【手写简单神经网络】两种方法实现MNIST数据集下载、解析及识别的Python

 （方法一）第一隐藏层为30，第二隐藏层为60 ，输出层为10的简单神经网络：

import numpy as np
from dataset.mnist import load_mnist
import matplotlib.pylab as plt


def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def sigmoid_grad(x):
    return (1.0 - sigmoid(x)) * sigmoid(x)


def softmax(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))


def cross_entropy_error(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


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


# (x_train,t_train),(x_test,t_test)=load_mnist(normalize=True,one_hot_label=True)
# 两层神经网络的类
class TwoLayerNet:
    def __init__(self, input_size, hidden_size1, hidden_size2, output_size, weight_init_std=0.01):
        # 初始化权重
        self.params = {}
        self.params['W1'] = weight_init_std * np.random.randn(input_size, hidden_size1)
        self.params['b1'] = np.zeros(hidden_size1)
        self.params['W2'] = weight_init_std * np.random.randn(hidden_size1, hidden_size2)
        self.params['b2'] = np.zeros(hidden_size2)
        self.params['W3'] = weight_init_std * np.random.randn(hidden_size2, output_size)
        self.params['b3'] = np.zeros(output_size)

    def predict(self, x):
        W1, W2, W3 = self.params['W1'], self.params['W2'], self.params['W3']
        b1, b2, b3 = self.params['b1'], self.params['b2'], self.params['b3']

        a1 = np.dot(x, W1) + b1
        z1 = sigmoid(a1)
        a2 = np.dot(z1, W2) + b2
        z2 = sigmoid(a2)
        a3 = np.dot(z2, W3) + b3
        y = softmax(a3)

        return y

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