├── .gitignore ├── images ├── gmm.png ├── knn.png ├── lda.png ├── pca.png ├── svm.png ├── kmeans.gif ├── kmeans.png ├── adaboost.png ├── perceptron.gif ├── perceptron.png ├── adaboost-sketch.png ├── logistic_regression.gif └── logistic_regression.png ├── src ├── em.py ├── pca.py ├── knn.py ├── utils.py ├── kmeans.py ├── multi_logistic_regression.py ├── perceptron.py ├── logistic_regression.py ├── gmm.py ├── lda.py ├── decision_tree.py ├── naive_bayes.py ├── hmm.py ├── adaboost.py └── svm.py ├── README.md └── LICENSE /.gitignore: -------------------------------------------------------------------------------- 1 | .vscode 2 | __pycache__ 3 | test_tool.ipynb -------------------------------------------------------------------------------- /images/gmm.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/gmm.png -------------------------------------------------------------------------------- /images/knn.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/knn.png -------------------------------------------------------------------------------- /images/lda.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/lda.png -------------------------------------------------------------------------------- /images/pca.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/pca.png -------------------------------------------------------------------------------- /images/svm.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/svm.png -------------------------------------------------------------------------------- /images/kmeans.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/kmeans.gif -------------------------------------------------------------------------------- /images/kmeans.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/kmeans.png -------------------------------------------------------------------------------- /images/adaboost.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/adaboost.png -------------------------------------------------------------------------------- /images/perceptron.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/perceptron.gif -------------------------------------------------------------------------------- /images/perceptron.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/perceptron.png -------------------------------------------------------------------------------- /images/adaboost-sketch.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/adaboost-sketch.png -------------------------------------------------------------------------------- /images/logistic_regression.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/logistic_regression.gif -------------------------------------------------------------------------------- /images/logistic_regression.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/luokn/ml/HEAD/images/logistic_regression.png -------------------------------------------------------------------------------- /src/em.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : em.py 4 | # @Data : 2020/5/27 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | 10 | 11 | class EM: # 三硬币模型 12 | """ 13 | Expectation-maximization algorithm(期望最大算法) 14 | """ 15 | 16 | def __init__(self, prob: list): 17 | self.prob = np.array(prob) 18 | 19 | def fit(self, X: np.ndarray, iterations=100): 20 | for _ in range(iterations): 21 | M = self._expect(X) # E步 22 | self._maximize(X, M) # M步 23 | 24 | def _expect(self, X: np.ndarray): # E步 25 | p1, p2, p3 = self.prob 26 | a = p1 * (p2**X) * ((1 - p2)**(1 - X)) 27 | b = (1 - p1) * (p3**X) * ((1 - p3)**(1 - X)) 28 | return a / (a + b) 29 | 30 | def _maximize(self, X: np.ndarray, M: np.ndarray): # M步 31 | self.prob[0] = np.sum(M) / len(X) 32 | self.prob[1] = np.sum(M * X) / np.sum(M) 33 | self.prob[2] = np.sum((1 - M) * X) / np.sum(1 - M) 34 | 35 | 36 | # EM算法与高斯混合模型可参见./gmm.py 37 | 38 | if __name__ == "__main__": 39 | x = np.array([1, 1, 0, 1, 0, 0, 1, 0, 1, 1]) 40 | 41 | em = EM([0.5, 0.5, 0.5]) 42 | em.fit(x) 43 | print(em.prob) # [0.5, 0.6, 0.6] 44 | 45 | em = EM([0.4, 0.6, 0.7]) 46 | em.fit(x) 47 | print(em.prob) # [0.4064, 0.5368, 0.6432] 48 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 |

经典机器学习算法的极简实现

2 | 3 | [](src/adaboost.py) 4 | [](src/decision_tree.py) 5 | [](src/em.py) 6 | [](src/gmm.py) 7 | [](src/kmeans.py) 8 | [](src/knn.py) 9 | [](src/lda.py) 10 | [](src/logistic_regression.py) 11 | [](src/naive_bayes.py) 12 | [](src/pca.py) 13 | [](src/perceptron.py) 14 | [](src/svm.py) 15 | [](src/multi_logistic_regression.py) 16 | -------------------------------------------------------------------------------- /src/pca.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : pca.py 4 | # @Data : 2020/5/20 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | from matplotlib import pyplot as plt 10 | 11 | 12 | class PCA: 13 | """ 14 | Principal Components Analysis(主成因分析) 15 | """ 16 | 17 | def __init__(self, k: int): 18 | """ 19 | Args: 20 | k (int): 主成因个数 21 | """ 22 | self.k = k 23 | 24 | def __call__(self, X: np.ndarray): 25 | X_norm = X - X.mean(axis=0) # 去中心化 26 | L, V = np.linalg.eig(X_norm.T @ X_norm) # 对协方差矩阵进行特征值分解 27 | topk = np.argsort(L)[::-1][:self.k] # 找出前K大特征值对应的索引 28 | return X_norm @ V[:, topk] # 将去中心化的X乘以前K大特征值对应的特征向量 29 | 30 | 31 | def load_data(n_samples_per_class=200): 32 | X = np.concatenate([ 33 | np.random.randn(n_samples_per_class, 2) + np.array([2, 0]), 34 | np.random.randn(n_samples_per_class, 2), 35 | np.random.randn(n_samples_per_class, 2) + np.array([-2, 0]), 36 | ]) 37 | theta = np.pi / 4 # 逆时针旋转45° 38 | scale = np.diag([1.2, 0.5]) # 缩放矩阵 39 | rotate = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]]) # 旋转矩阵 40 | return X @ scale @ rotate.T 41 | 42 | 43 | if __name__ == "__main__": 44 | X = load_data() 45 | 46 | plt.figure(figsize=[15, 5]) 47 | plt.subplot(1, 3, 1) 48 | plt.title("Ground Truth") 49 | plt.xlim(-5, 5) 50 | plt.ylim(-5, 5) 51 | for x in X.reshape(3, -1, 2): 52 | plt.scatter(x[:, 0], x[:, 1], marker=".") 53 | 54 | # 不降维 55 | Y = PCA(2)(X) 56 | plt.subplot(1, 3, 2) 57 | plt.title("PCA 2D") 58 | plt.xlim(-5, 5) 59 | plt.ylim(-5, 5) 60 | for y in Y.reshape(3, -1, 2): 61 | plt.scatter(y[:, 0], y[:, 1], marker=".") 62 | 63 | # 降为1维 64 | Z = PCA(1)(X) 65 | plt.subplot(1, 3, 3) 66 | plt.title("PCA 1D") 67 | plt.xlim(-5, 5) 68 | plt.ylim(-5, 5) 69 | for z in Z.reshape(3, -1): 70 | plt.scatter(z, np.zeros_like(z), marker=".") 71 | 72 | plt.show() 73 | -------------------------------------------------------------------------------- /src/knn.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : knn.py 4 | # @Data : 2020/5/20 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | from matplotlib import pyplot as plt 10 | from numpy import linalg as LA 11 | 12 | 13 | class KNN: 14 | """ 15 | K nearest neighbor classifier(K近邻分类器) 16 | """ 17 | 18 | def __init__(self, k: int): 19 | """ 20 | Args: 21 | k (int): 分类近邻数 22 | """ 23 | self.k, self.X, self.y = k, None, None 24 | 25 | def fit(self, X: np.ndarray, y: np.ndarray): 26 | self.X, self.y = X, y # 训练集X与Y，类别已知 27 | 28 | def __call__(self, X: np.ndarray): 29 | y_pred = np.zeros([len(X)], dtype=int) # X对应的类别 30 | for i, x in enumerate(X): 31 | dist = LA.norm(self.X - x, axis=1) # 计算x与所有已知类别点的距离 32 | topk = np.argsort(dist)[:self.k] # 取距离最小的k个点对应的索引 33 | y_pred[i] = np.bincount(self.y[topk]).argmax() # 取近邻点最多的类别作为x的类别 34 | return y_pred 35 | 36 | 37 | def load_data(n_samples_per_class=200, n_classes=5): 38 | X = np.concatenate([np.random.randn(n_samples_per_class, 2) + 3 * np.random.randn(2) for _ in range(n_classes)]) 39 | y = np.concatenate([np.full(n_samples_per_class, label) for label in range(n_classes)]) 40 | 41 | training_set, test_set = np.split(np.random.permutation(len(X)), [int(len(X) * 0.6)]) 42 | return X, y, training_set, test_set 43 | 44 | 45 | if __name__ == "__main__": 46 | n_classes = 5 47 | X, y, training_set, test_set = load_data(n_classes=n_classes) 48 | 49 | plt.figure(figsize=[12, 6]) 50 | plt.subplot(1, 2, 1) 51 | plt.title("Ground Truth") 52 | for label in range(n_classes): 53 | plt.scatter(X[y == label, 0], X[y == label, 1], label=f"class {label}", marker=".") 54 | plt.legend() 55 | 56 | knn = KNN(k=10) 57 | knn.fit(X[training_set], y[training_set]) 58 | y_pred = knn(X) 59 | acc = np.sum(y_pred[test_set] == y[test_set]) / len(y_pred[test_set]) 60 | print(f"Accuracy = {100 * acc:.2f}%") 61 | 62 | plt.subplot(1, 2, 2) 63 | plt.title("Prediction") 64 | for label in range(n_classes): 65 | plt.scatter(X[y_pred == label, 0], X[y_pred == label, 1], label=f"class {label}", marker=".") 66 | plt.legend() 67 | 68 | plt.show() 69 | -------------------------------------------------------------------------------- /src/utils.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : utils.py 4 | # @Data : 2022/05/18 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | from typing import List, Optional 9 | 10 | import numpy as np 11 | from matplotlib import pyplot as plt 12 | from sklearn import metrics 13 | 14 | 15 | def plot_roc_curve( 16 | title: str, 17 | y_truth: np.ndarray, 18 | y_score: np.ndarray, 19 | classes: List[str], 20 | out_file: Optional[str] = None, 21 | show_fig: bool = False, 22 | ): 23 | """ 24 | Plot ROC curve for multi-class classification. 25 | 26 | Args: 27 | title (str): Title of the plot. 28 | y_truth (np.ndarray): Ground truth labels. 29 | y_score (np.ndarray): Predicted scores. 30 | classes (List[str]): List of class names. 31 | out_file (Optional[str], optional): Path to save the plot. Defaults to None. Defaults to None. 32 | show_fig (bool, optional): Whether to show the plot. Defaults to False. 33 | """ 34 | plt.figure(figsize=[8, 8], dpi=200) 35 | plt.title(title) 36 | plt.xlim([0, 1]) 37 | plt.ylim([0, 1]) 38 | plt.xlabel("FPR") 39 | plt.ylabel("TPR") 40 | 41 | # Plot the diagonal line. 42 | plt.plot([0, 1], [0, 1], "k-.", lw=1) 43 | 44 | # Plot the ROC curve for each class. 45 | fpr_all, tpr_all = [], [] 46 | for i, name in enumerate(classes): 47 | fpr, tpr, _ = metrics.roc_curve(y_truth[:, i], y_score[:, i]) 48 | fpr_all += [fpr] 49 | tpr_all += [tpr] 50 | auc = metrics.auc(fpr, tpr) 51 | plt.plot(fpr, tpr, lw=1, label=f"ROC curve of class {name} (AUC = {auc:0.3f})") 52 | 53 | # Plot the micro-average ROC curve. 54 | micro_fpr, micro_tpr, _ = metrics.roc_curve(y_truth.reshape(-1), y_score.reshape(-1)) 55 | micro_auc = metrics.auc(micro_fpr, micro_tpr) 56 | plt.plot(micro_fpr, micro_tpr, "--", lw=1, label=f"Micro-average ROC curve (AUC = {micro_auc:0.3f})") 57 | 58 | # Plot the macro-average ROC curve. 59 | macro_fpr = np.unique(np.concatenate(fpr_all)) 60 | macro_tpr = sum((np.interp(macro_fpr, fpr, tpr) for fpr, tpr in zip(fpr_all, tpr_all))) / len(classes) 61 | macro_auc = metrics.auc(macro_fpr, macro_tpr) 62 | plt.plot(macro_fpr, macro_tpr, "--", lw=1, label=f"Macro-average ROC curve (AUC = {macro_auc:0.3f})") 63 | 64 | plt.legend() 65 | if out_file is not None: 66 | plt.savefig(out_file) 67 | print(f"Save ROC curve to {out_file}") 68 | if show_fig: 69 | plt.show() 70 | -------------------------------------------------------------------------------- /src/kmeans.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : kmeans.py 4 | # @Data : 2020/5/21 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import random 9 | 10 | import numpy as np 11 | from matplotlib import pyplot as plt 12 | 13 | 14 | class KMeans: 15 | """ 16 | K-means clustering(K均值聚类) 17 | """ 18 | 19 | def __init__(self, n_clusters: int, iterations=100, eps=1e-3): 20 | """ 21 | Args: 22 | n_clusters (int): 聚类类别数. 23 | iterations (int, optional): 迭代次数, 默认为100. 24 | eps (float, optional): 中心点最小更新量, 默认为1e-3. 25 | """ 26 | self.n_clusters, self.iterations, self.eps, self.centers = n_clusters, iterations, eps, None 27 | 28 | def fit(self, X: np.ndarray): 29 | """ 30 | Args: 31 | X (np.ndarray): 输入 32 | """ 33 | # 随机选择k个点作为中心点 34 | self.centers = X[random.sample(range(len(X)), self.n_clusters)] 35 | 36 | for _ in range(self.iterations): 37 | y_pred = self(X) 38 | 39 | # 各类别的均值作为新的中心点, 40 | centers = np.stack([ 41 | # 存在元素属于类别i则计算类别i所有点的均值，否则随机选择一个点作为类别i的均值 42 | np.mean(X[y_pred == i], axis=0) if np.any(y_pred == i) else random.choice(X) 43 | for i in range(self.n_clusters) 44 | ]) 45 | 46 | # 中心点最大更新值小于eps则停止迭代 47 | if np.abs(self.centers - centers).max() < self.eps: 48 | break 49 | 50 | # 将更新后的均值作为各类别中心点 51 | self.centers = centers 52 | 53 | def __call__(self, X: np.ndarray): 54 | return np.array([np.argmin(np.linalg.norm(self.centers - x, axis=1)) for x in X]) # 每一点类别为最近的中心点类别 55 | 56 | 57 | def load_data(n_samples_per_class=200, n_classes=5): 58 | X = np.concatenate([np.random.randn(n_samples_per_class, 2) + 3 * np.random.randn(2) for _ in range(n_classes)]) 59 | y = np.concatenate([np.full(n_samples_per_class, label) for label in range(n_classes)]) 60 | return X, y 61 | 62 | 63 | if __name__ == "__main__": 64 | n_classes = 5 65 | X, y = load_data(n_classes=n_classes) 66 | 67 | plt.figure(figsize=[12, 6]) 68 | plt.subplot(1, 2, 1) 69 | plt.title("Ground Truth") 70 | for label in range(n_classes): 71 | plt.scatter(X[y == label, 0], X[y == label, 1], marker=".") 72 | 73 | kmeans = KMeans(n_clusters=n_classes) 74 | kmeans.fit(X) 75 | y_pred = kmeans(X) 76 | 77 | plt.subplot(1, 2, 2) 78 | plt.title("Clustering") 79 | for label in range(n_classes): 80 | plt.scatter(X[y_pred == label, 0], X[y_pred == label, 1], marker=".") 81 | 82 | plt.scatter(kmeans.centers[:, 0], kmeans.centers[:, 1], marker="*") 83 | 84 | plt.show() 85 | -------------------------------------------------------------------------------- /src/multi_logistic_regression.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import random 3 | from sklearn.datasets import load_iris 4 | 5 | 6 | def create_data(batchsize: int = 149, train_rate: int = 0.8): 7 | batchsize = min(batchsize, 149) 8 | train_batch = int(train_rate * batchsize) 9 | iris = load_iris() 10 | X = iris.data 11 | y = np.reshape(iris.target, (-1, 1)) 12 | shuffle_idxs = np.arange(batchsize) 13 | random.shuffle(shuffle_idxs) 14 | X = X[shuffle_idxs] 15 | y = y[shuffle_idxs] 16 | X_train = X[:train_batch] 17 | y_train = y[:train_batch] 18 | X_test = X[train_batch:] 19 | y_test = y[train_batch:] 20 | return X_train, y_train, X_test, y_test 21 | 22 | 23 | class MultiLogisticRegression: 24 | def __init__(self, input_dim: int, output_dim: int, lr: float) -> None: 25 | self.i_d = input_dim 26 | self.o_d = output_dim 27 | self.lr = lr 28 | self.weight = np.zeros((input_dim + 1, output_dim)) 29 | pass 30 | def fit(self, X_pad: np.ndarray, Y_unfold: np.ndarray): 31 | pred = self.softmax(X_pad @ self.weight) 32 | err = pred - Y_unfold 33 | grad = X_pad.T @ err 34 | self.weight -= self.lr * grad 35 | 36 | def train(self, X: np.ndarray, Y: np.ndarray, iter: int, batch_size: int): 37 | B = len(X) 38 | shuffle_idxs = np.arange(B) 39 | X_pad = self.pad(X) 40 | Y_unfold = np.eye(self.o_d)[np.round(np.reshape(Y, (-1,)).astype(np.int32))] 41 | for _ in range(iter): 42 | random.shuffle(shuffle_idxs) 43 | X_pad_shuffle = X_pad[shuffle_idxs] 44 | Y_unfold_shuffle = Y_unfold[shuffle_idxs] 45 | for i in range(B // batch_size): 46 | x_batch = X_pad_shuffle[batch_size * i : batch_size * (i + 1)] 47 | y_batch = Y_unfold_shuffle[batch_size * i : batch_size * (i + 1)] 48 | self.fit(x_batch, y_batch) 49 | if batch_size * (B // batch_size) < B: 50 | x_batch = X_pad_shuffle[batch_size * (i + 1) :] 51 | y_batch = Y_unfold_shuffle[batch_size * (i + 1) :] 52 | self.fit(x_batch, y_batch) 53 | 54 | def __call__(self, X: np.ndarray): 55 | pred = self.softmax(self.pad(X) @ self.weight) 56 | return np.reshape(np.argmax(pred, axis=1), (-1, 1)) 57 | 58 | @staticmethod 59 | def pad(X: np.ndarray): 60 | return np.concatenate((X, np.ones((X.shape[0], 1))), axis=1) 61 | 62 | @staticmethod 63 | def softmax(Y_unfold: np.ndarray): 64 | Y_exp = np.exp(Y_unfold) 65 | return Y_exp / np.reshape(np.sum(Y_exp, axis=1), (-1, 1)) # numpy 广播用法 66 | 67 | 68 | if __name__ == "__main__": 69 | X_train, y_train, X_test, y_test = create_data() 70 | model = MultiLogisticRegression(4, 3, 1e-2) 71 | model.train(X_train, y_train, iter=100, batch_size=32) 72 | pred = model(X_test) 73 | mistakes = np.sum(np.where(np.abs(pred - y_test) > 0.5, 1, 0)) 74 | print("Accuracy:{}%".format(100 * (1 - mistakes / len(pred)))) 75 | -------------------------------------------------------------------------------- /src/perceptron.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : perceptron.py 4 | # @Data : 2020/5/20 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | from matplotlib import pyplot as plt 10 | 11 | 12 | class Perceptron: 13 | """ 14 | Perceptron classifier(感知机分类器) 15 | """ 16 | 17 | def __init__(self, input_dim: int, lr=5e-4): 18 | """ 19 | Args: 20 | input_dim (int): 输入特征维度 21 | """ 22 | self.weights = np.random.randn(input_dim + 1) # 权重 23 | self.lr = lr # 学习率 24 | 25 | def fit(self, X: np.ndarray, y: np.ndarray): 26 | for x, y in zip(pad(X), y): 27 | if y * (x @ self.weights) <= 0: # 分类错误, y 与 wx + b 符号不同 28 | neg_grad = x * y # 计算weights的负梯度 29 | self.weights += self.lr * neg_grad # 沿负梯度方向更新weights 30 | 31 | def __call__(self, X: np.ndarray) -> np.ndarray: 32 | y_pred = pad(X) @ self.weights 33 | return np.where(y_pred > 0, 1, -1) 34 | 35 | 36 | def pad(x): 37 | return np.concatenate([x, np.ones([len(x), 1])], axis=1) 38 | 39 | 40 | def load_data(n_samples_per_class=500): 41 | X = np.concatenate([ 42 | np.random.randn(n_samples_per_class, 2) + np.array([1, -1]), 43 | np.random.randn(n_samples_per_class, 2) + np.array([-1, 1]), 44 | ]) 45 | y = np.array([-1] * n_samples_per_class + [1] * n_samples_per_class) 46 | 47 | training_set, test_set = np.split(np.random.permutation(len(X)), [int(len(X) * 0.6)]) 48 | return X, y, training_set, test_set 49 | 50 | 51 | def train_perceptron(model, X, y, epochs=100): 52 | indices = np.arange(len(X)) 53 | for _ in range(epochs): 54 | np.random.shuffle(indices) 55 | model.fit(X[indices], y[indices]) 56 | 57 | 58 | if __name__ == "__main__": 59 | X, y, training_set, test_set = load_data() 60 | 61 | plt.figure(figsize=[12, 6]) 62 | plt.subplot(1, 2, 1) 63 | plt.title("Ground Truth") 64 | plt.xlim(-4, 4) 65 | plt.ylim(-4, 4) 66 | plt.scatter(X[y == -1, 0], X[y == -1, 1], marker=".") 67 | plt.scatter(X[y == +1, 0], X[y == +1, 1], marker=".") 68 | 69 | perceptron = Perceptron(input_dim=2) 70 | train_perceptron(perceptron, X[training_set], y[training_set]) 71 | y_pred = perceptron(X) 72 | acc = np.sum(y_pred[test_set] == y[test_set]) / len(test_set) 73 | print(f"Accuracy = {100 * acc:.2f}%") 74 | 75 | plt.subplot(1, 2, 2) 76 | plt.title("Prediction") 77 | plt.xlim(-4, 4) 78 | plt.ylim(-4, 4) 79 | plt.scatter(X[y_pred == -1, 0], X[y_pred == -1, 1], marker=".") 80 | plt.scatter(X[y_pred == +1, 0], X[y_pred == +1, 1], marker=".") 81 | 82 | w = perceptron.weights 83 | a, b = -w[0] / w[1], -w[2] / w[1] 84 | line_x = np.linspace(-4, 4, 400) 85 | line_y = a * line_x + b 86 | plt.plot(line_x, line_y, lw=1) 87 | 88 | plt.fill_between(line_x, np.full(400, -4), line_y, alpha=0.1) 89 | plt.fill_between(line_x, np.full(400, +4), line_y, alpha=0.1) 90 | 91 | plt.show() 92 | -------------------------------------------------------------------------------- /src/logistic_regression.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : logistic_regression.py 4 | # @Data : 2020/5/21 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | from matplotlib import pyplot as plt 10 | 11 | 12 | class LogisticRegression: 13 | """ 14 | Logistic regression classifier(逻辑斯蒂回归分类器) 15 | """ 16 | 17 | def __init__(self, input_dim: int, lr=5e-4): 18 | """ 19 | Args: 20 | input_dim (int): 特征维度 21 | lr (float): 学习率, 默认为5e-4 22 | """ 23 | self.weights = np.random.randn(input_dim + 1) # 随机初始化参数 24 | self.lr = lr # 学习率 25 | 26 | def fit(self, X: np.ndarray, y: np.ndarray): 27 | X_pad = pad(X) # 为X填充1作为偏置 28 | pred = sigmoid(X_pad @ self.weights) # 计算预测值 29 | grad = X_pad.T @ (pred - y) / len(pred) # 计算梯度 30 | self.weights -= self.lr * grad # 沿负梯度更新参数 31 | 32 | def __call__(self, X: np.ndarray) -> np.ndarray: 33 | y_pred = sigmoid(pad(X) @ self.weights) # 计算预测值 34 | return np.where(y_pred > 0.5, 1, 0) # 将(0, 1)之间分布的概率转化为{0, 1}标签 35 | 36 | 37 | def pad(x): 38 | return np.concatenate([x, np.ones([len(x), 1])], axis=1) 39 | 40 | 41 | def sigmoid(x): 42 | return 1 / (1 + np.exp(-x)) 43 | 44 | 45 | def load_data(n_samples_per_class=500): 46 | X = np.concatenate([ 47 | np.random.randn(n_samples_per_class, 2) + np.array([1, -1]), 48 | np.random.randn(n_samples_per_class, 2) + np.array([-1, 1]), 49 | ]) 50 | y = np.array([0] * n_samples_per_class + [1] * n_samples_per_class) 51 | 52 | training_set, test_set = np.split(np.random.permutation(len(X)), [int(len(X) * 0.6)]) 53 | return X, y, training_set, test_set 54 | 55 | 56 | def train_logistic_regression(model, X, y, epochs=100, batch_size=32): 57 | indices = np.arange(len(X)) 58 | for _ in range(epochs): 59 | np.random.shuffle(indices) 60 | for i in range(batch_size, len(X) + 1, batch_size): 61 | model.fit(X[indices[i - batch_size:i]], y[indices[i - batch_size:i]]) 62 | 63 | 64 | if __name__ == "__main__": 65 | X, y, training_set, test_set = load_data() 66 | 67 | plt.figure(figsize=[12, 6]) 68 | plt.subplot(1, 2, 1) 69 | plt.title("Ground Truth") 70 | plt.xlim(-4, 4) 71 | plt.ylim(-4, 4) 72 | plt.scatter(X[y == 0, 0], X[y == 0, 1], marker=".") 73 | plt.scatter(X[y == 1, 0], X[y == 1, 1], marker=".") 74 | 75 | logistic_regression = LogisticRegression(2) 76 | train_logistic_regression(logistic_regression, X, y, epochs=500) 77 | y_pred = logistic_regression(X) 78 | acc = np.sum(y_pred[test_set] == y[test_set]) / len(test_set) 79 | print(f"Accuracy = {100 * acc:.2f}%") 80 | 81 | plt.subplot(1, 2, 2) 82 | plt.title("Prediction") 83 | plt.xlim(-4, 4) 84 | plt.ylim(-4, 4) 85 | plt.scatter(X[y_pred == 0, 0], X[y_pred == 0, 1], marker=".") 86 | plt.scatter(X[y_pred == 1, 0], X[y_pred == 1, 1], marker=".") 87 | 88 | w = logistic_regression.weights 89 | a, b = -w[0] / w[1], -w[2] / w[1] 90 | line_x = np.linspace(-4, 4, 400) 91 | line_y = a * line_x + b 92 | plt.plot(line_x, line_y, lw=1) 93 | 94 | plt.fill_between(line_x, np.full(400, -4), line_y, alpha=0.1) 95 | plt.fill_between(line_x, np.full(400, +4), line_y, alpha=0.1) 96 | 97 | plt.show() 98 | -------------------------------------------------------------------------------- /src/gmm.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : gmm.py 4 | # @Data : 2020/5/31 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import random 9 | 10 | import numpy as np 11 | from matplotlib import pyplot as plt 12 | from scipy.stats import multivariate_normal 13 | 14 | 15 | class GMM: 16 | """ 17 | Gaussian mixture model(高斯混合模型) 18 | """ 19 | 20 | def __init__(self, n_components: int, iterations=100, cov_reg=1e-06): 21 | """ 22 | Args: 23 | n_components (int): 聚类类别数 24 | """ 25 | self.n_components, self.iterations, self.cov_reg = n_components, iterations, cov_reg 26 | self.weights = np.full(self.n_components, 1 / self.n_components) 27 | self.means, self.covs = None, None 28 | 29 | def fit(self, X: np.ndarray): 30 | """ 31 | Args: 32 | X (np.ndarray): 输入 33 | iterations (int, optional): 迭代次数. Defaults to 100. 34 | cov_reg (float, optional): 防止协方差矩阵奇异的微小变量. Defaults to 1e-06. 35 | """ 36 | # 随机选择n_components个点作为高斯分布中心 37 | self.means = np.array(X[random.sample(range(X.shape[0]), self.n_components)]) 38 | 39 | # 初始高斯分布协方差均为单位矩阵 40 | self.covs = np.stack([np.eye(X.shape[1]) for _ in range(self.n_components)]) 41 | for _ in range(self.iterations): 42 | G = self.expect(X) # E步 43 | self.maximize(X, G) # M步 44 | 45 | def __call__(self, X: np.ndarray): 46 | G = self.expect(X) 47 | return np.argmax(G, axis=1) 48 | 49 | def expect(self, X: np.ndarray): # E步 50 | C = np.zeros([X.shape[0], self.n_components]) 51 | for k, mean, cov in zip(range(self.n_components), self.means, self.covs): 52 | dist = multivariate_normal(mean=mean, cov=cov) 53 | C[:, k] = self.weights[k] * dist.pdf(X) 54 | S = np.sum(C, axis=1, keepdims=True) 55 | S[S == 0] = self.n_components 56 | return C / S 57 | 58 | def maximize(self, X: np.ndarray, G: np.ndarray): # M步 59 | N = np.sum(G, axis=0) 60 | for k in range(self.n_components): 61 | G_k = G[:, k].reshape(-1, 1) 62 | self.means[k] = np.sum(G_k * X, axis=0) / N[k] 63 | X_norm = X - self.means[k] 64 | self.covs[k] = (G_k * X_norm).T @ X_norm / N[k] 65 | self.weights = N / X.shape[0] 66 | self.covs += self.cov_reg * np.eye(X.shape[1]) # 添加微小量防止奇异 67 | 68 | 69 | def load_data(n_samples_per_class=500): 70 | X = np.concatenate([ 71 | np.random.multivariate_normal(mean=[4, 0], cov=[[2, 0], [0, 2]], size=[n_samples_per_class]), 72 | np.random.multivariate_normal(mean=[0, 4], cov=[[2, 0], [0, 2]], size=[n_samples_per_class]), 73 | ]) 74 | y = np.array([0] * n_samples_per_class + [1] * n_samples_per_class) 75 | return X, y 76 | 77 | 78 | if __name__ == "__main__": 79 | X, y = load_data() 80 | plt.figure(figsize=[15, 7]) 81 | plt.subplot(1, 2, 1) 82 | plt.title("Ground Truth") 83 | plt.scatter(X[y == 0, 0], X[y == 0, 1], marker=".") 84 | plt.scatter(X[y == 1, 0], X[y == 1, 1], marker=".") 85 | 86 | gmm = GMM(2) 87 | gmm.fit(X) 88 | y_pred = gmm(X) 89 | 90 | plt.subplot(1, 2, 2) 91 | plt.title("Prediction") 92 | plt.scatter(X[y_pred == 0, 0], X[y_pred == 0, 1], marker=".") 93 | plt.scatter(X[y_pred == 1, 0], X[y_pred == 1, 1], marker=".") 94 | 95 | plt.show() 96 | -------------------------------------------------------------------------------- /src/lda.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : lda.py 4 | # @Data : 2020/5/31 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | from matplotlib import pyplot as plt 10 | from numpy import linalg as LA 11 | 12 | 13 | class LDA: 14 | """ 15 | Linear Discriminant Analysis(线性判别分析) 16 | """ 17 | 18 | def __init__(self, k: int): 19 | """ 20 | Args: 21 | k (int): 降维维度 22 | """ 23 | self.k, self.W = k, None 24 | 25 | def fit(self, X: np.ndarray, Y: np.ndarray): 26 | assert self.k <= X.shape[1] - 1 # S_W^{-2} S_B 最多只有N - 1个非0特征值 27 | S_W = np.zeros([X.shape[1], X.shape[1]]) # 类内(within-class)散度矩阵 28 | S_B = np.zeros_like(S_W) # 类间(between-class)散度矩阵 29 | M = np.mean(X, axis=0) # 全部样本均值 30 | for Xi in (X[Y == i] for i in np.unique(Y)): 31 | Mi = np.mean(Xi, axis=0) 32 | S_W += (Xi - Mi).T @ (Xi - Mi) 33 | S_B += len(Xi) * (Mi - M).reshape(-1, 1) @ (Mi - M).reshape(1, -1) 34 | L, V = LA.eig(LA.inv(S_W) @ S_B) # 计算 S_W^{-1} S_B 的特征值与特征向量 35 | topk = np.argsort(L)[::-1][:self.k] # 按照特征值降序排列，取前K大特征值 36 | self.W = V[:, topk] # 选择topk对应的特征向量 37 | 38 | def __call__(self, X: np.ndarray): 39 | return X @ self.W 40 | 41 | 42 | class PCA: 43 | """ 44 | Principal Components Analysis(主成因分析) 45 | """ 46 | 47 | def __init__(self, k: int): 48 | """ 49 | Args: 50 | k (int): 主成因个数 51 | """ 52 | self.k = k 53 | 54 | def __call__(self, X: np.ndarray): 55 | X_norm = X - X.mean(axis=0) # 去中心化 56 | L, V = np.linalg.eig(X_norm.T @ X_norm) # 对协方差矩阵进行特征值分解 57 | topk = np.argsort(L)[::-1][:self.k] # 找出前K大特征值对应的索引 58 | return X_norm @ V[:, topk] # 将去中心化的X乘以前K大特征值对应的特征向量 59 | 60 | 61 | def load_data(n_samlpes_per_class=500): 62 | theta = np.pi / 4 63 | scale = np.array([[2, 0], [0, 0.5]]) # 缩放 64 | rotate = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]]) # 旋转 65 | X = np.concatenate([ 66 | np.random.randn(n_samlpes_per_class, 2) + np.array([0, -2]), 67 | np.random.randn(n_samlpes_per_class, 2) + np.array([0, +2]), 68 | ]) 69 | X = X @ scale @ rotate # 对数据进行缩放和旋转 70 | y = np.array([0] * n_samlpes_per_class + [1] * n_samlpes_per_class) 71 | return X, y 72 | 73 | 74 | if __name__ == "__main__": 75 | X, y = load_data() 76 | 77 | plt.figure(figsize=[18, 6]) 78 | plt.subplot(1, 3, 1) 79 | plt.title("Ground Truth") 80 | plt.xlim(-5, 5) 81 | plt.ylim(-5, 5) 82 | plt.scatter(X[y == 0, 0], X[y == 0, 1], marker=".") 83 | plt.scatter(X[y == 1, 0], X[y == 1, 1], marker=".") 84 | 85 | lda = LDA(1) 86 | lda.fit(X, y) 87 | Z = lda(X) 88 | 89 | plt.subplot(1, 3, 2) 90 | plt.title("LDA") 91 | plt.xlim(-5, 5) 92 | plt.ylim(-5, 5) 93 | plt.scatter(Z[y == 0, 0], np.zeros([500]), marker=".") 94 | plt.scatter(Z[y == 1, 0], np.zeros([500]), marker=".") 95 | 96 | # 和PCA对比 97 | pca = PCA(1) 98 | Z = pca(X) 99 | plt.subplot(1, 3, 3) 100 | plt.title("PCA") 101 | plt.xlim(-5, 5) 102 | plt.ylim(-5, 5) 103 | plt.scatter(Z[y == 0, 0], np.zeros([500]), marker=".") 104 | plt.scatter(Z[y == 1, 0], np.zeros([500]), marker=".") 105 | 106 | plt.show() 107 | -------------------------------------------------------------------------------- /src/decision_tree.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : decision_tree.py 4 | # @Data : 2020/5/23 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | 10 | 11 | class DecisionTree: 12 | """ 13 | Decision tree classifier(决策树分类器, ID3生成算法) 14 | """ 15 | 16 | def __init__(self): 17 | self.rate, self.root = None, None 18 | 19 | def fit(self, X: np.ndarray, y: np.ndarray, rate: float = 0.95): 20 | self.rate = rate 21 | self.root = self.build_tree(X, y, np.arange(X.shape[0]), np.arange(X.shape[1])) 22 | 23 | def __call__(self, X: np.ndarray): 24 | return np.array([self.predict(self.root, x) for x in X]) 25 | 26 | def predict(self, node, x: np.ndarray): 27 | if isinstance(node, dict): # 如果节点是树(字典)类型 28 | col, trees = node["col"], node["trees"] 29 | # 根据值进行下一次递归 30 | return self.predict(trees[x[col]], x) 31 | return node # 如果节点是叶子类型则直接返回该值 32 | 33 | def build_tree(self, X: np.ndarray, y: np.ndarray, rows: np.ndarray, cols: np.ndarray): 34 | cats = np.bincount(y[rows]) 35 | 36 | # 无特征可分或者满足一定的单一性 37 | if len(cols) == 0 or np.max(cats) / len(rows) > self.rate: 38 | return np.argmax(cats) # 返回最单一的类别 39 | 40 | # 最大信息增益特征 41 | k = np.argmax([self.calc_info_gain(X, y, rows, f) for f in cols]) 42 | col = cols[k] 43 | cols = np.delete(cols, k) # 除去选择的特征 44 | 45 | # 为选择的特征创建子树 46 | trees = { 47 | value: self.build_tree(X, y, rows[X[rows, col] == value], cols) 48 | for value in np.unique(X[rows, col]).tolist() # 为该特征的每一个取值都建立子树 49 | } 50 | return {"col": col, "trees": trees} 51 | 52 | @staticmethod 53 | def calc_exp_ent(y: np.ndarray, rows: np.ndarray): # 计算经验熵 54 | prob = np.bincount(y[rows]) / len(rows) 55 | prob = prob[prob.nonzero()] # 除去0概率 56 | return np.sum(-prob * np.log(prob)) # 经验熵 57 | 58 | @classmethod 59 | def calc_cnd_ent(cls, X: np.ndarray, y: np.ndarray, rows: np.ndarray, col: int): # 计算条件熵 60 | ent = 0 # 经验条件熵 61 | for value in np.unique(X[rows, col]): 62 | indices_ = rows[X[rows, col] == value] 63 | ent += len(indices_) / len(rows) * cls.calc_exp_ent(y, indices_) 64 | return ent # 条件熵 65 | 66 | @classmethod 67 | def calc_info_gain(cls, X: np.ndarray, y: np.ndarray, rows: np.ndarray, col: int): # 计算信息增益 68 | exp_ent = cls.calc_exp_ent(y, rows) # 经验熵 69 | cnd_ent = cls.calc_cnd_ent(X, y, rows, col) # 经验条件熵 70 | return exp_ent - cnd_ent # 信息增益 71 | 72 | 73 | def load_data(): 74 | X = np.array([ 75 | [0, 0, 0], 76 | [0, 0, 0], 77 | [0, 0, 1], 78 | [0, 0, 1], 79 | [0, 1, 0], 80 | [0, 1, 0], 81 | [0, 1, 1], 82 | [0, 1, 1], 83 | [1, 0, 0], 84 | [1, 0, 0], 85 | [1, 0, 1], 86 | [1, 0, 1], 87 | [1, 1, 0], 88 | [1, 1, 0], 89 | [1, 1, 1], 90 | [1, 1, 1], 91 | ]) 92 | y = np.where(X.sum(axis=1) >= 2, 1, 0) 93 | return X, y 94 | 95 | 96 | if __name__ == "__main__": 97 | X, y = load_data() 98 | decision_tree = DecisionTree() 99 | decision_tree.fit(X, y, rate=0.95) 100 | y_pred = decision_tree(X) 101 | 102 | print(decision_tree.root) 103 | print(y) 104 | print(y_pred) 105 | 106 | acc = np.sum(y_pred == y) / len(y_pred) 107 | print(f"Accuracy = {100 * acc:.2f}%") 108 | -------------------------------------------------------------------------------- /src/naive_bayes.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : naive_bayes.py 4 | # @Data : 2020/5/22 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | 10 | 11 | class NaiveBayesClassifier: 12 | """ 13 | Naive Bayes classifier(朴素贝叶斯分类器) 14 | """ 15 | 16 | def __init__(self): 17 | self.P_prior, self.P_cond = None, None 18 | 19 | def fit(self, X: np.ndarray, y: np.ndarray): 20 | # 计算X的各个特征与标签Y有多少类别 21 | x_categories, y_categories = np.max(X, axis=0) + 1, np.max(y) + 1 22 | self.x_categories, self.y_categories = x_categories, y_categories 23 | # 先验概率, prior_prob[i] = P(Y = i)，标签类别的取值概率 24 | self.P_prior = self.estimate_prob(y, y_categories) 25 | # 条件概率, cond_prob[i][j,k] = P(X_i = a_{ij} | Y = k)，标签类别为k的条件下i特征取a_{ij}的概率 26 | self.P_cond = [np.zeros([n, y_categories]) for n in x_categories] 27 | self.X_prior = [np.zeros((n,)) for n in x_categories] 28 | for i, n in enumerate(x_categories): 29 | for k in range(y_categories): 30 | self.P_cond[i][:, k] = self.estimate_prob(X[y == k, i], n) 31 | self.X_prior[i] = np.sum(self.P_prior * self.P_cond[i], axis=1) 32 | 33 | def __call__(self, X: np.ndarray) -> np.ndarray: 34 | y_pred = np.zeros([len(X)], dtype=int) 35 | for i, x in enumerate(X): 36 | # 先验概率的对数,加上条件概率的对数 37 | P = np.log(self.P_prior) + np.sum( 38 | np.array( 39 | [np.log(p_cond[x[ii]]) for ii, p_cond in enumerate(self.P_cond)] 40 | ), 41 | axis=0, 42 | ) 43 | y_pred[i] = np.argmax(P) 44 | return y_pred 45 | 46 | def predict_prob(self, X: np.ndarray): 47 | P = np.zeros([len(X), len(self.P_cond)]) 48 | for i, x in enumerate(X): 49 | P_log = np.log(self.P_prior) + np.sum( 50 | np.array( 51 | [np.log(p_cond[x[ii]]) for ii, p_cond in enumerate(self.P_cond)] 52 | ), 53 | axis=0, 54 | ) 55 | x_log = np.sum( 56 | np.log( 57 | np.array( 58 | [prior_x[x[ii]] for ii, prior_x in enumerate(self.X_prior)] 59 | ) 60 | ) 61 | ) 62 | P[i] = np.exp(P_log - x_log) 63 | return P 64 | 65 | @staticmethod 66 | def estimate_prob(x: np.ndarray, n: int): 67 | return (np.bincount(x, minlength=n) + 1) / (len(x) + n) # 使用贝叶斯估计 68 | 69 | 70 | def load_data(): 71 | # 参照李航《统计学习方法（第一版）》第四章例4.1 72 | X = np.array( 73 | [ 74 | [0, 0], 75 | [0, 1], 76 | [0, 1], 77 | [0, 0], 78 | [0, 0], 79 | [1, 0], 80 | [1, 1], 81 | [1, 1], 82 | [1, 2], 83 | [1, 2], 84 | [2, 2], 85 | [2, 1], 86 | [2, 1], 87 | [2, 2], 88 | [2, 2], 89 | ], 90 | dtype=int, 91 | ) 92 | y = np.array([0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0], dtype=int) 93 | return X, y 94 | 95 | 96 | if __name__ == "__main__": 97 | X, y = load_data() 98 | naive_bayes = NaiveBayesClassifier() 99 | naive_bayes.fit(X, y) 100 | pred = naive_bayes(X) 101 | 102 | print(naive_bayes.P_prior) # 先验概率 103 | print(naive_bayes.P_cond[0]) # 条件概率 104 | print(naive_bayes.P_cond[1]) # 条件概率 105 | acc = np.sum(pred == y) / len(pred) 106 | print(f"Accuracy = {100 * acc:.2f}%") 107 | print(naive_bayes.predict_prob([[1, 0]])) # 输出 [[1, 0]]的概率 108 | -------------------------------------------------------------------------------- /src/hmm.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import random 3 | 4 | 5 | class HMM: 6 | """ 7 | hmm 主要可以由以下三个问题组成: 8 | 1. 给定模型参数和观测序列, 计算该观测序列出现的概率. (前向算法) 9 | 2. 给定模型参数和观测序列, 计算最有可能出现的状态序列. (Viterbi 算法) 10 | 3. 根据观测序列推测最有可能出现的模型参数. (EM 算法) 11 | """ 12 | 13 | def __init__(self, s_num: int, y_num: int) -> None: 14 | self.P = np.ones((s_num, s_num)) / s_num 15 | self.Q = np.ones((s_num, y_num)) / y_num 16 | self.pi = np.ones((s_num,)) / s_num 17 | 18 | def forward(self, y: np.ndarray): 19 | return forward(y, self.P, self.Q, self.pi) 20 | 21 | def backward(self, y: np.ndarray): 22 | return backward(y, self.P, self.Q) 23 | 24 | def viterbi(self, y: np.ndarray): 25 | return viterbi(y, self.P, self.Q, self.pi) 26 | 27 | def fit(self, y: np.ndarray, iter: int = 100): 28 | for _ in range(iter): 29 | self.em_step(y) 30 | 31 | def em_step(self, y: np.ndarray): 32 | alpha = self.forward(y) 33 | beta = self.backward(y) 34 | 35 | gamma = alpha / np.sum(alpha[-1]) * beta 36 | 37 | ksi = np.zeros((len(y) - 1, len(self.P), len(self.P))) 38 | 39 | for t in range(len(y) - 1): 40 | ksi[t] = ( 41 | np.reshape(alpha[t], (-1, 1)) 42 | * self.P 43 | * self.Q[:, int(y[t + 1])] 44 | * beta[t + 1] 45 | ) / np.sum(alpha[-1]) 46 | 47 | self.pi = gamma[0] 48 | self.P = np.sum(ksi, axis=0) / np.reshape( 49 | np.sum(gamma, axis=0) - gamma[-1], (-1, 1) 50 | ) 51 | 52 | self.Q = np.zeros_like(self.Q) 53 | for j in range(self.Q.shape[1]): 54 | self.Q[:, j] = np.sum(np.reshape(y == j, (-1, 1)) * gamma, axis=0) 55 | self.Q /= np.reshape(np.sum(gamma, axis=0), (-1, 1)) 56 | 57 | 58 | def forward(y: np.ndarray, P: np.ndarray, Q: np.ndarray, pi: np.ndarray): 59 | n = len(y) 60 | alpha = np.zeros((n, P.shape[1])) 61 | alpha[0] = pi * Q[:, int(y[0])] 62 | for i in range(1, n): 63 | alpha[i] = ( 64 | np.sum(np.reshape(alpha[i - 1], (-1, 1)) * P, axis=0) * Q[:, int(y[i])] 65 | ) 66 | return alpha 67 | 68 | 69 | def backward(y: np.ndarray, P: np.ndarray, Q: np.ndarray): 70 | n = len(y) 71 | beta = np.ones((n, P.shape[1])) 72 | for i in range(-2, -n - 1, -1): 73 | beta[i] = np.sum(beta[i + 1] * P * Q[:, int(y[i + 1])], axis=1) 74 | return beta 75 | 76 | 77 | def viterbi(y: np.ndarray, P: np.ndarray, Q: np.ndarray, pi: np.ndarray): 78 | n = len(y) 79 | A = np.zeros((n, len(pi))) 80 | gamma = pi * Q[:, int(y[0])] 81 | for i in range(1, n): 82 | A[i] = np.argmax(np.reshape(gamma, (-1, 1)) * P, axis=0) 83 | gamma = np.max(np.reshape(gamma, (-1, 1)) * P, axis=0) * Q[:, int(y[i])] 84 | ans = np.zeros((n,)) 85 | ans[-1] = np.argmax(gamma) 86 | for i in range(-2, -n - 1, -1): 87 | ans[i] = A[i + 1][int(ans[i + 1])] 88 | return ans 89 | 90 | 91 | def generate_data(P: np.ndarray, Q: np.ndarray, pi: np.ndarray, T: int): 92 | s = np.zeros((T,)) 93 | y = np.zeros((T,)) 94 | s[0] = random_choose(pi) 95 | y[0] = random_choose(Q[int(s[0])]) 96 | for i in range(1, T): 97 | s[i] = random_choose(P[int(s[i - 1])]) 98 | y[i] = random_choose(Q[int(s[i])]) 99 | return s, y 100 | 101 | 102 | def random_choose(probs: np.ndarray): 103 | x = random.random() 104 | prob = probs.copy() 105 | if x < prob[0]: 106 | return 0 107 | for i in range(1, len(prob)): 108 | prob[i] += prob[i - 1] 109 | if x < prob[i]: 110 | return i 111 | return len(prob) - 1 112 | 113 | 114 | if __name__ == "__main__": 115 | P = np.array([[0.3, 0.7], [0.6, 0.4]]) 116 | Q = np.array([[0.9, 0.1], [0.1, 0.9]]) 117 | pi = np.array([0.5, 0.5]) 118 | hmm = HMM(2, 2) 119 | hmm.P = P 120 | s, y = generate_data(P, Q, pi, 5) 121 | hmm.fit(y, 20) 122 | print(hmm.Q) 123 | -------------------------------------------------------------------------------- /src/adaboost.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : adaboost.py 4 | # @Data : 2020/5/27 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | from matplotlib import pyplot as plt 10 | 11 | 12 | class AdaBoost: 13 | 14 | def __init__(self, n_estimators: int, lr: float = 1e-2, eps: float = 1e-5): 15 | """ 16 | Args: 17 | n_estimators (int): 弱分类器个数. 18 | lr (float, optional): 学习率, 默认为1e-2. 19 | eps (float, optional): 误差下限, 默认为1e-5. 20 | """ 21 | self.estimators = [] # 弱分类器及其权重 22 | self.n_estimators, self.lr, self.eps = n_estimators, lr, eps 23 | 24 | def fit(self, X: np.ndarray, y: np.ndarray): 25 | """ 26 | Args: 27 | X (np.ndarray): 样本特征. 28 | Y (np.ndarray): 样本标签. 29 | """ 30 | weights = np.full(len(X), 1 / len(X)) # 样本权重 31 | for _ in range(self.n_estimators): 32 | estimator = WeakEstimator(lr=self.lr) 33 | 34 | # 带权重训练弱分类器 35 | error = estimator.fit(X, y, weights=weights) 36 | 37 | # 误差达到下限，则提前停止迭代 38 | if error < self.eps: 39 | break 40 | 41 | # 更新弱分类器权重 42 | alpha = np.log((1 - error) / error) / 2 43 | 44 | # 更新样本权重 45 | weights *= np.exp(-alpha * y * estimator(X)) 46 | weights /= np.sum(weights) # 除以规范化因子 47 | 48 | # 添加此弱分类器及其权重 49 | self.estimators += [(alpha, estimator)] 50 | 51 | def __call__(self, X: np.ndarray) -> np.ndarray: 52 | y_pred = sum((alpha * estimator(X) for alpha, estimator in self.estimators)) 53 | return np.where(y_pred > 0, 1, -1) 54 | 55 | 56 | class WeakEstimator: # 弱分类器, 一阶决策树 57 | 58 | def __init__(self, lr: float = 1e-3): 59 | # 学习率、符号{-1，1}、划分特征、划分阈值 60 | self.lr, self.sign, self.feature, self.threshold, = lr, 1, None, None 61 | 62 | def fit(self, X: np.ndarray, y: np.ndarray, weights: np.ndarray): 63 | min_error = np.inf # 最小带权误差 64 | for feature, x in enumerate(X.T): 65 | for threshold in np.arange(np.min(x) - self.lr, np.max(x) + self.lr, self.lr): 66 | # 取分类错误的样本权重求和 67 | pos_error = np.sum(weights[np.where(x > threshold, 1, -1) != y]) 68 | if pos_error < min_error: 69 | min_error, self.feature, self.threshold, self.sign = pos_error, feature, threshold, 1 70 | 71 | neg_error = 1 - pos_error 72 | if neg_error < min_error: 73 | min_error, self.feature, self.threshold, self.sign = neg_error, feature, threshold, -1 74 | return min_error 75 | 76 | def __call__(self, X: np.ndarray) -> np.ndarray: 77 | return np.where(X[:, self.feature] > self.threshold, self.sign, -self.sign) 78 | 79 | 80 | def load_data(n_samples_per_class=500): 81 | X = np.concatenate([ 82 | np.random.randn(n_samples_per_class, 2) + np.array([1, -1]), 83 | np.random.randn(n_samples_per_class, 2) + np.array([-1, 1]), 84 | ]) 85 | y = np.array([1] * n_samples_per_class + [-1] * n_samples_per_class) 86 | 87 | training_set, test_set = np.split(np.random.permutation(len(X)), [int(len(X) * 0.8)]) 88 | return X, y, training_set, test_set 89 | 90 | 91 | if __name__ == "__main__": 92 | X, y, training_set, test_set = load_data() 93 | 94 | plt.figure("AdaBoost", figsize=[12, 6]) 95 | plt.subplot(1, 2, 1) 96 | plt.title("Ground Truth") 97 | plt.xlim(-4, 4) 98 | plt.ylim(-4, 4) 99 | plt.scatter(X[y == -1, 0], X[y == -1, 1], marker=".") 100 | plt.scatter(X[y == +1, 0], X[y == +1, 1], marker=".") 101 | 102 | adaboost = AdaBoost(n_estimators=20) 103 | adaboost.fit(X[training_set], y[training_set]) 104 | y_pred = adaboost(X) 105 | acc = np.sum(y_pred[test_set] == y[test_set]) / len(test_set) 106 | print(f"Accuracy = {100 * acc:.2f}%") 107 | 108 | plt.subplot(1, 2, 2) 109 | plt.title("Prediction") 110 | plt.xlim(-4, 4) 111 | plt.ylim(-4, 4) 112 | plt.scatter(X[y_pred == -1, 0], X[y_pred == -1, 1], marker=".") 113 | plt.scatter(X[y_pred == +1, 0], X[y_pred == +1, 1], marker=".") 114 | 115 | plt.show() 116 | -------------------------------------------------------------------------------- /src/svm.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | # @File : svm.py 4 | # @Data : 2020/5/23 5 | # @Author : Luo Kun 6 | # @Contact: luokun485@gmail.com 7 | 8 | import numpy as np 9 | from matplotlib import pyplot as plt 10 | 11 | 12 | class LinearKernel: # 线性核函数 13 | 14 | def __call__(self, a: np.ndarray, b: np.ndarray): 15 | return np.sum(a * b, axis=-1) 16 | 17 | 18 | class PolyKernel: # 多项式核函数 19 | 20 | def __call__(self, a: np.ndarray, b: np.ndarray): 21 | return (np.sum(a * b, axis=-1) + 1)**2 22 | 23 | 24 | class RBFKernel: # 高斯核函数 25 | 26 | def __init__(self, sigma): 27 | self.divisor = 2 * sigma**2 28 | 29 | def __call__(self, a: np.ndarray, b: np.ndarray): 30 | return np.exp(-np.sum((a - b)**2, axis=-1) / self.divisor) 31 | 32 | 33 | class SVM: 34 | """ 35 | Support Vector Machines(支持向量机) 36 | """ 37 | 38 | def __init__(self, kernel="linear", C=1.0, iterations=100, tol=1e-3, sigma=1.0): 39 | """ 40 | Args: 41 | kernel (str, optional): 核函数. Defaults to 'linear'. 42 | C (float, optional): 惩罚因子. Defaults to 1.0. 43 | iterations (int, optional): 最大迭代次数. Defaults to 100. 44 | tol (float, optional): 绝对误差限. Defaults to 1e-3. 45 | sigma (float, optional): 高斯核函数的sigma. Defaults to 1.0. 46 | """ 47 | assert kernel in ["linear", "poly", "rbf"] 48 | 49 | if kernel == "linear": 50 | self.K = LinearKernel() # 线性核函数 51 | elif kernel == "poly": 52 | self.K = PolyKernel() # 多项式核函数 53 | elif kernel == "rbf": 54 | self.K = RBFKernel(sigma) # 径向基核函数 55 | 56 | self.C, self.iterations, self.tol, self.alpha, self.b = C, iterations, tol, None, 0.0 57 | 58 | self.X, self.y = None, None 59 | 60 | def fit(self, X: np.ndarray, y: np.ndarray): 61 | self.X, self.y = X, y 62 | 63 | # 拉格朗日乘子 64 | self.alpha = np.ones([len(X)]) 65 | for _ in range(self.iterations): 66 | # 此次迭代缓存的误差 67 | E = np.array([self.__E(i) for i in range(len(X))]) 68 | 69 | # 外层循环，寻找第一个alpha 70 | for i1 in range(len(X)): 71 | 72 | # 计算误差(不使用E缓存) 73 | E1 = self.__E(i1) 74 | if E1 == 0 or self.__satisfy_kkt(i1): 75 | # 误差为0或满足KKT条件 76 | continue 77 | 78 | # 大于0则选择最小,小于0选择最大的 79 | i2 = np.argmin(E) if E1 > 0 else np.argmax(E) # 内层循环，寻找第二个alpha 80 | if i1 == i2: 81 | continue 82 | E2 = self.__E(i2) 83 | x1, x2, y1, y2 = X[i1], X[i2], y[i1], y[i2] 84 | alpha1, alpha2 = self.alpha[i1], self.alpha[i2] 85 | k11, k22, k12 = self.K(x1, x1), self.K(x2, x2), self.K(x1, x2) 86 | 87 | # 计算剪切范围 88 | if y1 * y2 < 0: 89 | L = max(0, alpha2 - alpha1) 90 | H = min(self.C, self.C + alpha2 - alpha1) 91 | else: 92 | L = max(0, alpha1 + alpha2 - self.C) 93 | H = min(self.C, alpha1 + alpha2) 94 | if L == H: 95 | continue 96 | eta = k11 + k22 - 2 * k12 97 | if eta <= 0: 98 | continue 99 | 100 | # 计算新alpha 101 | alpha2_new = np.clip(alpha2 + y2 * (E1 - E2) / eta, L, H) 102 | alpha1_new = alpha1 + y1 * y2 * (alpha2 - alpha2_new) 103 | 104 | # 计算新b 105 | alpha2_delta, alpha1_delta = alpha2_new - alpha2, alpha1_new - alpha1 106 | b1_new = -E1 - y1 * k11 * alpha1_delta - y2 * k12 * alpha2_delta + self.b 107 | b2_new = -E2 - y1 * k12 * alpha1_delta - y2 * k22 * alpha2_delta + self.b 108 | 109 | # 更新参数 110 | self.alpha[i1] = alpha1_new 111 | self.alpha[i2] = alpha2_new 112 | if 0 < alpha1_new < self.C: 113 | self.b = b1_new 114 | elif 0 < alpha2_new < self.C: 115 | self.b = b2_new 116 | else: 117 | self.b = (b1_new + b2_new) / 2 118 | 119 | # 更新误差缓存 120 | E[i1] = self.__E(i1) 121 | E[i2] = self.__E(i2) 122 | 123 | def __call__(self, X: np.ndarray): 124 | y_pred = np.array([self.__g(x) for x in X]) 125 | return np.where(y_pred > 0, 1, -1) # 将(-\infinity, \infinity)之间的分布转为{-1, +1}标签 126 | 127 | @property 128 | def support_vectors(self): # 支持向量 129 | return self.X[self.alpha > 0] 130 | 131 | def __g(self, x): # g(x) =\sum_{i=0}^N alpha_i y_i \kappa(x_i, x) 132 | return np.sum(self.alpha * self.y * self.K(self.X, x)) + self.b 133 | 134 | def __E(self, i): # E_i = g(x_i) - y_i 135 | return self.__g(self.X[i]) - self.y[i] 136 | 137 | def __satisfy_kkt(self, i): # 是否满足KKT条件 138 | g_i, y_i = self.__g(self.X[i]), self.y[i] 139 | if np.abs(self.alpha[i]) < self.tol: 140 | return g_i * y_i >= 1 141 | if np.abs(self.alpha[i]) > self.C - self.tol: 142 | return g_i * y_i <= 1 143 | return np.abs(g_i * y_i - 1) < self.tol 144 | 145 | 146 | def load_data(n_samples_per_class=500): 147 | assert n_samples_per_class % 10 == 0, "n_samples_per_class must be divisible by 10" 148 | 149 | # 随机生成数据 150 | X_neg = np.random.randn(n_samples_per_class // 10, 10, 2) 151 | X_pos = np.random.randn(n_samples_per_class, 2) 152 | 153 | # 将负样本放置到圆环区域 154 | for i, theta in enumerate(np.linspace(0, 2 * np.pi, len(X_neg))): 155 | X_neg[i] += 5 * np.array([np.cos(theta), np.sin(theta)]) 156 | 157 | X = np.concatenate([X_neg.reshape(-1, 2), X_pos]) 158 | y = np.array([-1] * n_samples_per_class + [1] * n_samples_per_class) 159 | 160 | # 打乱索引，拆分训练集和测试集 161 | training_set, test_set = np.split(np.random.permutation(len(X)), [int(len(X) * 0.6)]) 162 | return X, y, training_set, test_set 163 | 164 | 165 | if __name__ == "__main__": 166 | X, y, training_set, test_set = load_data() 167 | 168 | plt.figure(figsize=[15, 5]) 169 | plt.subplot(1, 3, 1) 170 | plt.title("Ground Truth") 171 | plt.xlim(-8, 8) 172 | plt.ylim(-8, 8) 173 | plt.scatter(X[y == -1, 0], X[y == -1, 1], marker=".") 174 | plt.scatter(X[y == +1, 0], X[y == +1, 1], marker=".") 175 | 176 | svm = SVM(kernel="rbf", C=100, sigma=5) 177 | svm.fit(X[training_set], y[training_set]) 178 | y_pred = svm(X) 179 | acc = np.sum(y_pred[test_set] == y[test_set]) / len(test_set) 180 | print(f"Accuracy = {100 * acc:.2f}%") 181 | 182 | plt.subplot(1, 3, 2) 183 | plt.title("Prediction") 184 | plt.xlim(-8, 8) 185 | plt.ylim(-8, 8) 186 | plt.scatter(X[y_pred == -1, 0], X[y_pred == -1, 1], marker=".") 187 | plt.scatter(X[y_pred == +1, 0], X[y_pred == +1, 1], marker=".") 188 | 189 | vectors = svm.support_vectors 190 | plt.subplot(1, 3, 3) 191 | plt.title("Support vectors") 192 | plt.xlim(-8, 8) 193 | plt.ylim(-8, 8) 194 | plt.scatter(X[y_pred == -1, 0], X[y_pred == -1, 1], marker=".") 195 | plt.scatter(X[y_pred == +1, 0], X[y_pred == +1, 1], marker=".") 196 | plt.scatter(vectors[:, 0], vectors[:, 1], marker=".") 197 | 198 | plt.show() 199 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------