降维

import numpy as np
from sklearn import datasets
import matplotlib.pyplot as plt


class PCA():
    # 计算协方差矩阵
    def calc_cov(self, X):
        m = X.shape[0]
        # 数据标准化
        X = (X - np.mean(X, axis=0)) / np.var(X, axis=0)
        return 1 / m * np.matmul(X.T, X)

    def pca(self, X, n_components):
        # 计算协方差矩阵
        cov_matrix = self.calc_cov(X)
        # 计算协方差矩阵的特征值和对应特征向量
        eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)
        # 对特征值排序
        idx = eigenvalues.argsort()[::-1]
        # 取最大的前n_component组
        eigenvectors = eigenvectors[:, idx]
        eigenvectors = eigenvectors[:, :n_components]
        # Y=PX转换
        return np.matmul(X, eigenvectors)


# 导入sklearn的鸢尾花数据集
iris = datasets.load_iris()
X = iris.data
y = iris.target

# 将数据降维到3个主成分
X_trans = PCA().pca(X, 3)
colors = ['navy', 'turquoise', 'darkorange']

# 绘制不同类别
for c, i, target_name in zip(colors, [0, 1, 2], iris.target_names):
    plt.scatter(X_trans[y == i, 0], X_trans[y == i, 1],
                color=c, lw=2, label=target_name)
plt.legend()
plt.show()

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import fetch_olivetti_faces
from sklearn.decomposition import PCA

dataset = fetch_olivetti_faces(shuffle=True)
data = dataset['data']
print(data.shape)  # 原始数据的形状

pca = PCA(n_components=128)
pca.fit(data)

plt.subplot(1, 2, 1)
plt.title('raw first figure')
plt.imshow(data[0].reshape((64, 64)))

data_pca = pca.transform(data)
print(data_pca.shape)  # 降维后数据的形状

data_recover = pca.inverse_transform(data_pca).reshape(400, 64, 64)
print(data_recover.shape)

plt.subplot(1, 2, 2)
plt.title('recovered first figure (n_components=128)')
plt.imshow(data_recover[0])
plt.show()

# 获取主成分，即特征脸
comp = pca.components_
print(comp.shape)

for i in range(16):
    plt.subplot(4, 4, i + 1)
    plt.imshow(comp[i].reshape((64, 64)))
plt.show()

import numpy as np
import matplotlib.pyplot as plt
import scipy.io as sio
from sklearn.manifold import TSNE

# 数据获取 (需要预先将数据导入当前目录下)
# A F K M类恒星数据各1000条
X_a = sio.loadmat('spectra_data\A.mat')['P1'][:1000]
X_f = sio.loadmat('spectra_data\F.mat')['P1'][:1000]
X_k = sio.loadmat('spectra_data\K.mat')['P1'][:1000]
X_m = sio.loadmat('spectra_data\M.mat')['P1'][:1000]
X_label = ['A', 'F', 'K', 'M']
X = np.vstack((X_a, X_f, X_k, X_m))

# 类别标签
y_a = np.full((X_a.shape[0],), 0)
y_f = np.full((X_f.shape[0],), 1)
y_k = np.full((X_k.shape[0],), 2)
y_m = np.full((X_m.shape[0],), 3)
y = np.hstack((y_a, y_f, y_k, y_m))

# 数据归一化
for i in range(X.shape[0]):
    X[i] -= np.min(X[i])
    if np.max(X[i]) != 0:
        X[i] /= np.max(X[i])

print('Data shape: ', X.shape)
print('Label shape: ', y.shape)

# 降维
tsne = TSNE()
X_tsne = tsne.fit_transform(X)

# 绘制降维结果
plt.scatter(X_tsne[y == 0, 0], X_tsne[y == 0, 1], label='A')
plt.scatter(X_tsne[y == 1, 0], X_tsne[y == 1, 1], label='F')
plt.scatter(X_tsne[y == 2, 0], X_tsne[y == 2, 1], label='K')
plt.scatter(X_tsne[y == 3, 0], X_tsne[y == 3, 1], label='M')
plt.legend()
plt.show()