pip install opencv-python

pip install paddle

import cv2import paddle
# 图片矢量化def img2vector(image):    img = cv2.imread(image, 0)  # 读取图片    imgVector = paddle.reshape(paddle.to_tensor(img, dtype='float32'), [1, -1]) # 重塑为1行多列    return imgVector

import osimport numpy as np
class ORLDataset:    def __init__(self, data_path, k, train=True):        self.data_path = data_path        self.k = k        self.train = train
    def load_orl(self):        train_images = []        train_labels = []        test_images = []        test_labels = []        sample = np.random.permutation(10) + 1  # 生成随机序列
        for i in range(40):  # 共有40个人            people_num = i + 1            for j in range(10):  # 每人10张照片                image_path = os.path.join(self.data_path, 's' + str(people_num), str(sample[j]) + '.pgm')                img = img2vector(image_path)  # 读取图片并进行矢量化                if j < self.k:  # 构成训练集                    train_images.append(img)                    train_labels.append(people_num)                else:  # 构成测试集                    test_images.append(img)                    test_labels.append(people_num)        if self.train:            return paddle.concat(train_images, axis=0), paddle.to_tensor(train_labels, dtype='int64')        else:            return paddle.concat(test_images, axis=0), paddle.to_tensor(test_labels, dtype='int64')

 data = paddle.cast(data, 'float32')rows, cols = data.shape

 data_mean = paddle.mean(data, axis=0)  # 计算均值A = data - paddle.tile(data_mean, repeat_times=[rows, 1])  # 数据中心化

$$A = X - \bar{X}$$

 C = paddle.matmul(A, A, transpose_y=True)

 $$C = AA^T$$

 eig_vals, eig_vects = paddle.linalg.eigh(C)

 $$C\vec{v} = \lambda\vec{v}$$

 eig_vects = paddle.matmul(A.T, eig_vects[:, :r])

 $$Vr = [\vec{v}1, \vec{v}2, \ldots, \vec{v}r]$$

 for i in range(r):    eig_vects[:, i] = eig_vects[:, i] / paddle.norm(eig_vects[:, i])

 $$\hat{\vec{v}}i = \frac{\vec{v}i}{|\vec{v}_i|}$$

 final_data = paddle.matmul(A, eig_vects)  # 降维后的数据return final_data, data_mean, eig_vects

 $$Y = AV_r$$

def PCA(data, r):  # 降低到r维    data = paddle.cast(data, 'float32')    rows, cols = data.shape    data_mean = paddle.mean(data, axis=0)  # 计算均值    A = data - paddle.tile(data_mean, repeat_times=[rows, 1])  # 数据中心化
# 计算协方差矩阵    C = paddle.matmul(A, A, transpose_y=True)
# 计算特征值和特征向量    eig_vals, eig_vects = paddle.linalg.eigh(C)
# 选取前r个特征向量    eig_vects = paddle.matmul(A.T, eig_vects[:, :r])
for i inrange(r):        eig_vects[:, i] = eig_vects[:, i] / paddle.norm(eig_vects[:, i])  # 特征向量标准化
    final_data = paddle.matmul(A, eig_vects)  # 降维后的数据return final_data, data_mean, eig_vects

def face_recognize(data_path):    for r in range(10, 41, 10):        print(f"当降维到{r}时:")        dataset_train = ORLDataset(data_path, k=7, train=True)        dataset_test = ORLDataset(data_path, k=7, train=False)
        train_data, train_labels = dataset_train.load_orl()        test_data, test_labels = dataset_test.load_orl()
        data_train_new, data_mean, V_r = PCA(train_data, r)        temp_face = test_data - data_mean        data_test_new = paddle.matmul(temp_face, V_r)
        true_num = 0        for i in range(len(test_labels)):            diffMat = data_train_new - data_test_new[i]            sqDiffMat = paddle.square(diffMat)            sqDistances = paddle.sum(sqDiffMat, axis=1)            sortedDistIndices = paddle.argsort(sqDistances)            if train_labels[sortedDistIndices[0]] == test_labels[i]:                true_num += 1
        accuracy = float(true_num) / len(test_labels)        print(f'当每个人选择7张照片进行训练时，The classify accuracy is: {accuracy:.2%}')