第六章.卷积神经网络(CNN)
6.2 CNN的实现(搭建手写数字识别的CNN)

1.网络构成

在这里插入图片描述
2.代码实现

import pickle
import matplotlib.pyplot as plt
import numpy as np
import sys, os

sys.path.append(os.pardir)

from dataset.mnist import load_mnist
from collections import OrderedDict


# 从图像到矩阵
def im2col(input_data, filter_h, filter_w, stride=1, pad=0):
    N, C, H, W = input_data.shape
    out_h = (H + 2 * pad - filter_h) // stride + 1
    out_w = (W + 2 * pad - filter_w) // stride + 1

    img = np.pad(input_data, [(0, 0), (0, 0), (pad, pad), (pad, pad)], 'constant')
    col = np.zeros((N, C, filter_h, filter_w, out_h, out_w))

    for y in range(filter_h):
        y_max = y + stride * out_h
        for x in range(filter_w):
            x_max = x + stride * out_w
            col[:, :, y, x, :, :] = img[:, :, y:y_max:stride, x:x_max:stride]

    col = col.transpose(0, 4, 5, 1, 2, 3).reshape(N * out_h * out_w, -1)

    return col


# 从矩阵到图像
def col2im(col, input_shape, filter_h, filter_w, stride=1, pad=0):
    N, C, H, W = input_shape
    out_h = (H + 2 * pad - filter_h) // stride + 1
    out_w = (W + 2 * pad - filter_w) // stride + 1
    col = col.reshape(N, out_h, out_w, C, filter_h, filter_w).transpose(0, 3, 4, 5, 1, 2)

    img = np.zeros((N, C, H + 2 * pad + stride - 1, W + 2 * pad + stride - 1))
    for y in range(filter_h):
        y_max = y + stride * out_h
        for x in range(filter_w):
            x_max = x + stride * out_w
            img[:, :, y:y_max:stride, x:x_max:stride] += col[:, :, y, x, :, :]

    return img[:, :, pad:H + pad, pad:W + pad]


class SGD:

    def __init__(self, lr=0.01):
        self.lr = lr

    def update(self, params, grads):
        for key in params.keys():
            params[key] -= self.lr * grads[key]


class Momentum:

    def __init__(self, lr=0.01, momentum=0.9):
        self.lr = lr
        self.momentum = momentum
        self.v = None

    def update(self, params, grads):
        if self.v is None:
            self.v = {}
            for key, val in params.items():
                self.v[key] = np.zeros_like(val)

        for key in params.keys():
            self.v[key] = self.momentum * self.v[key] - self.lr * grads[key]
            params[key] += self.v[key]


class Nesterov:

    def __init__(self, lr=0.01, momentum=0.9):
        self.lr = lr
        self.momentum = momentum
        self.v = None

    def update(self, params, grads):
        if self.v is None:
            self.v = {}
            for key, val in params.items():
                self.v[key] = np.zeros_like(val)

        for key in params.keys():
            self.v[key] *= self.momentum
            self.v[key] -= self.lr * grads[key]
            params[key] += self.momentum * self.momentum * self.v[key]
            params[key] -= (1 + self.momentum) * self.lr * grads[key]


class AdaGrad:

    def __init__(self, lr=0.01):
        self.lr = lr
        self.h = None

    def update(self, params, grads):
        if self.h is None:
            self.h = {}
            for key, val in params.items():
                self.h[key] = np.zeros_like(val)

        for key in params.keys():
            self.h[key] += grads[key] * grads[key]
            params[key] -= self.lr * grads[key] / (np.sqrt(self.h[key]) + 1e-7)


class RMSprop:

    def __init__(self, lr=0.01, decay_rate=0.99):
        self.lr = lr
        self.decay_rate = decay_rate
        self.h = None

    def update(self, params, grads):
        if self.h is None:
            self.h = {}
            for key, val in params.items():
                self.h[key] = np.zeros_like(val)

        for key in params.keys():
            self.h[key] *= self.decay_rate
            self.h[key] += (1 - self.decay_rate) * grads[key] * grads[key]
            params[key] -= self.lr * grads[key] / (np.sqrt(self.h[key]) + 1e-7)


class Adam:

    def __init__(self, lr=0.001, beta1=0.9, beta2=0.999):
        self.lr = lr
        self.beta1 = beta1
        self.beta2 = beta2
        self.iter = 0
        self.m = None
        self.v = None

    def update(self, params, grads):
        if self.m is None:
            self.m, self.v = {}, {}
            for key, val in params.items():
                self.m[key] = np.zeros_like(val)
                self.v[key] = np.zeros_like(val)

        self.iter += 1
        lr_t = self.lr * np.sqrt(1.0 - self.beta2 ** self.iter) / (1.0 - self.beta1 ** self.iter)

        for key in params.keys():
            # self.m[key] = self.beta1*self.m[key] + (1-self.beta1)*grads[key]
            # self.v[key] = self.beta2*self.v[key] + (1-self.beta2)*(grads[key]**2)
            self.m[key] += (1 - self.beta1) * (grads[key] - self.m[key])
            self.v[key] += (1 - self.beta2) * (grads[key] ** 2 - self.v[key])

            params[key] -= lr_t * self.m[key] / (np.sqrt(self.v[key]) + 1e-7)

            # unbias_m += (1 - self.beta1) * (grads[key] - self.m[key]) # correct bias
            # unbisa_b += (1 - self.beta2) * (grads[key]*grads[key] - self.v[key]) # correct bias
            # params[key] += self.lr * unbias_m / (np.sqrt(unbisa_b) + 1e-7)


# 激活函数Relu
class Relu:
    def __init__(self):
        self.mask = None

    def forward(self, x):
        self.mask = (x <= 0)
        out = x.copy()
        out[self.mask] = 0
        return out

    def backward(self, dout):
        dout[self.mask] = 0
        dx = dout
        return dx


# 卷积层
class Convolution:
    def __init__(self, W, b, stride=1, pad=0):
        self.W = W
        self.b = b
        self.stride = stride
        self.pad = pad

        # 中间数据（backward时使用）
        self.x = None
        self.col = None
        self.col_W = None

        # 权重和偏置参数的梯度
        self.dW = None
        self.db = None

    # 正向传播
    def forward(self, x):
        FN, C, FH, FW = self.W.shape
        N, C, H, W = x.shape
        out_h = int((H + 2 * self.pad - FH) / self.stride) + 1
        out_w = int((W + 2 * self.pad - FW) / self.stride) + 1

        col = im2col(x, FH, FW, self.stride, self.pad)
        col_W = self.W.reshape(FN, -1).T

        out = np.dot(col, col_W) + self.b
        out = out.reshape(N, out_h, out_w, -1).transpose(0, 3, 1, 2)

        self.x = x
        self.col = col
        self.col_W = col_W

        return out

    # 反向传播
    def backward(self, dout):
        FN, C, FH, FW = self.W.shape
        dout = dout.transpose(0, 2, 3, 1).reshape(-1, FN)

        self.db = np.sum(dout, axis=0)
        self.dW = np.dot(self.col.T, dout)
        self.dW = self.dW.transpose(1, 0).reshape(FN, C, FH, FW)

        dcol = np.dot(dout, self.col_W.T)
        dx = col2im(dcol, self.x.shape, FH, FW, self.stride, self.pad)

        return dx


# 池化层
class Pooling:
    def __init__(self, pool_h, pool_w, stride=1, pad=0):
        self.pool_h = pool_h
        self.pool_w = pool_w
        self.stride = stride
        self.pad = pad

        self.x = None
        self.arg_max = None

    # 正向传播
    def forward(self, x):
        N, C, H, W = x.shape
        out_h = int(1 + (H - self.pool_h) / self.stride)
        out_w = int(1 + (W - self.pool_w) / self.stride)

        col = im2col(x, self.pool_h, self.pool_w, self.stride, self.pad)
        col = col.reshape(-1, self.pool_h * self.pool_w)

        arg_max = np.argmax(col, axis=1)
        out = np.max(col, axis=1)
        out = out.reshape(N, out_h, out_w, C).transpose(0, 3, 1, 2)

        self.x = x
        self.arg_max = arg_max

        return out

    # 反向传播
    def backward(self, dout):
        dout = dout.transpose(0, 2, 3, 1)

        pool_size = self.pool_h * self.pool_w
        dmax = np.zeros((dout.size, pool_size))
        dmax[np.arange(self.arg_max.size), self.arg_max.flatten()] = dout.flatten()
        dmax = dmax.reshape(dout.shape + (pool_size,))

        dcol = dmax.reshape(dmax.shape[0] * dmax.shape[1] * dmax.shape[2], -1)
        dx = col2im(dcol, self.x.shape, self.pool_h, self.pool_w, self.stride, self.pad)

        return dx


# Affine层
class Affine:
    def __init__(self, W, b):
        self.W = W
        self.b = b

        self.x = None
        self.original_x_shape = None
        # 权重和偏置参数的导数
        self.dW = None
        self.db = None

    def forward(self, x):
        # 对应张量
        self.original_x_shape = x.shape  # 例如：x.shape=(209, 64, 64, 3)
        x = x.reshape(x.shape[0], -1)  # x=(209, 64*64*3)
        self.x = x

        out = np.dot(self.x, self.W) + self.b

        return out

    def backward(self, dout):
        dx = np.dot(dout, self.W.T)
        self.dW = np.dot(self.x.T, dout)
        self.db = np.sum(dout, axis=0)

        dx = dx.reshape(*self.original_x_shape)  # 还原输入数据的形状（对应张量）
        return dx


# 输出层
class SoftmaxWithLoss:
    def __init__(self):
        self.loss = None  # 损失
        self.y = None  # softmax的输出
        self.t = None  # 监督数据(one_hot vector)

    # 输出层函数：softmax
    def softmax(self, x):
        if x.ndim == 2:
            x = x.T
            x = x - np.max(x, axis=0)
            y = np.exp(x) / np.sum(np.exp(x), axis=0)
            return y.T

        x = x - np.max(x)  # 溢出对策
        return np.exp(x) / np.sum(np.exp(x))

    # 交叉熵误差
    def cross_entropy_error(self, y, t):
        if y.ndim == 1:
            t = t.reshape(1, t.size)
            y = y.reshape(1, y.size)

        # 监督数据是one-hot-vector的情况下，转换为正确解标签的索引
        if t.size == y.size:
            t = t.argmax(axis=1)

        batch_size = y.shape[0]
        return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size

    # 正向传播
    def forward(self, x, t):
        self.t = t
        self.y = self.softmax(x)
        self.loss = self.cross_entropy_error(self.y, self.t)
        return self.loss

    # 反向传播
    def backward(self, dout=1):
        batch_size = self.t.shape[0]
        if self.t.size == self.y.size:  # 监督数据是one-hot-vector的情况
            dx = (self.y - self.t) / batch_size
        else:
            dx = self.y.copy()
            dx[np.arange(batch_size), self.t] -= 1
            dx = dx / batch_size

        return dx


class Trainer:
    """进行神经网络的训练的类
    """

    def __init__(self, network, x_train, t_train, x_test, t_test,
                 epochs=20, mini_batch_size=100,
                 optimizer='SGD', optimizer_param={'lr': 0.01},
                 evaluate_sample_num_per_epoch=None, verbose=True):
        self.network = network
        self.verbose = verbose
        self.x_train = x_train
        self.t_train = t_train
        self.x_test = x_test
        self.t_test = t_test
        self.epochs = epochs
        self.batch_size = mini_batch_size
        self.evaluate_sample_num_per_epoch = evaluate_sample_num_per_epoch

        # optimzer
        optimizer_class_dict = {'sgd': SGD, 'momentum': Momentum, 'nesterov': Nesterov,
                                'adagrad': AdaGrad, 'rmsprpo': RMSprop, 'adam': Adam}
        self.optimizer = optimizer_class_dict[optimizer.lower()](**optimizer_param)

        self.train_size = x_train.shape[0]
        self.iter_per_epoch = max(self.train_size / mini_batch_size, 1)
        self.max_iter = int(epochs * self.iter_per_epoch)
        self.current_iter = 0
        self.current_epoch = 0

        self.train_loss_list = []
        self.train_acc_list = []
        self.test_acc_list = []

    def train_step(self):
        batch_mask = np.random.choice(self.train_size, self.batch_size)
        x_batch = self.x_train[batch_mask]
        t_batch = self.t_train[batch_mask]

        grads = self.network.gradient(x_batch, t_batch)
        self.optimizer.update(self.network.params, grads)

        loss = self.network.loss(x_batch, t_batch)
        self.train_loss_list.append(loss)
        if self.verbose: print("train loss:" + str(loss))

        if self.current_iter % self.iter_per_epoch == 0:
            self.current_epoch += 1

            x_train_sample, t_train_sample = self.x_train, self.t_train
            x_test_sample, t_test_sample = self.x_test, self.t_test
            if not self.evaluate_sample_num_per_epoch is None:
                t = self.evaluate_sample_num_per_epoch
                x_train_sample, t_train_sample = self.x_train[:t], self.t_train[:t]
                x_test_sample, t_test_sample = self.x_test[:t], self.t_test[:t]

            train_acc = self.network.accuracy(x_train_sample, t_train_sample)
            test_acc = self.network.accuracy(x_test_sample, t_test_sample)
            self.train_acc_list.append(train_acc)
            self.test_acc_list.append(test_acc)

            if self.verbose: print(
                "=== epoch:" + str(self.current_epoch) + ", train acc:" + str(train_acc) + ", test acc:" + str(
                    test_acc) + " ===")
        self.current_iter += 1

    def train(self):
        for i in range(self.max_iter):
            self.train_step()

        test_acc = self.network.accuracy(self.x_test, self.t_test)

        if self.verbose:
            print("=============== Final Test Accuracy ===============")
            print("test acc:" + str(test_acc))


# 手写数字识别CNN的实现类: conv - relu - pool - affine - relu - affine - softmax
class SimpleConvNet:
    def __init__(self, input_dim=(1, 28, 28), conv_param={'filter_num': 30, 'filter_size': 5, 'pad': 0, 'stride': 1},
                 hidden_size=100, output_size=10, weight_int_std=0.01):
        filter_num = conv_param['filter_num']
        filter_size = conv_param['filter_size']
        filter_pad = conv_param['pad']
        filter_stride = conv_param['stride']

        input_size = input_dim[1]
        conv_output_size = (input_size + 2 * filter_pad - filter_size) / filter_stride + 1
        pool_output_size = int(filter_num * (conv_output_size / 2) * (conv_output_size / 2))

        # 初始化权重
        self.params = {}
        self.params['W1'] = weight_int_std * np.random.randn(filter_num, input_dim[0], filter_size, filter_size)
        self.params['b1'] = np.zeros(filter_num)
        self.params['W2'] = weight_int_std * np.random.randn(pool_output_size, hidden_size)
        self.params['b2'] = np.zeros(hidden_size)
        self.params['W3'] = weight_int_std * np.random.randn(hidden_size, output_size)
        self.params['b3'] = np.zeros(output_size)

        # 生成层
        self.layers = OrderedDict()
        self.layers['Conv1'] = Convolution(self.params['W1'], self.params['b1'], filter_stride, filter_pad)
        self.layers['Relu1'] = Relu()
        self.layers['pool1'] = Pooling(pool_h=2, pool_w=2, stride=2)
        self.layers['Affine1'] = Affine(self.params['W2'], self.params['b2'])
        self.layers['Relu2'] = Relu()
        self.layers['Affine2'] = Affine(self.params['W3'], self.params['b3'])
        self.last_layer = SoftmaxWithLoss()

    # 推理函数
    def predict(self, x):
        for layer in self.layers.values():
            x = layer.forward(x)

        return x

    # 损失函数
    def loss(self, x, t):
        y = self.predict(x)
        return self.last_layer.forward(y, t)

    # 识别精度
    def accuracy(self, x, t, batch_size=100):
        if t.ndim != 1: t = np.argmax(t, axis=1)

        acc = 0.0
        for i in range(int(x.shape[0] / batch_size)):
            tx = x[i * batch_size:(i + 1) * batch_size]
            tt = t[i * batch_size:(i + 1) * batch_size]
            y = self.predict(tx)
            y = np.argmax(y, axis=1)
            acc += np.sum(y == tt)

        return acc / x.shape[0]

    def numerical_gradient(f, x):
        h = 1e-4  # 0.0001
        grad = np.zeros_like(x)

        it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
        while not it.finished:
            idx = it.multi_index
            tmp_val = x[idx]
            x[idx] = float(tmp_val) + h
            fxh1 = f(x)  # f(x+h)

            x[idx] = tmp_val - h
            fxh2 = f(x)  # f(x-h)
            grad[idx] = (fxh1 - fxh2) / (2 * h)

            x[idx] = tmp_val  # 还原值
            it.iternext()

        return grad

    # 数值微分
    def numerical_gradient(self, x, t):
        loss_w = lambda w: self.loss(x, t)
        grads = {}
        for idx in (1, 2, 3):
            grads['W' + str(idx)] = self.numerical_gradient(loss_w, self.params['W' + str(idx)])
            grads['b' + str(idx)] = self.numerical_gradient(loss_w, self.params['b' + str(idx)])

        return grads

    # 误差反向传播法求梯度
    def gradient(self, x, t):
        self.loss(x, t)
        dout = 1
        dout = self.last_layer.backward(dout)

        layers = list(self.layers.values())
        layers.reverse()
        for layer in layers:
            dout = layer.backward(dout)

        # 设定
        grads = {}
        grads['W1'], grads['b1'] = self.layers['Conv1'].dW, self.layers['Conv1'].db
        grads['W2'], grads['b2'] = self.layers['Affine1'].dW, self.layers['Affine1'].db
        grads['W3'], grads['b3'] = self.layers['Affine2'].dW, self.layers['Affine2'].db

        return grads

    # 保存参数
    def save_param(self, file_name='params.pkl'):
        params = {}
        for key, val in self.params.items():
            params[key] = val

        with open(file_name, 'wb') as f:
            pickle.dump(params, f)

    # 加载参数
    def load_param(self, file_name='params.pkl'):
        with open(file_name, 'rb') as f:
            params = pickle.load(f)
        for key, val in params.items():
            self.params[key] = val

        for i, key in enumerate(['Conv1', 'Affine1', 'Affine2']):
            self.layers[key].W = self.params['W' + str(i + 1)]
            self.layers[key].b = self.params['b' + str(i + 1)]

#加载数据
(x_train,t_train),(x_test,t_test)=load_mnist(flatten=False)

#较少数据
x_train,t_train=x_train[:5000],t_train[:5000]
x_test,t_test=x_test[:1000],t_test[:1000]

max_epoch=20
network=SimpleConvNet( input_dim=(1, 28, 28), conv_param={'filter_num': 30, 'filter_size': 5, 'pad': 0, 'stride': 1},
                 hidden_size=100, output_size=10, weight_int_std=0.01)

trainer=Trainer(network, x_train, t_train, x_test, t_test,
                 epochs=max_epoch, mini_batch_size=100,
                 optimizer='Adam', optimizer_param={'lr': 0.001},
                 evaluate_sample_num_per_epoch=1000)

trainer.train()

#保存参数
network.save_param("params.pkl")
print("Save Network Parameters!")

#绘制图像
x=np.arange(max_epoch)
plt.plot(x,trainer.train_acc_list,marker='o',label='train',markevery=2)
plt.plot(x,trainer.test_acc_list,marker='s',label='test',markevery=2)
plt.xlabel("epochs")
plt.ylabel("accuracy")
plt.ylim(0, 1.0)
plt.legend(loc='lower right')
plt.show()