Python实现12种降维算法的示例代码_python_

from __future__ import print_function from sklearn import datasets import matplotlib.pyplot as plt import matplotlib.cm as cmx import matplotlib.colors as colors import numpy as np %matplotlib inline def shuffle_data(X, y, seed=None): if seed: np.random.seed(seed) idx = np.arange(X.shape[0]) np.random.shuffle(idx) return X[idx], y[idx] # 正规化数据集 X def normalize(X, axis=-1, p=2): lp_norm = np.atleast_1d(np.linalg.norm(X, p, axis)) lp_norm[lp_norm == 0] = 1 return X / np.expand_dims(lp_norm, axis) # 标准化数据集 X def standardize(X): X_std = np.zeros(X.shape) mean = X.mean(axis=0) std = X.std(axis=0) # 做除法运算时请永远记住分母不能等于 0 的情形 # X_std = (X - X.mean(axis=0)) / X.std(axis=0) for col in range(np.shape(X)[1]): if std[col]: X_std[:, col] = (X_std[:, col] - mean[col]) / std[col] return X_std # 划分数据集为训练集和测试集 def train_test_split(X, y, test_size=0.2, shuffle=True, seed=None): if shuffle: X, y = shuffle_data(X, y, seed) n_train_samples = int(X.shape[0] * (1-test_size)) x_train, x_test = X[:n_train_samples], X[n_train_samples:] y_train, y_test = y[:n_train_samples], y[n_train_samples:] return x_train, x_test, y_train, y_test # 计算矩阵 X 的协方差矩阵 def calculate_covariance_matrix(X, Y=np.empty((0,0))): if not Y.any(): Y = X n_samples = np.shape(X)[0] covariance_matrix = (1 / (n_samples-1)) * (X - X.mean(axis=0)).T.dot(Y - Y.mean(axis=0)) return np.array(covariance_matrix, dtype=float) # 计算数据集 X 每列的方差 def calculate_variance(X): n_samples = np.shape(X)[0] variance = (1 / n_samples) * np.diag((X - X.mean(axis=0)).T.dot(X - X.mean(axis=0))) return variance # 计算数据集 X 每列的标准差 def calculate_std_dev(X): std_dev = np.sqrt(calculate_variance(X)) return std_dev # 计算相关系数矩阵 def calculate_correlation_matrix(X, Y=np.empty([0])): # 先计算协方差矩阵 covariance_matrix = calculate_covariance_matrix(X, Y) # 计算 X, Y 的标准差 std_dev_X = np.expand_dims(calculate_std_dev(X), 1) std_dev_y = np.expand_dims(calculate_std_dev(Y), 1) correlation_matrix = np.divide(covariance_matrix, std_dev_X.dot(std_dev_y.T)) return np.array(correlation_matrix, dtype=float) class PCA(): """ 主成份分析算法 PCA，非监督学习算法. """ def __init__(self): self.eigen_values = None self.eigen_vectors = None self.k = 2 def transform(self, X): """ 将原始数据集 X 通过 PCA 进行降维 """ covariance = calculate_covariance_matrix(X) # 求解特征值和特征向量 self.eigen_values, self.eigen_vectors = np.linalg.eig(covariance) # 将特征值从大到小进行排序，注意特征向量是按列排的，即 self.eigen_vectors 第 k 列是 self.eigen_values 中第 k 个特征值对应的特征向量 idx = self.eigen_values.argsort()[::-1] eigenvalues = self.eigen_values[idx][:self.k] eigenvectors = self.eigen_vectors[:, idx][:, :self.k] # 将原始数据集 X 映射到低维空间 X_transformed = X.dot(eigenvectors) return X_transformed def main(): # Load the dataset data = datasets.load_iris() X = data.data y = data.target # 将数据集 X 映射到低维空间 X_trans = PCA().transform(X) x1 = X_trans[:, 0] x2 = X_trans[:, 1] cmap = plt.get_cmap('viridis') colors = [cmap(i) for i in np.linspace(0, 1, len(np.unique(y)))] class_distr = [] # Plot the different class distributions for i, l in enumerate(np.unique(y)): _x1 = x1[y == l] _x2 = x2[y == l] _y = y[y == l] class_distr.append(plt.scatter(_x1, _x2, color=colors[i])) # Add a legend plt.legend(class_distr, y, loc=1) # Axis labels plt.xlabel('Principal Component 1') plt.ylabel('Principal Component 2') plt.show() if __name__ == "__main__": main()

# coding:utf-8 # 实现KPCA from sklearn.datasets import load_iris from sklearn.decomposition import KernelPCA import numpy as np import matplotlib.pyplot as plt from scipy.spatial.distance import pdist, squareform ''' author: heucoder email: 812860165@qq.com date: 2019.6.13 ''' def sigmoid(x, coef = 0.25): x = np.dot(x, x.T) return np.tanh(coef*x+1) def linear(x): x = np.dot(x, x.T) return x def rbf(x, gamma = 15): sq_dists = pdist(x, 'sqeuclidean') mat_sq_dists = squareform(sq_dists) return np.exp(-gamma*mat_sq_dists) def kpca(data, n_dims=2, kernel = rbf): ''' :param data: (n_samples, n_features) :param n_dims: target n_dims :param kernel: kernel functions :return: (n_samples, n_dims) ''' K = kernel(data) # N = K.shape[0] one_n = np.ones((N, N)) / N K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n) # eig_values, eig_vector = np.linalg.eig(K) idx = eig_values.argsort()[::-1] eigval = eig_values[idx][:n_dims] eigvector = eig_vector[:, idx][:, :n_dims] print(eigval) eigval = eigval**(1/2) vi = eigvector/eigval.reshape(-1,n_dims) data_n = np.dot(K, vi) return data_n if __name__ == "__main__": data = load_iris().data Y = load_iris().target data_1 = kpca(data, kernel=rbf) sklearn_kpca = KernelPCA(n_components=2, kernel="rbf", gamma=15) data_2 = sklearn_kpca.fit_transform(data) plt.figure(figsize=(8,4)) plt.subplot(121) plt.title("my_KPCA") plt.scatter(data_1[:, 0], data_1[:, 1], c = Y) plt.subplot(122) plt.title("sklearn_KPCA") plt.scatter(data_2[:, 0], data_2[:, 1], c = Y) plt.show()

#coding:utf-8 import numpy as np from sklearn.discriminant_analysis import LinearDiscriminantAnalysis from sklearn.datasets import load_iris import matplotlib.pyplot as plt ''' author: heucoder email: 812860165@qq.com date: 2019.6.13 ''' def lda(data, target, n_dim): ''' :param data: (n_samples, n_features) :param target: data class :param n_dim: target dimension :return: (n_samples, n_dims) ''' clusters = np.unique(target) if n_dim > len(clusters)-1: print("K is too much") print("please input again") exit(0) #within_class scatter matrix Sw = np.zeros((data.shape[1],data.shape[1])) for i in clusters: datai = data[target == i] datai = datai-datai.mea
                
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