -33,7 +36,7 @@ # Analysis complexity (test not training, loop, number of samples), feature encoding (categorical -- label/one-hot encoding), discretization(continuous ?) -distance Manhattan? Euclidean? + normalization, Min-max normalization: (x - min) / (max - min) Z-score normalization: (x - mean) / std(x) @@ -53,4 +56,4 @@ low dimension (PCA, feature extraction), O(N) simple low dimension (feature) data training -- no time consumption - prediction, loop over all samples, complexity depends on number of samples linearly, bottleneck for big data \ No newline at end of file + prediction, loop over all samples, complexity depends on number of samples linearly, bottleneck for big data O(N*D) \ No newline at end of file diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index e69de29..537f194 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -0,0 +1,174 @@ +import numpy as np +import matplotlib as plt + +class KNN: + def __init__(self, k=5, weights='uniform', algorithm='auto', norm=True, dist='euc'): + self.k = k + self.weights = weights + self.algrthm = algorithm + self.norm = norm + self.dist = dist + + def fit(self, train_data, train_label, verbose=False): + """ + Find the best k and(/or) algorithm. + train_data: numpy.ndarray, shape = (N, K); + train_label: numpy.ndarray, shape = (N,); + where N is number of data (samples), and K is dimension of data. + Use k-fold cross validation to choose hyperparameter -- number of nearest neighbours. + k: determined by number of samples (data size) + with data size presumed to be small, we use 10-fold cross validation at least. + """ + # check data input + assert train_data.shape[0] == train_label.shape[0] + assert train_data.shape[1] + + num_samples = train_data.shape[0] + feature_dim = train_data.shape[1] + + if self.norm: + train_data, denom, f_min = self.min_max_norm(train_data) + self.denom = denom + self.f_min = f_min + + self.train_data = train_data + self.train_label = train_label + + # check feature dimension + if feature_dim > 1000: + print('Warning: High dimension.') + + # decide k in k-fold cross validation + boundary = 0.1 * num_samples + + if boundary < 1: + # leave-one-out cross validation + num_folds = num_samples + val_size = 1 + + else: + # 10-fold cross validation + num_folds = 10 + val_size = int(boundary) + + # set upper bound for number of neighbours (K) + if num_samples < 20: + k_up_bound = num_samples + else: + k_up_bound = 20 + + ks = [k for k in range(1, k_up_bound)] #candidates for hyperparameter k + + best_k = ks[0] + best_acc = 0 + + for k in ks: + k_acc_sum = 0 + for i in range(num_folds): + start_idx = 0 + end_idx = start_idx + val_size + val_data = train_data[start_idx: end_idx] + val_label = train_label[start_idx: end_idx] + start_idx += val_size + + val_pred = self.predict(val_data) + + curr_acc = np.mean(val_pred==val_label) + k_acc_sum += curr_acc + + mean_acc_k = k_acc_sum / num_folds + + if best_acc < mean_acc_k: + best_acc = mean_acc_k + best_k = k + + if verbose: + print('current best_acc: {0}; best_k: {1}'.format((best_acc, best_k))) + + if verbose: + print('After cross validation, the final best k is: {0}'.format(best_k)) + + self.k = best_k + + return best_k + + + def predict(self, test_data): + """ + To predict labels of test_data. + test_data: numpy.ndarray, shape = (N, K); + where N is number of data (samples), and K is dimension of data. + """ + + # brute-force, euclidean_dist + num_samples = test_data.shape[0] + if self.norm: + data = (test_data - self.f_min) / self.denom # min-max normalization + + preds = [] + for sample in data: + distances = [self.euc_distance(sample, X) for X in self.train_data] + labels = self.train_label[np.argsort(distances)[:self.k]] + + if (labels >= 0).all(): + # if all labels are non-negative integers, we can use np.bincount() directly; + pred = np.bincount(labels).argmax() + + else: + votes = {} + for i in labels: + label = str(i) + if label in votes: + votes[label] += 1 + else: + votes[label] = 1 + pred = int(max(votes, key=lambda x: votes[x])) + + preds.append(pred) + + preds = np.array(preds) + + return preds + + + + + def euc_distance(self, x1, x2): + """ + Get Euclidean Distance between 2 samples. + x1 & x2: numpy.ndarray, shape = (K,); + where K is dimension of data. + """ + distance = np.sqrt(np.sum((x1 - x2)**2)) + return distance + + def manhattan_distance(self, x1, x2): + """ + Get Manhattan distance between 2 samples. + x1 & x2: numpy.ndarray, shape = (K,); + where K is dimension of data. + """ + distance = np.sum(np.absolute(x1 - x2)) + return distance + + + def min_max_norm(self, data): + """ + Min-max Normalization + data: numpy.ndarray, shape = (N, K); + where N is number of data (samples), and K is dimension of data. + """ + feature_max = data.max(axis=0) + feature_min = data.min(axis=0) + denom = feature_max - feature_min + data_normed = (data - feature_min) / denom + return data_normed, denom, feature_min + + + + +def get_data(num_samples=10): + pass + + + diff --git a/assignment-1/submission/18300110042/tester_demo.py b/assignment-1/submission/18300110042/tester_demo.py new file mode 100644 index 0000000..3dd9283 --- /dev/null +++ b/assignment-1/submission/18300110042/tester_demo.py @@ -0,0 +1,24 @@ +import numpy as np + +from source import KNN + +train_data = np.array([ + [1, 2, 3, 4], + [4, 2, 3, 1], + [12, 12, 13, 14], + [14, 12, 13, 11], + [12, 14, 15, 16] +]) +train_label = np.array([0, 0, 1, 1, 1]) + +test_data = np.array([ + [3, 4, 4, 2], + [18, 14, 15, 16] +]) +test_label = np.array([0, 1]) + +model = KNN() +model.fit(train_data, train_label) +res = model.predict(test_data) + +print("acc =",np.mean(np.equal(res, test_label))) \ No newline at end of file -- Gitee From 9268685e71d9a7f33a26690c650b5c54af4b26c1 Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 21 Mar 2021 00:04:38 +0800 Subject: [PATCH 004/103] some comments --- assignment-1/submission/18300110042/README.md | 1 + assignment-1/submission/18300110042/source.py | 6 +++++- 2 files changed, 6 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18300110042/README.md b/assignment-1/submission/18300110042/README.md index d51fe63..5b1c925 100644 --- a/assignment-1/submission/18300110042/README.md +++ b/assignment-1/submission/18300110042/README.md @@ -20,6 +20,7 @@ extreme case: leave-one-out cross validation larger k, lower bias, higher variance smaller k, higher bias, lower variance + bias, variance trade off KNN, normally, select k from 1 diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 537f194..6eb8f58 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -167,7 +167,11 @@ class KNN: -def get_data(num_samples=10): +def get_data(num_samples=10, num_classes=2): + """ + Generate data following Gaussian Distribution. + + """ pass -- Gitee From d22d05b93df975601bdd0d35c4fd46c358d26e9c Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 21 Mar 2021 18:14:55 +0800 Subject: [PATCH 005/103] add get_data --- assignment-1/submission/18300110042/source.py | 92 ++++++++++++++++++- 1 file changed, 88 insertions(+), 4 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 6eb8f58..6501ea8 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -167,12 +167,96 @@ class KNN: -def get_data(num_samples=10, num_classes=2): +def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=False): """ - Generate data following Gaussian Distribution. - + Generate random variables following 2-dimensional Gaussian Distribution. + num_samples: list, number of samples following each distribution. + num_classes: int, number of classes (different distributions). + mode: string, if mode == 'random', generate means and covariances randomly (following uniform distribution in [0,100]); else use default set. """ - pass + assert len(num_samples) == num_classes + + if mode == 'random': + Xs = [] + + for i in range(num_classes): + mean = np.random.uniform(-100, 100, 2) + cov = np.zeros((2,2)) + cov[0,0] += np.random.uniform(0, 100, 1) + cov[1,1] += np.random.uniform(0, 100, 1) + x = np.random.multivariate_normal(mean, cov, (num_samples[i],)) + + Xs.append(x) + + else: + mean_1 = (1, 50) + mean_2 = (-5, 25) + mean_3 = (10, 20) + + cov_1 = np.zeros((2,2)) + cov_1[0,0] += 1 + cov_1[1,1] += 10 + + cov_2 = np.zeros((2,2)) + cov_2[0,0] += 10 + cov_2[0,1] += 15 + cov_2[1,0] += 15 + cov_2[1,1] += 40 + + cov_3 = np.zeros((2,2)) + cov_3[0,0] += 20 + cov_3[1,1] += 30 + + set_1 = np.random.multivariate_normal(mean_1, cov_1, (num_samples[0],)) + set_2 = np.random.multivariate_normal(mean_2, cov_2, (num_samples[1],)) + set_3 = np.random.multivariate_normal(mean_3, cov_3, (num_samples[2],)) + + Xs = [set_1, set_2, set_3] + + data = np.concatenate(Xs) + labels = [] + for i in range(num_classes): + label = np.zeros(num_samples[i], dtype=int) + i + labels.append(label) + + labels = np.concatenate(labels) + indices = np.arange(np.sum(num_samples)) + np.random.shuffle(indices) + data = data[indices] + labels = labels[indices] + + train_size = int(0.8 * np.sum(num_samples)) + train_data, test_data = data[:train_size], data[train_size:] + train_label, test_label = labels[:train_size], labels[train_size:] + + if save: + np.save('train_data.npy', train_data) + np.save('train_label.npy', train_label) + np.save('test_data.npy', test_data) + np.save('test_label.npy', test_label) + + return train_data, train_label, test_data, test_label + +def load_data(): + try: + train_data = np.load('train_data.npy') + train_label = np.load('train_label.npy') + test_data = np.load('test_data.npy') + test_label = np.load('test_label.npy') + + print('Data loaded successfully.') + + return train_data, train_label, test_data, test_label + + except: + print('Sorry, no data available.') + exit() + +def plot_data(): + """ + Visualize + """ + pass -- Gitee From 377122f60bb45cd8b9da72f97365272ba51bb225 Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 21 Mar 2021 23:01:33 +0800 Subject: [PATCH 006/103] generate_&_plot_data finished --- assignment-1/submission/18300110042/source.py | 49 +++++++++++++++++-- 1 file changed, 45 insertions(+), 4 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 6501ea8..64191ea 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -1,5 +1,5 @@ import numpy as np -import matplotlib as plt +import matplotlib.pyplot as plt class KNN: def __init__(self, k=5, weights='uniform', algorithm='auto', norm=True, dist='euc'): @@ -239,7 +239,11 @@ def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=Fal return train_data, train_label, test_data, test_label + def load_data(): + """ + Load data if available. + """ try: train_data = np.load('train_data.npy') train_label = np.load('train_label.npy') @@ -254,9 +258,46 @@ def load_data(): print('Sorry, no data available.') exit() -def plot_data(): + +def plot_data(data, labels, title='data', save=False, +colours=['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:brown', 'tab:pink', 'tab:grey', 'tab:olive', 'tab:cyan']): """ - Visualize + Visualize the input data in a 2D plane, with different colours for each kind of labels. + data: numpy.ndarray, shape = (N, K); + label: numpy.ndarray, shape = (N,); + where N denotes the number of samples in data; K denotes the dimension of feature (data). + title: string, data descriptions. + save: bool, whether to save the figure. + colours: list of string, specify the colours of dots plotted in matplotlob.pyplot. + Default is mcolors.TABLEAU_COLORS (Tableau Palette). """ - pass + assert data.shape[0] == labels.shape[0] + + num_samples = data.shape[0] + label_record = sorted(set(labels)) + assert len(colours) >= len(label_record) + + label_dict = {k: v for v, k in enumerate(label_record)} + data_record = [[] for l in label_record] + + for i in range(num_samples): + data_record[label_dict[labels[i]]].append(data[i]) + + #data_record = np.stack(data_record, axis=0) + plt.title(title) + for t in range(len(label_record)): + data_t = np.array(data_record[t]) + plt.scatter(data_t[:, 0], data_t[:, 1], c=colours[t]) + + if save: + plt.savefig(f'data_plotted_{title}') + + plt.show() + + +def plot_decision_boundary(): + """ + Visualize the decision boundary of KNN. + """ + pass \ No newline at end of file -- Gitee From d80fa125e7886724a8b226063cd85b92cf7ad71d Mon Sep 17 00:00:00 2001 From: xny Date: Sat, 27 Mar 2021 23:58:50 +0800 Subject: [PATCH 007/103] roughly finish --- assignment-1/submission/18300110042/README.md | 1 + .../decision_boundary_plotted_9ks.png | Bin 0 -> 280085 bytes assignment-1/submission/18300110042/source.py | 420 ++++++++++++++---- .../submission/18300110042/tester_demo.py | 2 +- 4 files changed, 325 insertions(+), 98 deletions(-) create mode 100644 assignment-1/submission/18300110042/decision_boundary_plotted_9ks.png diff --git a/assignment-1/submission/18300110042/README.md b/assignment-1/submission/18300110042/README.md index 5b1c925..bb0641a 100644 --- a/assignment-1/submission/18300110042/README.md +++ b/assignment-1/submission/18300110042/README.md @@ -26,6 +26,7 @@ # Distance Manhattan? Euclidean? 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algorithm='brute-force', norm='standard', dist='euc', verbose=False): + """ + k: int, number of nearest neighbours, default = 0, which means to select through cross validation in the 'fit' process; + if k > 0, use the fixed k set here. + weights: int, whether to set different weights to neighbours w.r.t. their distances, default = 0; + weights calculated by: w(x, xi) = exp(-l ||x - xi|| ** 2), + where l is a hyperparameter set here manually OR to be selected in 'fit' process (if l is set to -1). + algorithm: string, which algorithm to find the nearest neighbours. + options: + 'auto': choose KDtree or brute-force automatically (); + 'brute-force': use brute-force algorithm, i.e., loop over all the training data; + 'KDtree': use KD-tree data structure to search the nearest neighbours. + norm: string, whether or how to normalize the data. + options: + 'N': no normalization; + 'min_max': apply min-max normalization; + 'standard': apply standardization; + 'auto': choose method of normalization during 'fit' process. + dist: string, how to calculate the distances, default = 'euc'; + options: + 'euc' means the Euclidean distance; + 'manhattan' means the Manhattan distance. + """ self.k = k self.weights = weights self.algrthm = algorithm self.norm = norm self.dist = dist + self.verbose = verbose - def fit(self, train_data, train_label, verbose=False): + + def fit(self, train_data, train_label): """ Find the best k and(/or) algorithm. train_data: numpy.ndarray, shape = (N, K); @@ -24,73 +48,49 @@ class KNN: assert train_data.shape[1] num_samples = train_data.shape[0] - feature_dim = train_data.shape[1] - - if self.norm: - train_data, denom, f_min = self.min_max_norm(train_data) - self.denom = denom - self.f_min = f_min - - self.train_data = train_data - self.train_label = train_label + #feature_dim = train_data.shape[1] # check feature dimension - if feature_dim > 1000: + if train_data.shape[1] > 1000: print('Warning: High dimension.') - # decide k in k-fold cross validation - boundary = 0.1 * num_samples - - if boundary < 1: - # leave-one-out cross validation - num_folds = num_samples - val_size = 1 - - else: - # 10-fold cross validation - num_folds = 10 - val_size = int(boundary) - - # set upper bound for number of neighbours (K) - if num_samples < 20: - k_up_bound = num_samples - else: - k_up_bound = 20 - - ks = [k for k in range(1, k_up_bound)] #candidates for hyperparameter k - - best_k = ks[0] - best_acc = 0 - - for k in ks: - k_acc_sum = 0 - for i in range(num_folds): - start_idx = 0 - end_idx = start_idx + val_size - val_data = train_data[start_idx: end_idx] - val_label = train_label[start_idx: end_idx] - start_idx += val_size - - val_pred = self.predict(val_data) - - curr_acc = np.mean(val_pred==val_label) - k_acc_sum += curr_acc + self.train_data = train_data + self.train_label = train_label - mean_acc_k = k_acc_sum / num_folds + if self.k and self.norm != 'auto' and self.weights != -1: + self.train_data_normed = self.normalize(train_data, mode='train') + return self - if best_acc < mean_acc_k: - best_acc = mean_acc_k - best_k = k + else: + dl_indices = np.arange(num_samples) + return self.fit_cv(dl_indices=dl_indices) + + """hyperparameters = dict() + # select hyperparameters in 10-fold cross validation + if not self.k: + # set upper bound for number of neighbours (K) + if num_samples < 20: + k_up_bound = num_samples + else: + k_up_bound = 20 + ks = [k for k in range(1, k_up_bound)] #candidates for hyperparameter k + hyperparameters['k'] = ks + + if self.norm == 'auto': + hyperparameters['norm'] = ['N', 'min_max', 'standard'] + + if self.weights == -1: + hyperparameters['weights'] = [0, 0.1, 0.2, 0.5, 1, 2] - if verbose: - print('current best_acc: {0}; best_k: {1}'.format((best_acc, best_k))) + best_hp = self.cross_validation(train_data, train_label, num_folds=10, hyperparameters=hyperparameters, verbose=verbose) + + for hp in best_hp: + setattr(self, hp, best_hp[hp]) + self.train_data = self.normalize(train_data, mode='train') + self.train_label = train_label + + return self""" - if verbose: - print('After cross validation, the final best k is: {0}'.format(best_k)) - - self.k = best_k - - return best_k def predict(self, test_data): @@ -98,23 +98,26 @@ class KNN: To predict labels of test_data. test_data: numpy.ndarray, shape = (N, K); where N is number of data (samples), and K is dimension of data. + mode: string, indicate the process; + options: + 'test': for test; + 'val': for validation. + """ + return self.predict_cv(test_data, train_data=self.train_data_normed, train_label=self.train_label) """ - - # brute-force, euclidean_dist num_samples = test_data.shape[0] - if self.norm: - data = (test_data - self.f_min) / self.denom # min-max normalization + samples = self.normalize(test_data, mode='test') preds = [] - for sample in data: - distances = [self.euc_distance(sample, X) for X in self.train_data] - labels = self.train_label[np.argsort(distances)[:self.k]] - - if (labels >= 0).all(): - # if all labels are non-negative integers, we can use np.bincount() directly; - pred = np.bincount(labels).argmax() + labels, distances = self.get_nearest_neighbours(samples, self.train_data, self.train_label) + if (labels >= 0).all(): + # if all labels are non-negative integers, we can use np.bincount() directly; + for label in labels: + pred = np.bincount(label).argmax() + preds.append(pred) - else: + else: + for label in labels: votes = {} for i in labels: label = str(i) @@ -123,46 +126,222 @@ class KNN: else: votes[label] = 1 pred = int(max(votes, key=lambda x: votes[x])) + preds.append(pred) + + preds = np.array(preds) + return preds""" - preds.append(pred) - preds = np.array(preds) + def fit_cv(self, dl_indices): + #assert data.shape[0] == labels.shape[0] + + if self.k and self.norm != 'auto' and self.weights != -1: + train_data = self.normalize(self.train_data[dl_indices], mode='train') + train_label = self.train_label[dl_indices] + return train_data, train_label + + else: # cross validation + hyperparameters = dict() + num_samples = dl_indices.shape[0] + # select hyperparameters in 10-fold cross validation + if not self.k: + # set upper bound for number of neighbours (K) + if num_samples < 20: + k_up_bound = num_samples + else: + k_up_bound = 20 + ks = [k for k in range(1, k_up_bound)] #candidates for hyperparameter k + hyperparameters['k'] = ks + + if self.norm == 'auto': + hyperparameters['norm'] = ['N', 'min_max', 'standard'] + + if self.weights == -1: + hyperparameters['weights'] = [0, 0.1, 0.2, 0.5, 1, 2] - return preds + #dl_indices = np.arange(data.shape[0]) + + best_hp, _ = self.cross_validation(dl_indices, num_folds=10, hyperparameters=hyperparameters) + + for hp in best_hp: + setattr(self, hp, best_hp[hp]) + self.train_data_normed = self.normalize(self.train_data, mode='train') + return self + def predict_cv(self, test_data, train_data, train_label): + num_samples = test_data.shape[0] + samples = self.normalize(test_data, mode='test') + preds = [] + labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) - def euc_distance(self, x1, x2): + if (labels >= 0).all(): + # if all labels are non-negative integers, we can use np.bincount() directly; + for label in labels: + pred = np.bincount(label).argmax() + preds.append(pred) + else: + for label in labels: + votes = {} + for i in labels: + label = str(i) + if label in votes: + votes[label] += 1 + else: + votes[label] = 1 + pred = int(max(votes, key=lambda x: votes[x])) + preds.append(pred) + + preds = np.array(preds) + #print(preds) + return preds + + + + def cross_validation(self, dl_indices, num_folds, hyperparameters): """ - Get Euclidean Distance between 2 samples. - x1 & x2: numpy.ndarray, shape = (K,); - where K is dimension of data. """ - distance = np.sqrt(np.sum((x1 - x2)**2)) - return distance + assert dl_indices.shape[0] <= self.train_label.shape[0] + num_samples = dl_indices.shape[0] - def manhattan_distance(self, x1, x2): + best_acc = 0 + best_hp = dict() + best_comb = None + records = dict() + + keys, values = zip(*sorted(hyperparameters.items())) + hps = [tuple(hp) for hp in values] + combns = [[]] + for hp in hps: + combns = [x + [y] for x in combns for y in hp] + + for comb in combns: + for i in range(len(keys)): + setattr(self, keys[i], comb[i]) + #num_samples = data.shape[0] + #idx = np.arange(num_samples) + np.random.shuffle(dl_indices) + #data_temp = self.train_data[dl_indices] + #label_temp = self.train_label[dl_indices] + boundary = num_samples / num_folds + if boundary < 1: + # leave-one-out cross validation + print('Not enough data >>> apply leave-one-out cross validation.') + num_folds = num_samples + val_size = 1 + else: + val_size = int(boundary) + + curr_acc_sum = 0 + start_idx = 0 + for f in range(num_folds): + end_idx = start_idx + val_size + #val_data = data_temp[start_idx: end_idx] + #val_label = label_temp[start_idx: end_idx] + #train_data = np.delete(data_temp, [i for i in range(start_idx, end_idx)], axis=0) + #train_label = np.delete(label_temp, [i for i in range(start_idx, end_idx)], axis=0) + val_idx = dl_indices[start_idx: end_idx] + train_idx = np.delete(dl_indices, [i for i in range(start_idx, end_idx)], axis=0) + + train_data_normed, train_label = self.fit_cv(train_idx) + val_data = self.train_data[val_idx] + val_label = self.train_label[val_idx] + + val_pred = self.predict_cv(val_data, train_data_normed, train_label) + + curr_acc = np.mean(val_pred == val_label) + curr_acc_sum += curr_acc + + start_idx = end_idx + + mean_acc_curr = curr_acc_sum / num_folds + records['_'.join([str(p) for p in comb])] = mean_acc_curr + + if best_acc <= mean_acc_curr: + best_acc = mean_acc_curr + best_comb = comb + for i in range(len(keys)): + best_hp[keys[i]] = comb[i] + + if self.verbose: + print('current_acc: {0}; \ncurrent_best_acc: {1}; \nbest_params: {2}'.format(mean_acc_curr, best_acc, best_hp)) + + if self.verbose: + print('After cross validation, the final best_params: {0}'.format(best_hp)) + + #for i in range(len(keys)): + #setattr(self, keys[i], best_comb[i]) + #setattr(self, 'train_data', data) + #setattr(self, 'train_label', labels) + return best_hp, records + + + + def get_nearest_neighbours(self, samples, data, labels): + """ + get k nearest neighbours: corresponding distances and labels; + samples: numpy.ndarray, shape = (N1, K); + data: numpy.ndarray, shape = (N2, K); + labels: numpy.ndarray, shape = (N2,); + where N1 denotes the number of samples (test data); + N2 denotes the number of data (training data); + K is the dimension of data. """ - Get Manhattan distance between 2 samples. - x1 & x2: numpy.ndarray, shape = (K,); + distances = np.vstack([self.get_distance(sample, data) for sample in samples]) + indices = np.argsort(distances, axis=-1)[:, :self.k] + labels_rlv = labels[indices] + distances_rlv = np.vstack([distances[i][indices[i]] for i in range(indices.shape[0])]) + return labels_rlv, distances_rlv#, indices + + + def get_distance(self, x1, x2): + """ + Get distance between 2 samples. + x1 & x2: numpy.ndarray, shape = (K,) and (N, K) respectively; where K is dimension of data. """ - distance = np.sum(np.absolute(x1 - x2)) + if self.dist == 'manhattan': + distance = np.sum(np.absolute(x1 - x2), axis=-1) + else: # default: euclidean distance + distance = np.sqrt(np.sum((x1 - x2)**2, axis=-1)) return distance - - def min_max_norm(self, data): + def normalize(self, data, mode='train'): """ - Min-max Normalization data: numpy.ndarray, shape = (N, K); where N is number of data (samples), and K is dimension of data. + mode:string, specify whether to train or test + options: + 'train': fit given data -- set parameters; + 'test': use previously calculated parameters. """ - feature_max = data.max(axis=0) - feature_min = data.min(axis=0) - denom = feature_max - feature_min - data_normed = (data - feature_min) / denom - return data_normed, denom, feature_min + if mode == 'test': + if self.norm == 'min_max': + return (data - self.f_min) / self.denom + elif self.norm == 'standard': # standardization + return (data - self.mean) / self.sigma + else: # no normalization + return data + + else: # under training process, fit given data + if self.norm == 'min_max': + feature_max = data.max(axis=0) + feature_min = data.min(axis=0) + denom = feature_max - feature_min + data_normed = (data - feature_min) / denom + self.f_min = feature_min + self.denom = denom + return data_normed + elif self.norm == 'standard': # standardization + mean = np.mean(data, axis=0) + sigma = np.std(data, axis=0) + data_normed = (data - mean) / sigma + self.mean = mean + self.sigma = sigma + return data_normed + else: # no normalization + return data @@ -264,7 +443,7 @@ colours=['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:br """ Visualize the input data in a 2D plane, with different colours for each kind of labels. data: numpy.ndarray, shape = (N, K); - label: numpy.ndarray, shape = (N,); + labels: numpy.ndarray, shape = (N,); where N denotes the number of samples in data; K denotes the dimension of feature (data). title: string, data descriptions. save: bool, whether to save the figure. @@ -296,8 +475,55 @@ colours=['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:br plt.show() -def plot_decision_boundary(): +def plot_decision_boundary(model, data, labels, ks=[1,3,5,9,11,13,15,17,19], save=False, +colours=['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:brown', 'tab:pink', 'tab:grey', 'tab:olive', 'tab:cyan']): """ Visualize the decision boundary of KNN. + model: KNN class; + data: numpy.ndarray, shape = (N, K); + labels: numpy.ndarray, shape = (N,); + where N denotes the number of samples in data; K denotes the dimension of feature (data). + ks: list of integers, candidates for k (number of nearest neighbours) + here, we suppose len(k) == 9; + save: bool, whether to save the figure; + colours: list of string, specify the colours of dots plotted in matplotlob.pyplot. + Default is mcolors.TABLEAU_COLORS (Tableau Palette). """ - pass \ No newline at end of file + assert data.shape[0] == labels.shape[0] + label_record = sorted(set(labels)) + assert len(colours) >= len(label_record) + label_dict = {k: v for v, k in enumerate(label_record)} + + models = [] + + for i in range(len(ks)): + models.append(model(k=ks[i]).fit(data, labels)) + + x_min, x_max = np.min(data[:, 0]) - 1, np.max(data[:, 0]) + 1 + y_min, y_max = np.min(data[:, 1]) - 1, np.max(data[:, 1]) + 1 + xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1), np.arange(y_min, y_max, 0.1)) + + assert len(ks) == 9 + + fig, axs = plt.subplots(3, 3, sharex='col', sharey='row', figsize=(15,12)) + indices = [(x, y) for x in [0,1,2] for y in [0,1,2]] + titles = ['KNN (k=%d)' % k for k in ks] + + for idx, model, title in zip(indices, models, titles): + Z = model.predict(np.c_[xx.ravel(), yy.ravel()]) + Z = Z.reshape(xx.shape) + + axs[idx[0], idx[1]].contourf(xx, yy, Z, alpha=0.5) + colour_labels = [colours[label_dict[label]] for label in labels] + axs[idx[0], idx[1]].scatter(data[:,0], data[:,1], s=20, c=colour_labels, edgecolors=colour_labels) + axs[idx[0], idx[1]].set_title(title) + + if save: + plt.savefig(f'decision_boundary_plotted_{len(ks)}ks') + + plt.show() + + + + + \ No newline at end of file diff --git a/assignment-1/submission/18300110042/tester_demo.py b/assignment-1/submission/18300110042/tester_demo.py index 3dd9283..b71a5fd 100644 --- a/assignment-1/submission/18300110042/tester_demo.py +++ b/assignment-1/submission/18300110042/tester_demo.py @@ -17,7 +17,7 @@ test_data = np.array([ ]) test_label = np.array([0, 1]) -model = KNN() +model = KNN(verbose=True) model.fit(train_data, train_label) res = model.predict(test_data) -- Gitee From cc6af8186596db2c0c56e33149546dfc66021e5f Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 28 Mar 2021 02:33:39 +0800 Subject: [PATCH 008/103] basis finished, lacking weights & KDtree --- assignment-1/submission/18300110042/source.py | 90 +++++-------------- 1 file changed, 22 insertions(+), 68 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 28df18d..da2534f 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -51,8 +51,8 @@ class KNN: #feature_dim = train_data.shape[1] # check feature dimension - if train_data.shape[1] > 1000: - print('Warning: High dimension.') + #if train_data.shape[1] > 1000: + #print('Warning: High dimension.') self.train_data = train_data self.train_label = train_label @@ -65,34 +65,7 @@ class KNN: dl_indices = np.arange(num_samples) return self.fit_cv(dl_indices=dl_indices) - """hyperparameters = dict() - # select hyperparameters in 10-fold cross validation - if not self.k: - # set upper bound for number of neighbours (K) - if num_samples < 20: - k_up_bound = num_samples - else: - k_up_bound = 20 - ks = [k for k in range(1, k_up_bound)] #candidates for hyperparameter k - hyperparameters['k'] = ks - if self.norm == 'auto': - hyperparameters['norm'] = ['N', 'min_max', 'standard'] - - if self.weights == -1: - hyperparameters['weights'] = [0, 0.1, 0.2, 0.5, 1, 2] - - best_hp = self.cross_validation(train_data, train_label, num_folds=10, hyperparameters=hyperparameters, verbose=verbose) - - for hp in best_hp: - setattr(self, hp, best_hp[hp]) - self.train_data = self.normalize(train_data, mode='train') - self.train_label = train_label - - return self""" - - - def predict(self, test_data): """ To predict labels of test_data. @@ -104,35 +77,14 @@ class KNN: 'val': for validation. """ return self.predict_cv(test_data, train_data=self.train_data_normed, train_label=self.train_label) - """ - num_samples = test_data.shape[0] - - samples = self.normalize(test_data, mode='test') - preds = [] - labels, distances = self.get_nearest_neighbours(samples, self.train_data, self.train_label) - if (labels >= 0).all(): - # if all labels are non-negative integers, we can use np.bincount() directly; - for label in labels: - pred = np.bincount(label).argmax() - preds.append(pred) - - else: - for label in labels: - votes = {} - for i in labels: - label = str(i) - if label in votes: - votes[label] += 1 - else: - votes[label] = 1 - pred = int(max(votes, key=lambda x: votes[x])) - preds.append(pred) - - preds = np.array(preds) - return preds""" def fit_cv(self, dl_indices): + """ + conduct 'fit' process during cross validation and finally set hyperparameters to ones having best performance. + dl_indices: numpy.ndarray, shape = (N,), specify which sample to select in self.train_data and self.train_label; + where N is number of indices. + """ #assert data.shape[0] == labels.shape[0] if self.k and self.norm != 'auto' and self.weights != -1: @@ -171,10 +123,18 @@ class KNN: def predict_cv(self, test_data, train_data, train_label): + """ + predict labels of test_data. + test_data: numpy.ndarray, shape = (N1, K); + train_data: numpy.ndarray, data for training here, shape = (N2, K); + train_label: numpy.ndarray, labels for training, shape = (N2,); + where N1 & N2 are number of test and training samples respectively and K is the dimension of feature. + """ num_samples = test_data.shape[0] samples = self.normalize(test_data, mode='test') preds = [] labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) + #weights = np.exp(-self.weights * distances ** 2) if (labels >= 0).all(): # if all labels are non-negative integers, we can use np.bincount() directly; @@ -201,6 +161,10 @@ class KNN: def cross_validation(self, dl_indices, num_folds, hyperparameters): """ + conduct Grid Search for hyperparameters through cross validation. + dl_indices: np.ndarray, indices of self.train_data for cross validation; + num_folds: int, number of folds for cross validation, if larger than number of samples, apply leave-one-out cross validation; + hyperparameters: dict, where keys(string) are names of hyperparameters and values(list) are list of corresponding candidates. """ assert dl_indices.shape[0] <= self.train_label.shape[0] num_samples = dl_indices.shape[0] @@ -219,11 +183,9 @@ class KNN: for comb in combns: for i in range(len(keys)): setattr(self, keys[i], comb[i]) - #num_samples = data.shape[0] - #idx = np.arange(num_samples) + np.random.shuffle(dl_indices) - #data_temp = self.train_data[dl_indices] - #label_temp = self.train_label[dl_indices] + boundary = num_samples / num_folds if boundary < 1: # leave-one-out cross validation @@ -237,10 +199,6 @@ class KNN: start_idx = 0 for f in range(num_folds): end_idx = start_idx + val_size - #val_data = data_temp[start_idx: end_idx] - #val_label = label_temp[start_idx: end_idx] - #train_data = np.delete(data_temp, [i for i in range(start_idx, end_idx)], axis=0) - #train_label = np.delete(label_temp, [i for i in range(start_idx, end_idx)], axis=0) val_idx = dl_indices[start_idx: end_idx] train_idx = np.delete(dl_indices, [i for i in range(start_idx, end_idx)], axis=0) @@ -270,10 +228,6 @@ class KNN: if self.verbose: print('After cross validation, the final best_params: {0}'.format(best_hp)) - #for i in range(len(keys)): - #setattr(self, keys[i], best_comb[i]) - #setattr(self, 'train_data', data) - #setattr(self, 'train_label', labels) return best_hp, records @@ -307,6 +261,7 @@ class KNN: distance = np.sqrt(np.sum((x1 - x2)**2, axis=-1)) return distance + def normalize(self, data, mode='train'): """ data: numpy.ndarray, shape = (N, K); @@ -366,7 +321,6 @@ def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=Fal x = np.random.multivariate_normal(mean, cov, (num_samples[i],)) Xs.append(x) - else: mean_1 = (1, 50) mean_2 = (-5, 25) -- Gitee From df86d410b53db98feec95f8b0f3a5cceb4003eef Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 28 Mar 2021 12:57:28 +0800 Subject: [PATCH 009/103] add weights --- assignment-1/submission/18300110042/source.py | 24 +++++++++---------- .../submission/18300110042/tester_demo.py | 2 +- 2 files changed, 13 insertions(+), 13 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index da2534f..0946390 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -134,27 +134,27 @@ class KNN: samples = self.normalize(test_data, mode='test') preds = [] labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) - #weights = np.exp(-self.weights * distances ** 2) + d_weights = np.exp(-self.weights * distances ** 2) - if (labels >= 0).all(): - # if all labels are non-negative integers, we can use np.bincount() directly; + if (labels >= 0).all() and not self.weights: + # if all labels are non-negative integers and we don't consider weights w.r.t. distances, use np.bincount() directly; for label in labels: pred = np.bincount(label).argmax() preds.append(pred) else: - for label in labels: + for i in range(num_samples): votes = {} - for i in labels: - label = str(i) - if label in votes: - votes[label] += 1 + label = labels[i] + for j in range(self.k): + l = label[j] + if l in votes: + votes[l] += d_weights[i][j] else: - votes[label] = 1 - pred = int(max(votes, key=lambda x: votes[x])) + votes[l] = d_weights[i][j] + pred = sorted(votes.items(), key=lambda x: x[1], reverse=True)[0][0] preds.append(pred) preds = np.array(preds) - #print(preds) return preds @@ -216,7 +216,7 @@ class KNN: mean_acc_curr = curr_acc_sum / num_folds records['_'.join([str(p) for p in comb])] = mean_acc_curr - if best_acc <= mean_acc_curr: + if best_acc < mean_acc_curr: best_acc = mean_acc_curr best_comb = comb for i in range(len(keys)): diff --git a/assignment-1/submission/18300110042/tester_demo.py b/assignment-1/submission/18300110042/tester_demo.py index b71a5fd..b9e3982 100644 --- a/assignment-1/submission/18300110042/tester_demo.py +++ b/assignment-1/submission/18300110042/tester_demo.py @@ -17,7 +17,7 @@ test_data = np.array([ ]) test_label = np.array([0, 1]) -model = KNN(verbose=True) +model = KNN(weights=-1, verbose=True) model.fit(train_data, train_label) res = model.predict(test_data) -- Gitee From 5ae621cbf1454ba570241643331e9e0063277a0c Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 28 Mar 2021 13:30:44 +0800 Subject: [PATCH 010/103] delete some comments add cv_record parameter for KNN --- assignment-1/submission/18300110042/source.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 0946390..86b78f4 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -2,7 +2,7 @@ import numpy as np import matplotlib.pyplot as plt class KNN: - def __init__(self, k=0, weights=0, algorithm='brute-force', norm='standard', dist='euc', verbose=False): + def __init__(self, k=0, weights=0, algorithm='brute-force', norm='standard', dist='euc', self.cv_records=False, verbose=False): """ k: int, number of nearest neighbours, default = 0, which means to select through cross validation in the 'fit' process; if k > 0, use the fixed k set here. @@ -85,7 +85,6 @@ class KNN: dl_indices: numpy.ndarray, shape = (N,), specify which sample to select in self.train_data and self.train_label; where N is number of indices. """ - #assert data.shape[0] == labels.shape[0] if self.k and self.norm != 'auto' and self.weights != -1: train_data = self.normalize(self.train_data[dl_indices], mode='train') @@ -111,9 +110,10 @@ class KNN: if self.weights == -1: hyperparameters['weights'] = [0, 0.1, 0.2, 0.5, 1, 2] - #dl_indices = np.arange(data.shape[0]) - - best_hp, _ = self.cross_validation(dl_indices, num_folds=10, hyperparameters=hyperparameters) + best_hp, cv_records = self.cross_validation(dl_indices, num_folds=10, hyperparameters=hyperparameters) + + if self.cv_records: + self.cv_records = cv_records for hp in best_hp: setattr(self, hp, best_hp[hp]) -- Gitee From f7791ada4533d7908440896cd7e2d8f3e2f3ee2b Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 28 Mar 2021 13:32:29 +0800 Subject: [PATCH 011/103] bug fixed --- assignment-1/submission/18300110042/source.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 86b78f4..4a4ffac 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -2,7 +2,7 @@ import numpy as np import matplotlib.pyplot as plt class KNN: - def __init__(self, k=0, weights=0, algorithm='brute-force', norm='standard', dist='euc', self.cv_records=False, verbose=False): + def __init__(self, k=0, weights=0, algorithm='brute-force', norm='standard', dist='euc', cv_records=False, verbose=False): """ k: int, number of nearest neighbours, default = 0, which means to select through cross validation in the 'fit' process; if k > 0, use the fixed k set here. @@ -30,6 +30,7 @@ class KNN: self.algrthm = algorithm self.norm = norm self.dist = dist + self.cv_records = cv_records self.verbose = verbose @@ -111,7 +112,7 @@ class KNN: hyperparameters['weights'] = [0, 0.1, 0.2, 0.5, 1, 2] best_hp, cv_records = self.cross_validation(dl_indices, num_folds=10, hyperparameters=hyperparameters) - + if self.cv_records: self.cv_records = cv_records -- Gitee From a55d0ff1a4f3b1792a0c4563cdbaf02f425f4896 Mon Sep 17 00:00:00 2001 From: xny Date: Sun, 28 Mar 2021 14:02:33 +0800 Subject: [PATCH 012/103] some modificaitions --- assignment-1/submission/18300110042/tester_demo.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/assignment-1/submission/18300110042/tester_demo.py b/assignment-1/submission/18300110042/tester_demo.py index b9e3982..0bcc0ab 100644 --- a/assignment-1/submission/18300110042/tester_demo.py +++ b/assignment-1/submission/18300110042/tester_demo.py @@ -1,6 +1,6 @@ import numpy as np -from source import KNN +from source import KNN, get_data, plot_data train_data = np.array([ [1, 2, 3, 4], @@ -17,8 +17,8 @@ test_data = np.array([ ]) test_label = np.array([0, 1]) -model = KNN(weights=-1, verbose=True) +model = KNN(weights=-1, cv_records=True, verbose=True) model.fit(train_data, train_label) res = model.predict(test_data) -print("acc =",np.mean(np.equal(res, test_label))) \ No newline at end of file +print("acc =",np.mean(np.equal(res, test_label))) -- Gitee From 100cb4db3ea175f2f3f02c3f94c021338b6ce80e Mon Sep 17 00:00:00 2001 From: xny Date: Mon, 29 Mar 2021 03:47:32 +0800 Subject: [PATCH 013/103] add kdtree (not finished yet) --- assignment-1/submission/18300110042/source.py | 161 +++++++++++++++++- .../submission/18300110042/tester_demo.py | 2 +- 2 files changed, 154 insertions(+), 9 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 4a4ffac..1f3e7db 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -2,7 +2,7 @@ import numpy as np import matplotlib.pyplot as plt class KNN: - def __init__(self, k=0, weights=0, algorithm='brute-force', norm='standard', dist='euc', cv_records=False, verbose=False): + def __init__(self, k=0, weights=0, algorithm='brute-force', leaf_size=30, norm='standard', dist='euc', cv_records=False, verbose=False): """ k: int, number of nearest neighbours, default = 0, which means to select through cross validation in the 'fit' process; if k > 0, use the fixed k set here. @@ -27,7 +27,8 @@ class KNN: """ self.k = k self.weights = weights - self.algrthm = algorithm + self.algorithm = algorithm + self.leaf_size = leaf_size self.norm = norm self.dist = dist self.cv_records = cv_records @@ -60,6 +61,9 @@ class KNN: if self.k and self.norm != 'auto' and self.weights != -1: self.train_data_normed = self.normalize(train_data, mode='train') + if self.algorithm == 'KDtree': + self.kdtree = self.build_kdtree(self.train_data_normed.copy()) + #print(self.kdtree) return self else: @@ -72,10 +76,6 @@ class KNN: To predict labels of test_data. test_data: numpy.ndarray, shape = (N, K); where N is number of data (samples), and K is dimension of data. - mode: string, indicate the process; - options: - 'test': for test; - 'val': for validation. """ return self.predict_cv(test_data, train_data=self.train_data_normed, train_label=self.train_label) @@ -90,6 +90,8 @@ class KNN: if self.k and self.norm != 'auto' and self.weights != -1: train_data = self.normalize(self.train_data[dl_indices], mode='train') train_label = self.train_label[dl_indices] + #if self.algorithm == 'KDtree': + #self.kdtree = self.build_kdtree(train_data.copy()) return train_data, train_label else: # cross validation @@ -120,6 +122,9 @@ class KNN: setattr(self, hp, best_hp[hp]) self.train_data_normed = self.normalize(self.train_data, mode='train') + if self.algorithm == 'KDtree': + self.kdtree = self.build_kdtree(self.train_data_normed.copy()) + return self @@ -134,8 +139,25 @@ class KNN: num_samples = test_data.shape[0] samples = self.normalize(test_data, mode='test') preds = [] - labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) - d_weights = np.exp(-self.weights * distances ** 2) + if self.algorithm == 'KDtree': + #labels, distances = + labels = [] + distances = [] + knns = self.search_knn_batch(train_data, test_data.copy(), mode='cv') + for knn in knns: + print('knn',knn) + indices = np.array([n[1] for n in knn]) + label = train_label[indices] + labels.append(label) + distance = np.array([n[0] for n in knn]) + distances.append(distance) + + labels = np.vstack(labels) + distances = np.vstack(distances) + + else: + labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) + #d_weights = np.exp(-self.weights * distances ** 2) if (labels >= 0).all() and not self.weights: # if all labels are non-negative integers and we don't consider weights w.r.t. distances, use np.bincount() directly; @@ -143,6 +165,7 @@ class KNN: pred = np.bincount(label).argmax() preds.append(pred) else: + d_weights = np.exp(-self.weights * distances ** 2) for i in range(num_samples): votes = {} label = labels[i] @@ -299,6 +322,128 @@ class KNN: else: # no normalization return data + def build_kdtree(self, data): + assert len(data.shape) == 2 + num_samples = data.shape[0] + num_dims = data.shape[1] + data_T = data.T.copy() + + # get bounds of hyper-rectangle + hyper_rec = np.zeros((2, num_dims)) + hyper_rec[0, :] = data_T.min(axis=1) + hyper_rec[1, :] = data_T.max(axis=1) + + # root of kd-tree + idx = np.argsort(data_T[0, :], kind='mergesort') + data_T[:, :] = data_T[:, idx] + split = data_T[0, num_samples//2] + + left_hprec = hyper_rec.copy() + right_hprec = hyper_rec.copy() + left_hprec[1, 0] = split + right_hprec[0, 0] = split + + tree = [(None, None, left_hprec, right_hprec, None, None)] + + stack = [(data_T[:, :num_samples//2], idx[:num_samples//2], 1, 0, True), + (data_T[:, num_samples//2:], idx[num_samples//2:], 1, 0, False)] + + while stack: + data_T, d_idx, depth, parent, left_branch = stack.pop() + num_samples = data_T.shape[1] + node_pt = len(tree) + + _d_idx, _data, _left_hprec, _right_hprec, left, right = tree[parent] + tree[parent] = (_d_idx, _data, _left_hprec, _right_hprec, node_pt, right) if left_branch \ + else (_d_idx, _data, _left_hprec, _right_hprec, left, node_pt) + + if num_samples <= self.leaf_size: + _d_idx = d_idx.copy() + _data = data_T.copy() + leaf = (_d_idx, _data, None, None, 0, 0) + tree.append(leaf) + + else: + split_dim = depth % num_dims + idx = np.argsort(data_T[split_dim, :], kind='mergesort') + data_T[:, :] = data_T[:, idx] + d_idx = d_idx[idx] + node_pt = len(tree) + stack.append((data_T[:, :num_samples//2], d_idx[:num_samples//2], depth+1, node_pt, True)) + stack.append((data_T[:, num_samples//2:], d_idx[num_samples//2:], depth+1, node_pt, False)) + + split = data_T[split_dim, num_samples//2] + + if left_branch: + left_hprec = _left_hprec.copy() + right_hprec = _right_hprec.copy() + else: + left_hprec = _right_hprec.copy() + right_hprec = _left_hprec.copy() + left_hprec[1, split_dim] = split + right_hprec[0, split_dim] = split + + tree.append((None, None, left_hprec, right_hprec, None, None)) + + return tree + + def intersect(self, hprec, r2, centroid): + maxv = hprec[1, :] + minv = hprec[0, :] + p = centroid.copy() + idx = p < minv + p[idx] = minv[idx] + idx = p > maxv + p[idx] = maxv[idx] + dcs = ((p - centroid) ** 2).sum() < r2 + return dcs + + def get_knn_kdtree(self, sample, leaf_idx, data): + num_data = data.shape[1] + num_dims = data.shape[0] + distances = np.sqrt(np.sum((data - sample) ** 2, axis=0)) + indices = np.argsort(distances, kind='mergesort')[:self.k] + return list(zip(distances[indices], leaf_idx[indices])) + + def search_knn(self, tree, sample): + stack = [tree[0]] + k_nn = [(np.inf, None)] * (self.k) + _datapt = sample[:, 0] + while stack: + leaf_idx, leaf_data, left_hprec, right_hprec, left, right = stack.pop() + if leaf_idx is not None: + _knn = self.get_knn_kdtree(sample, leaf_idx, leaf_data) + if _knn[0][0] < k_nn[-1][0]: + k_nn = sorted(k_nn + _knn)[:self.k] + else: + if self.intersect(left_hprec, k_nn[-1][0], _datapt): + stack.append(tree[left]) + + if self.intersect(right_hprec, k_nn[-1][0], _datapt): + stack.append(tree[right]) + return k_nn + + def search_knn_batch(self, train_data, test_data, mode='test'): + assert train_data.shape[1] == test_data.shape[1] + + if mode == 'cv': + tree = self.build_kdtree(train_data.copy()) + else: + tree = self.kdtree + #num_data = train_data.shape[0] + num_dims = train_data.shape[1] + + k_nn = [] + for sample in test_data: + + #sample_rs = sample.reshape((num_dims, 1)).repeat(self.leaf_size, axis=1) + sample_rs = sample.reshape((num_dims, 1)) + _knn = self.search_knn(tree, sample_rs) + #print(_knn) + k_nn.append(_knn[0:]) + + return k_nn + diff --git a/assignment-1/submission/18300110042/tester_demo.py b/assignment-1/submission/18300110042/tester_demo.py index 0bcc0ab..0ac332f 100644 --- a/assignment-1/submission/18300110042/tester_demo.py +++ b/assignment-1/submission/18300110042/tester_demo.py @@ -17,7 +17,7 @@ test_data = np.array([ ]) test_label = np.array([0, 1]) -model = KNN(weights=-1, cv_records=True, verbose=True) +model = KNN(k=1, algorithm='KDtree', verbose=True) model.fit(train_data, train_label) res = model.predict(test_data) -- Gitee From a1873962690cde96cf6670d8d744db70a6c6a68a Mon Sep 17 00:00:00 2001 From: xny Date: Mon, 29 Mar 2021 12:55:54 +0800 Subject: [PATCH 014/103] delete kdtree --- assignment-1/submission/18300110042/source.py | 53 ++++++++----------- 1 file changed, 22 insertions(+), 31 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 1f3e7db..2ae64fd 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -2,18 +2,13 @@ import numpy as np import matplotlib.pyplot as plt class KNN: - def __init__(self, k=0, weights=0, algorithm='brute-force', leaf_size=30, norm='standard', dist='euc', cv_records=False, verbose=False): + def __init__(self, k=0, weights=0, norm='standard', dist='euc', cv_records=False, verbose=False): """ k: int, number of nearest neighbours, default = 0, which means to select through cross validation in the 'fit' process; if k > 0, use the fixed k set here. weights: int, whether to set different weights to neighbours w.r.t. their distances, default = 0; weights calculated by: w(x, xi) = exp(-l ||x - xi|| ** 2), where l is a hyperparameter set here manually OR to be selected in 'fit' process (if l is set to -1). - algorithm: string, which algorithm to find the nearest neighbours. - options: - 'auto': choose KDtree or brute-force automatically (); - 'brute-force': use brute-force algorithm, i.e., loop over all the training data; - 'KDtree': use KD-tree data structure to search the nearest neighbours. norm: string, whether or how to normalize the data. options: 'N': no normalization; @@ -27,8 +22,6 @@ class KNN: """ self.k = k self.weights = weights - self.algorithm = algorithm - self.leaf_size = leaf_size self.norm = norm self.dist = dist self.cv_records = cv_records @@ -61,9 +54,8 @@ class KNN: if self.k and self.norm != 'auto' and self.weights != -1: self.train_data_normed = self.normalize(train_data, mode='train') - if self.algorithm == 'KDtree': - self.kdtree = self.build_kdtree(self.train_data_normed.copy()) - #print(self.kdtree) + #if self.algorithm == 'KDtree': + #self.kdtree = self.build_kdtree(self.train_data_normed.copy()) return self else: @@ -122,8 +114,8 @@ class KNN: setattr(self, hp, best_hp[hp]) self.train_data_normed = self.normalize(self.train_data, mode='train') - if self.algorithm == 'KDtree': - self.kdtree = self.build_kdtree(self.train_data_normed.copy()) + #if self.algorithm == 'KDtree': + #self.kdtree = self.build_kdtree(self.train_data_normed.copy()) return self @@ -139,24 +131,22 @@ class KNN: num_samples = test_data.shape[0] samples = self.normalize(test_data, mode='test') preds = [] - if self.algorithm == 'KDtree': + #if self.algorithm == 'KDtree': #labels, distances = - labels = [] - distances = [] - knns = self.search_knn_batch(train_data, test_data.copy(), mode='cv') - for knn in knns: - print('knn',knn) - indices = np.array([n[1] for n in knn]) - label = train_label[indices] - labels.append(label) - distance = np.array([n[0] for n in knn]) - distances.append(distance) - - labels = np.vstack(labels) - distances = np.vstack(distances) - - else: - labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) + #labels = [] + #distances = [] + #knns = self.search_knn_batch(train_data, test_data.copy(), mode='cv') + #for knn in knns: + #print('knn',knn) + #indices = np.array([n[1] for n in knn]) + #label = train_label[indices] + #labels.append(label) + #distance = np.array([n[0] for n in knn]) + #distances.append(distance) + #labels = np.vstack(labels) + #distances = np.vstack(distances) + + labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) #d_weights = np.exp(-self.weights * distances ** 2) if (labels >= 0).all() and not self.weights: @@ -322,6 +312,7 @@ class KNN: else: # no normalization return data + """ def build_kdtree(self, data): assert len(data.shape) == 2 num_samples = data.shape[0] @@ -443,7 +434,7 @@ class KNN: k_nn.append(_knn[0:]) return k_nn - + """ -- Gitee From 77c16aef7e4e640c6da8ff3c2a89f553d292818f Mon Sep 17 00:00:00 2001 From: xny Date: Mon, 29 Mar 2021 13:03:12 +0800 Subject: [PATCH 015/103] some comments --- assignment-1/submission/18300110042/source.py | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 2ae64fd..03b0ca2 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -19,6 +19,8 @@ class KNN: options: 'euc' means the Euclidean distance; 'manhattan' means the Manhattan distance. + cv_records: bool, when True, save records of accuracy during cross validation. + verbose: bool, when True, print progress during cross validation. """ self.k = k self.weights = weights @@ -614,7 +616,3 @@ colours=['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:br plt.show() - - - - \ No newline at end of file -- Gitee From f45f6bea12a9eb8c8a41fa7a40a117cdc1a9bdb5 Mon Sep 17 00:00:00 2001 From: xny Date: Tue, 30 Mar 2021 20:57:03 +0800 Subject: [PATCH 016/103] add KL_divergence --- assignment-1/submission/18300110042/source.py | 236 +++++++----------- 1 file changed, 85 insertions(+), 151 deletions(-) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 03b0ca2..1b09966 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -56,8 +56,6 @@ class KNN: if self.k and self.norm != 'auto' and self.weights != -1: self.train_data_normed = self.normalize(train_data, mode='train') - #if self.algorithm == 'KDtree': - #self.kdtree = self.build_kdtree(self.train_data_normed.copy()) return self else: @@ -84,8 +82,6 @@ class KNN: if self.k and self.norm != 'auto' and self.weights != -1: train_data = self.normalize(self.train_data[dl_indices], mode='train') train_label = self.train_label[dl_indices] - #if self.algorithm == 'KDtree': - #self.kdtree = self.build_kdtree(train_data.copy()) return train_data, train_label else: # cross validation @@ -116,9 +112,6 @@ class KNN: setattr(self, hp, best_hp[hp]) self.train_data_normed = self.normalize(self.train_data, mode='train') - #if self.algorithm == 'KDtree': - #self.kdtree = self.build_kdtree(self.train_data_normed.copy()) - return self @@ -133,23 +126,8 @@ class KNN: num_samples = test_data.shape[0] samples = self.normalize(test_data, mode='test') preds = [] - #if self.algorithm == 'KDtree': - #labels, distances = - #labels = [] - #distances = [] - #knns = self.search_knn_batch(train_data, test_data.copy(), mode='cv') - #for knn in knns: - #print('knn',knn) - #indices = np.array([n[1] for n in knn]) - #label = train_label[indices] - #labels.append(label) - #distance = np.array([n[0] for n in knn]) - #distances.append(distance) - #labels = np.vstack(labels) - #distances = np.vstack(distances) labels, distances = self.get_nearest_neighbours(samples, train_data, train_label) - #d_weights = np.exp(-self.weights * distances ** 2) if (labels >= 0).all() and not self.weights: # if all labels are non-negative integers and we don't consider weights w.r.t. distances, use np.bincount() directly; @@ -314,130 +292,6 @@ class KNN: else: # no normalization return data - """ - def build_kdtree(self, data): - assert len(data.shape) == 2 - num_samples = data.shape[0] - num_dims = data.shape[1] - data_T = data.T.copy() - - # get bounds of hyper-rectangle - hyper_rec = np.zeros((2, num_dims)) - hyper_rec[0, :] = data_T.min(axis=1) - hyper_rec[1, :] = data_T.max(axis=1) - - # root of kd-tree - idx = np.argsort(data_T[0, :], kind='mergesort') - data_T[:, :] = data_T[:, idx] - split = data_T[0, num_samples//2] - - left_hprec = hyper_rec.copy() - right_hprec = hyper_rec.copy() - left_hprec[1, 0] = split - right_hprec[0, 0] = split - - tree = [(None, None, left_hprec, right_hprec, None, None)] - - stack = [(data_T[:, :num_samples//2], idx[:num_samples//2], 1, 0, True), - (data_T[:, num_samples//2:], idx[num_samples//2:], 1, 0, False)] - - while stack: - data_T, d_idx, depth, parent, left_branch = stack.pop() - num_samples = data_T.shape[1] - node_pt = len(tree) - - _d_idx, _data, _left_hprec, _right_hprec, left, right = tree[parent] - tree[parent] = (_d_idx, _data, _left_hprec, _right_hprec, node_pt, right) if left_branch \ - else (_d_idx, _data, _left_hprec, _right_hprec, left, node_pt) - - if num_samples <= self.leaf_size: - _d_idx = d_idx.copy() - _data = data_T.copy() - leaf = (_d_idx, _data, None, None, 0, 0) - tree.append(leaf) - - else: - split_dim = depth % num_dims - idx = np.argsort(data_T[split_dim, :], kind='mergesort') - data_T[:, :] = data_T[:, idx] - d_idx = d_idx[idx] - node_pt = len(tree) - stack.append((data_T[:, :num_samples//2], d_idx[:num_samples//2], depth+1, node_pt, True)) - stack.append((data_T[:, num_samples//2:], d_idx[num_samples//2:], depth+1, node_pt, False)) - - split = data_T[split_dim, num_samples//2] - - if left_branch: - left_hprec = _left_hprec.copy() - right_hprec = _right_hprec.copy() - else: - left_hprec = _right_hprec.copy() - right_hprec = _left_hprec.copy() - left_hprec[1, split_dim] = split - right_hprec[0, split_dim] = split - - tree.append((None, None, left_hprec, right_hprec, None, None)) - - return tree - - def intersect(self, hprec, r2, centroid): - maxv = hprec[1, :] - minv = hprec[0, :] - p = centroid.copy() - idx = p < minv - p[idx] = minv[idx] - idx = p > maxv - p[idx] = maxv[idx] - dcs = ((p - centroid) ** 2).sum() < r2 - return dcs - - def get_knn_kdtree(self, sample, leaf_idx, data): - num_data = data.shape[1] - num_dims = data.shape[0] - distances = np.sqrt(np.sum((data - sample) ** 2, axis=0)) - indices = np.argsort(distances, kind='mergesort')[:self.k] - return list(zip(distances[indices], leaf_idx[indices])) - - def search_knn(self, tree, sample): - stack = [tree[0]] - k_nn = [(np.inf, None)] * (self.k) - _datapt = sample[:, 0] - while stack: - leaf_idx, leaf_data, left_hprec, right_hprec, left, right = stack.pop() - if leaf_idx is not None: - _knn = self.get_knn_kdtree(sample, leaf_idx, leaf_data) - if _knn[0][0] < k_nn[-1][0]: - k_nn = sorted(k_nn + _knn)[:self.k] - else: - if self.intersect(left_hprec, k_nn[-1][0], _datapt): - stack.append(tree[left]) - - if self.intersect(right_hprec, k_nn[-1][0], _datapt): - stack.append(tree[right]) - return k_nn - - def search_knn_batch(self, train_data, test_data, mode='test'): - assert train_data.shape[1] == test_data.shape[1] - - if mode == 'cv': - tree = self.build_kdtree(train_data.copy()) - else: - tree = self.kdtree - #num_data = train_data.shape[0] - num_dims = train_data.shape[1] - - k_nn = [] - for sample in test_data: - - #sample_rs = sample.reshape((num_dims, 1)).repeat(self.leaf_size, axis=1) - sample_rs = sample.reshape((num_dims, 1)) - _knn = self.search_knn(tree, sample_rs) - #print(_knn) - k_nn.append(_knn[0:]) - - return k_nn - """ - def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=False): @@ -451,19 +305,28 @@ def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=Fal if mode == 'random': Xs = [] + covs = [] + means = [] for i in range(num_classes): - mean = np.random.uniform(-100, 100, 2) + mean = np.random.uniform(-10, 10, 2) + means.append(mean) cov = np.zeros((2,2)) cov[0,0] += np.random.uniform(0, 100, 1) cov[1,1] += np.random.uniform(0, 100, 1) + covs.append(cov) + x = np.random.multivariate_normal(mean, cov, (num_samples[i],)) - Xs.append(x) - else: + + means = np.stack(means) + covs = np.stack(covs) + + elif mode == 'easy3': mean_1 = (1, 50) mean_2 = (-5, 25) mean_3 = (10, 20) + means = np.stack((mean_1,mean_2,mean_3)) cov_1 = np.zeros((2,2)) cov_1[0,0] += 1 @@ -478,13 +341,41 @@ def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=Fal cov_3 = np.zeros((2,2)) cov_3[0,0] += 20 cov_3[1,1] += 30 + covs = np.stack((cov_1, cov_2, cov_3)) set_1 = np.random.multivariate_normal(mean_1, cov_1, (num_samples[0],)) set_2 = np.random.multivariate_normal(mean_2, cov_2, (num_samples[1],)) set_3 = np.random.multivariate_normal(mean_3, cov_3, (num_samples[2],)) Xs = [set_1, set_2, set_3] - + + elif mode == 'hard3': + mean_1 = (1, 20) + mean_2 = (2, 20) + mean_3 = (3, 20) + means = np.stack((mean_1,mean_2,mean_3)) + + cov_1 = np.zeros((2,2)) + cov_1[0,0] += 1 + cov_1[1,1] += 10 + + cov_2 = np.zeros((2,2)) + cov_2[0,0] += 10 + cov_2[0,1] += 15 + cov_2[1,0] += 15 + cov_2[1,1] += 40 + + cov_3 = np.zeros((2,2)) + cov_3[0,0] += 20 + cov_3[1,1] += 30 + covs = np.stack((cov_1, cov_2, cov_3)) + + set_1 = np.random.multivariate_normal(mean_1, cov_1, (num_samples[0],)) + set_2 = np.random.multivariate_normal(mean_2, cov_2, (num_samples[1],)) + set_3 = np.random.multivariate_normal(mean_3, cov_3, (num_samples[2],)) + + Xs = [set_1, set_2, set_3] + data = np.concatenate(Xs) labels = [] for i in range(num_classes): @@ -509,7 +400,21 @@ def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=Fal np.save('test_data.npy', test_data) np.save('test_label.npy', test_label) - return train_data, train_label, test_data, test_label + return train_data, train_label, test_data, test_label, means, covs + + +def get_KLdiv(mean_1, cov_1, mean_2, cov_2): + assert len(mean_1) == len(mean_2) + num_dims = len(mean_1) + mu1 = np.array(mean_1) + mu2 = np.array(mean_2) + cov2_inv = np.linalg.inv(cov_2) + + logd = np.log(np.linalg.det(cov_2) / np.linalg.det(cov_1)) + trace_cov = np.trace(np.matmul(cov2_inv, cov_1)) + mean_cov = (mu2 - mu1).T.dot(cov2_inv).dot((mu2 - mu1)) + kldiv = 1/2 * (logd + trace_cov + mean_cov - num_dims) + return kldiv def load_data(): @@ -616,3 +521,32 @@ colours=['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:br plt.show() + +def plot_acc_kl(num_iters=20, k=5, save=False): + kldivs = [] + accs = [] + for i in range(num_iters): + train_data, train_label, test_data, test_label, means, covs = get_data(num_samples=[1000,1000], num_classes=2, mode='random', save=False) + #plot_data(train_data, train_label) + kldiv = get_KLdiv(means[0], covs[0], means[1], covs[1]) + kldivs.append(kldiv) + + model = KNN(k=k) + model.fit(train_data, train_label) + res = model.predict(test_data) + acc = np.mean(res == test_label) + accs.append(acc) + + kldivs = np.array(kldivs) + accs = np.array(accs) + sort_idx = np.argsort(kldivs) + + Xs = kldivs[sort_idx] + Ys = accs[sort_idx] + + plt.plot(Xs, Ys, marker='o', markerfacecolor='tab:orange') + plt.title(f'Accs k={k} w.r.t. KL divergence') + if save: + plt.savefig(f'accs_kldiv_{k}nns') + + plt.show() \ No newline at end of file -- Gitee From a32c45074687c2a216334e6255ae93c480a4fa4d Mon Sep 17 00:00:00 2001 From: xny Date: Tue, 30 Mar 2021 23:11:37 +0800 Subject: [PATCH 017/103] add readme --- assignment-1/submission/18300110042/README.md | 71 ++++++++++++++++--- assignment-1/submission/18300110042/source.py | 12 +++- 2 files changed, 71 insertions(+), 12 deletions(-) diff --git a/assignment-1/submission/18300110042/README.md b/assignment-1/submission/18300110042/README.md index bb0641a..c53281d 100644 --- a/assignment-1/submission/18300110042/README.md +++ b/assignment-1/submission/18300110042/README.md @@ -1,6 +1,65 @@ -# Introduction to KNN Classifier (maths) - supervised - MLE +# 课程报告 +这是`prml-21-spring/assignment-1`的课程报告,我的代码在 [source.py]() 中。 +#### 依赖包 +`numpy` +`matplotlib` + +## KNN Classifier +k近邻法是一种监督学习的算法,可以用于分类或回归问题,本次作业中用`python`实现了k近邻的分类器。 + +算法的输入是训练数据集 $$\left \{\left ( x_1, y_1 \right ), \left ( x_2, y_2 \right ) ,\cdots , \left ( x_N, y_N \right ) \right \}, $$ 其中 $x_i \in X$ 是某一样本的特征向量, $y_i \in Y = \left \{ c_1, \cdots c_K \right \} $ 是该样本的标签;以及某一需要判断的实例 $x.$ + +而输出则是某实例 $x$ 的标签 $y.$ + +将 $x$ 映射为 $y$ 时,需要 +- 通过某种距离算法,找出训练集中与 $x$ 最近的 $k$ 个样本; +- 根据某种规则(e.g., 投票或按照距离加权)决定 $x$ 的标签 $y$. + +作为一种基于实例的、非参的学习算法,k-NN需要存储整个数据集,并在计算的时候对整个数据集进行迭代。 +对于 $N$ 个样本,每个样本特征维度为 $D$ ,则对于一个目标样本的预测,需要的时间复杂度就是 $O(N*D)$ ,因而在数据量或特征维度较大的时候,k-NN的效率就会偏低。 + +### KNN类实现 +#### 初始化 +根据`KNN`的性质,本次试验中设计了如下几个初始化参数: +- `k`,决定k近邻的数量; +- `weights`,考虑根据距离计算不同点的权重; +- `norm`,设置数据归一化/标准化的方法; +- `dist`,设定距离的计算方法。 + +#### fit() 函数 +fit() 函数主要进行: +1. 数据的处理; +2. 需要时通过交叉验证决定最好的超参数. + +#### predict() 函数 +predict() 函数根据已有的数据推断测试数据的标签。 +在 `predict` 的过程中,需要进行距离的计算以及最终的决策,实验中选择的距离的算法,以及确定测试数据标签的规则都在这一步实现。 + +## 实验探究 +### 调整超参数 +在训练的过程中,通过交叉验证的方式调整超参数 `k`, `dist`, `norm`, `weights`. + +#### 平均准确率 + +#### k 对于决策边界的影响: +k较小时,决策边界较为陡峭;随着k的增大,决策边界趋向平缓 + +#### 距离计算方式 + +#### 归一化/标准化的影响 + +#### 根据距离计算权重 +可以看到当加入权重时,可以使用更大的k,得到更高的准确率 +decision boundary 变化 + +#### 调整数据分布(高斯分布的均值和方差) + + + +### 数据分布 +由于k-NN完全基于训练数据集,测试集样本与训练集属于同样的总体, + +## 总结 @@ -29,12 +88,6 @@ weights - -# KD-Tree - (low dimension), backtracking - O(log N)~ O(N) - - # Analysis complexity (test not training, loop, number of samples), feature encoding (categorical -- label/one-hot encoding), discretization(continuous ?) diff --git a/assignment-1/submission/18300110042/source.py b/assignment-1/submission/18300110042/source.py index 1b09966..df0f955 100644 --- a/assignment-1/submission/18300110042/source.py +++ b/assignment-1/submission/18300110042/source.py @@ -309,7 +309,7 @@ def get_data(num_samples=[100, 100, 100], num_classes=3, mode='random', save=Fal means = [] for i in range(num_classes): - mean = np.random.uniform(-10, 10, 2) + mean = np.random.uniform(-5, 5, 2) means.append(mean) cov = np.zeros((2,2)) cov[0,0] += np.random.uniform(0, 100, 1) @@ -525,11 +525,17 @@ colours=['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:br def plot_acc_kl(num_iters=20, k=5, save=False): kldivs = [] accs = [] - for i in range(num_iters): + count = 0 + while count < num_iters: + #for i in range(num_iters): train_data, train_label, test_data, test_label, means, covs = get_data(num_samples=[1000,1000], num_classes=2, mode='random', save=False) #plot_data(train_data, train_label) kldiv = get_KLdiv(means[0], covs[0], means[1], covs[1]) - kldivs.append(kldiv) + if kldiv > 25: + continue + else: + kldivs.append(kldiv) + count += 1 model = KNN(k=k) model.fit(train_data, train_label) -- Gitee From fcc29fa2b4ac49adee7d80b9c7d75eab117b5494 Mon Sep 17 00:00:00 2001 From: xny Date: Wed, 31 Mar 2021 01:46:01 +0800 Subject: [PATCH 018/103] decision boundary drawing finished --- .../decision_boundary_plotted_2classes.png | Bin 0 -> 426321 bytes .../decision_boundary_plotted_3classes.png | Bin 0 -> 353765 bytes .../decision_boundary_plotted_5classes.png | Bin 0 -> 463081 bytes 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