BP.py

"""
BP算法手工实现
"""
import numpy as np
from utils.dataset import dataSet

def sigmod(x):
    return 1.0 / (1.0 + np.exp(-x))


def bpstand(hideNum,X, Y):  # 标准的反向传播算法
    V = np.random.rand(X.shape[1], hideNum)  # 权值及偏置初始化
    V_b = np.random.rand(1, hideNum)
    W = np.random.rand(hideNum, Y.shape[1])
    W_b = np.random.rand(1, Y.shape[1])

    rate = 0.1
    error = 0.001
    maxTrainNum = 1000000
    trainNum = 0
    loss = 10

    while (loss > error) and (trainNum < maxTrainNum):
        for k in range(X.shape[0]):  # 标准bp方法一次只处理一个样本
            H = sigmod(X[k, :].dot(V) - V_b)  # 因为书上一直给出的是减去阈值，所以这里用减号。
            Y_ = sigmod(H.dot(W) - W_b)  # 其实大部分情况下人们都用的是加上偏置b这种表达方式
            loss = sum((Y[k] - Y_) ** 2) * 0.5  # 改成加号后只需要在下面更新参数时也用加号即可

            g = Y_ * (1 - Y_) * (Y[k] - Y_)  # 计算相应的梯度，及更新参数。 此处特别注意维度的正确对应关系
            e = H * (1 - H) * g.dot(W.T)
            W += rate * H.T.dot(g)
            W_b -= rate * g
            V += rate * X[k].reshape(1, X[k].size).T.dot(e)
            V_b -= rate * e
            trainNum += 1

    print("总训练次数：", trainNum)
    print("最终损失：", loss)
    print("V：", V)
    print("V_b：", V_b)
    print("W：", W)
    print("W_b：", W_b)


def bpAccum(hideNum,X, Y):  # 累积bp算法
    V = np.random.rand(X.shape[1], hideNum)
    V_b = np.random.rand(1, hideNum)
    W = np.random.rand(hideNum, Y.shape[1])
    W_b = np.random.rand(1, Y.shape[1])

    rate = 0.1
    error = 0.001
    maxTrainNum = 1000000
    trainNum = 0
    loss = 10

    while (loss > error) and (trainNum < maxTrainNum):
        H = sigmod(X.dot(V) - V_b)
        Y_ = sigmod(H.dot(W) - W_b)
        loss = 0.5 * sum((Y - Y_) ** 2) / X.shape[0]

        g = Y_ * (1 - Y_) * (Y - Y_)  # 对应元素相乘，类似于matlab中的点乘
        e = H * (1 - H) * g.dot(W.T)
        W += rate * H.T.dot(g)
        W_b -= rate * g.sum(axis=0)
        V += rate * X.T.dot(e)
        V_b -= rate * e.sum(axis=0)
        trainNum += 1

    print("总训练次数：", trainNum)
    print("最终损失：", loss)
    print("V：", V)
    print("V_b：", V_b)
    print("W：", W)
    print("W_b：", W_b)


if __name__ == '__main__':
    X, Y, _ = dataSet()
    Y = Y.reshape(Y.shape[0], 1)
    bpstand(5,X, Y)
    bpAccum(5,X, Y)