我的第一个神经网络

from sklearn import datasets
from sklearn import preprocessing
from sklearn.model_selection import train_test_split
from sklearn.neighbors import KNeighborsClassifier
import numpy as np


def sigmoid(x):
    # 激活函数 f(x) = 1 / (1 + e^(-x))
    return 1 / (1 + np.exp(-x))


def deri_sigmoid(x):
    # 激活函数求导 f'(x) = f(x) * (1 - f(x))
    k = sigmoid(x)
    return k * (1 - k)


def mse_loss(y_true, y_pred):
    # 计算损失
    return ((y_true - y_pred) ** 2).mean()


class OurNeuralNetwork():
    def __init__(self, N):
        # 初始化隐含层参数 Z = w*x+b  A = sigmiod(Z)
        self.W = [np.random.randn(2, 2) for _ in range(N)]
        self.B = [np.random.randn(2, 1) for _ in range(N)]
        self.A = [np.random.randn(1, 1) for _ in range(N)]
        self.Z = [np.random.randn(1, 1) for _ in range(N)]

        self.dW = [np.zeros((2, 2)) for _ in range(N)]
        self.dB = [np.zeros((2, 1)) for _ in range(N)]
        self.dA = [np.zeros((1, 1)) for _ in range(N)]
        self.dZ = [np.zeros((1, 1)) for _ in range(N)]

        # 初始化输出层参数
        self.WO = np.random.rand(1, 2)
        self.BO = np.random.rand(1, 1)
        self.AO = np.random.rand(1, 1)
        self.ZO = np.random.rand(1, 1)
        self.dWO = np.random.rand(1, 1)
        self.dBO = np.random.rand(1, 1)
        self.dAO = np.random.rand(1, 1)
        self.dZO = np.random.rand(1, 1)

        self.N = N  # N个隐含层

    def feedforward(self, x):
        # 前向反馈
        for i in range(self.N):
            if i == 0:
                self.Z[i] = np.dot(self.W[i], x) + self.B[i]   # Z[i] = W[i]*X + B[i]
            else:
                self.Z[i] = np.dot(self.W[i], self.A[i-1]) + self.B[i]  # Z[i] = W[i]*A[i-1] + B[i]
            self.A[i] = sigmoid(self.Z[i])

        # 计算输出层
        self.ZO = np.dot(self.WO, self.A[self.N-1]) + self.BO
        self.AO = sigmoid(self.ZO)
        return self.AO

    def train(self, data, all_y_trues):
        learn_rate = 0.1
        times = 5000
        for time in range(times):
            # 1.计算前向反馈
            for i in range(self.N):
                if i == 0:
                    self.Z[i] = np.dot(self.W[i], data) + self.B[i]
                else:
                    self.Z[i] = np.dot(self.W[i], self.A[i - 1]) + self.B[i]
                self.A[i] = sigmoid(self.Z[i])
            self.ZO = np.dot(self.WO, self.A[self.N - 1]) + self.BO
            self.AO = sigmoid(self.ZO)

            # 2.计算 输出层 误差和导数
            self.dAO = 2 * (self.AO - all_y_trues)
            self.dZO = deri_sigmoid(self.AO) * self.dAO
            m = self.A[self.N-1].shape[1]
            self.dWO = np.dot(self.dZO, self.A[self.N-1].T) / m
            self.dBO = np.sum(self.dZO, axis=1, keepdims=True) / m
            self.WO -= learn_rate * self.dWO
            self.BO -= learn_rate * self.dBO

            # 反向反馈
            for i in range(self.N-1, 0, -1):
                if i == self.N-1:  # 如果是最有一层 则根据输出层的信息来更新
                    self.dA[i] = np.dot(self.WO.T, self.dZO)
                else:  # 否则根据上一层的隐含层信息来更新
                    self.dA[i] = np.dot(self.W[i+1].T, self.dZ[i+1])
                self.dZ[i] = deri_sigmoid(self.Z[i]) * self.dA[i]
                m = self.A[i-1].shape[1]  # m表示有m个样本数据
                self.dW[i] = np.dot(self.dZ[i], self.A[i-1].T) / m
                self.dB[i] = np.sum(self.dZ[i], axis=1, keepdims=True) / m
                self.W[i] -= learn_rate * self.dW[i]
                self.B[i] -= learn_rate * self.dB[i]
            if self.N > 1:
                self.dA[0] = np.dot(self.W[1].T, self.dZ[1])
            else:
                self.dA[0] = np.dot(self.WO.T, self.dZO)
            self.dZ[0] = deri_sigmoid(self.Z[0]) * self.dA[0]
            m = data.shape[1]
            self.dW[0] = np.dot(self.dZ[0], data.T) / m
            self.dB[0] = np.sum(self.dZ[0], axis=1, keepdims=True) / m
            self.W[0] -= learn_rate * self.dW[0]
            self.B[0] -= learn_rate * self.dB[0]

            if time % 10 == 0:
                y_preds = np.apply_along_axis(self.feedforward, 0, data)
                loss = mse_loss(all_y_trues, y_preds)
                print("time %d loss: %0.3f" % (time, loss))


# Define dataset
data = np.array([
    [-2, -1], # Alice
    [25, 6],  # Bob
    [17, 4],  # Charlie
    [-15, -6] # diana
])
all_y_trues = np.array([
    1, # Alice
    0, # Bob
    0, # Charlie
    1 # diana
])


network = OurNeuralNetwork(2)

network.train(data.T, all_y_trues.T)  # 这里注意转置
emily = np.array([[-7], [-3]])
frank = np.array([[20], [2]])
print("Emily: %.3f" % network.feedforward(emily)) # 0.951 - F
print("Frank: %.3f" % network.feedforward(frank)) # 0.039 - M

训练结果(只有最后一部分)：

time 4710 loss: 0.241
time 4720 loss: 0.241
time 4730 loss: 0.241
time 4740 loss: 0.241
time 4750 loss: 0.241
time 4760 loss: 0.241
time 4770 loss: 0.241
time 4780 loss: 0.241
time 4790 loss: 0.241
time 4800 loss: 0.241
time 4810 loss: 0.241
time 4820 loss: 0.241
time 4830 loss: 0.241
time 4840 loss: 0.241
time 4850 loss: 0.241
time 4860 loss: 0.241
time 4870 loss: 0.241
time 4880 loss: 0.241
time 4890 loss: 0.241
time 4900 loss: 0.241
time 4910 loss: 0.241
time 4920 loss: 0.241
time 4930 loss: 0.241
time 4940 loss: 0.241
time 4950 loss: 0.241
time 4960 loss: 0.241
time 4970 loss: 0.241
time 4980 loss: 0.241
time 4990 loss: 0.241
Emily: 0.983
Frank: 0.017

 

神经网络描述图：