pca算法python语言代码

下面是PCA算法的Python代码：from numpy import array
from numpy import mean
from numpy import cov
from numpy.linalg import eig
# define a matrix
A = array([[1, 2], [3, 4], [5, 6]])
print(A)
# calculate the mean of each column
M = mean(A.T, axis=1)
print(M)
# center columns by subtracting column means
C = A - M
print(C)
# calculate covariance matrix of centered matrix
V = cov(C.T)
print(V)
# eigendecomposition of covariance matrix
values, vectors = eig(V)
print(vectors)
print(values)
# project data
P = vectors.T.dot(C.T)
print(P.T)

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DPC-KNN-PCA算法python完整代码

以下是DPC-KNN-PCA算法的Python完整代码，包括数据预处理、DPC-KNN-PCA算法实现和结果可视化：

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# 数据预处理
data = pd.read_csv('data.csv')
X = data.values[:, :-1]
y = data.values[:, -1]

# DPC-KNN-PCA算法实现
def DPC_KNN_PCA(X, k, alpha, beta, gamma):
    n, m = X.shape
    D = np.zeros((n, n))
    for i in range(n):
        for j in range(n):
            D[i, j] = np.linalg.norm(X[i] - X[j])
    D_sort = np.sort(D, axis=1)
    idx_sort = np.argsort(D, axis=1)
    K = np.zeros((n, k))
    for i in range(n):
        for j in range(k):
            K[i, j] = idx_sort[i, j+1]
    W = np.zeros((n, n))
    for i in range(n):
        for j in range(k):
            W[int(K[i, j]), i] = 1
    W = np.maximum(W, W.T)
    D_bar = np.diag(np.sum(W, axis=1))
    L = D_bar - W
    M = np.dot(X.T, L).dot(X)
    [U, S, V] = np.linalg.svd(M)
    U_pca = U[:, :2]
    Z = np.dot(X, U_pca)
    L_pca = np.dot(U_pca.T, M).dot(U_pca)
    D_pca = np.diag(np.sum(L_pca, axis=1))
    L_norm = np.linalg.inv(np.sqrt(D_pca)).dot(L_pca).dot(np.linalg.inv(np.sqrt(D_pca)))
    W_norm = np.exp(-alpha*L_norm) - np.eye(n)
    D_norm = np.diag(np.sum(W_norm, axis=1))
    L1_norm = D_norm - W_norm
    L2_norm = np.linalg.inv(np.sqrt(D_norm)).dot(L_norm).dot(np.linalg.inv(np.sqrt(D_norm)))
    W_dpc = np.exp(-beta*L1_norm - gamma*L2_norm) - np.eye(n)
    D_dpc = np.diag(np.sum(W_dpc, axis=1))
    L_dpc = D_dpc - W_dpc
    return Z, L_dpc

# 运行DPC-KNN-PCA算法并可视化结果
Z, L_dpc = DPC_KNN_PCA(X, 10, 0.5, 0.1, 0.1)
plt.scatter(Z[:, 0], Z[:, 1], c=y)
plt.show()

人脸识别特征脸提取PCA算法python代码实现

以下是使用PCA算法进行人脸识别中特征脸提取的Python代码实现：

import numpy as np
from PIL import Image
import os

# 读取数据集
def read_images(path, sz=None):
    c = 0
    X, y = [], []
    for dirname, dirnames, filenames in os.walk(path):
        for subdirname in dirnames:
            subject_path = os.path.join(dirname, subdirname)
            for filename in os.listdir(subject_path):
                try:
                    # 将图像转换为灰度图像
                    im = Image.open(os.path.join(subject_path, filename)).convert('L')
                    # 将图像大小重新调整为sz
                    if sz is not None:
                        im = im.resize(sz, Image.ANTIALIAS)
                    # 将图像转换为NumPy数组
                    X.append(np.asarray(im, dtype=np.uint8))
                    y.append(c)
                except IOError as e:
                    print("I/O error({0}): {1}".format(e.errno, e.strerror))
                except:
                    print("Unexpected error:", sys.exc_info()[0])
                    raise
            c = c+1
    return [X,y]

# 使用PCA算法进行特征脸提取
def pca(X):
    # 计算均值
    mean_X = X.mean(axis=0)
    # 中心化X
    X = X - mean_X
    # 计算协方差矩阵
    cov = np.dot(X.T, X)
    # 计算特征向量和特征值
    evals, evecs = np.linalg.eig(cov)
    # 将特征向量按特征值大小降序排列
    idx = np.argsort(evals)[::-1]
    evecs = evecs[:,idx]
    # 选择前k个特征向量
    k = 100
    evecs = evecs[:, :k]
    # 计算特征脸
    X_pca = np.dot(X, evecs)
    return X_pca

# 读取图像数据集
[X,y] = read_images('path/to/dataset')

# 将图像数据集转换为NumPy数组
X = np.asarray(X)

# 使用PCA算法进行特征脸提取
X_pca = pca(X)

# 显示特征脸
for i in range(X_pca.shape[1]):
    im = Image.fromarray(X_pca[:,i].reshape(112,92))
    im.show()

在上面的代码中，`read_images`函数用于读取图像数据集，`pca`函数用于使用PCA算法进行特征脸提取，`X_pca`存储了特征脸，最后使用`Image`模块将特征脸转换为图像并显示出来。