6.BP神经网络的python实现

from numpy import *
import matplotlib.pyplot as plt
import operator


class BPNet(object):
    def __init__(self):
        # 网络参数
        self.eb = 0.01  # 误差容限
        self.eta = 0.1  # 学习率
        self.mc = 0.3  # 动量因子
        self.maxiter = 2000  # 最大迭代次数
        self.errlist = []  # 误差列表
        self.dataMat = 0  # 数据集
        self.classLabels = 0  # 分类集
        self.nSampNum = 0  # 样本集行数
        self.nSampDim = 0  # 样本维度
        self.nHidden = 4;  # 隐含层神经元
        self.nOut = 1;  # 输出层
        self.iterator = 0  # 最优时迭代次数

    # 传递函数:
    def logistic(self, net):
        return 1.0 / (1.0 + exp(-net))

    # 传递函数的导函数
    def dlogit(self, net):
        return multiply(net, (1.0 - net))

    # 矩阵各元素平方之和
    def errorfunc(self, inX):
        return sum(power(inX, 2)) * 0.5

    # 数据标准化(归一化):        # 标准化
    def normalize(self, dataMat):
        [m, n] = shape(dataMat)
        for i in range(n - 1):
            dataMat[:, i] = (dataMat[:, i] - mean(dataMat[:, i])) / (std(dataMat[:, i]) + 1.0e-10)
        return dataMat

    # 加载数据集
    def loadDataSet(self, filename):
        self.dataMat = [];
        self.classLabels = []
        fr = open(filename)
        for line in fr.readlines():
            lineArr = line.strip().split()
            self.dataMat.append([float(lineArr[0]), float(lineArr[1]), 1.0])
            self.classLabels.append(int(lineArr[2]))
        self.dataMat = mat(self.dataMat)
        m, n = shape(self.dataMat)
        self.nSampNum = m;  # 样本数量
        self.nSampDim = n - 1;  # 样本维度

    # 增加新列
    def addcol(self, matrix1, matrix2):
        [m1, n1] = shape(matrix1)
        [m2, n2] = shape(matrix2)
        if m1 != m2:
            print
            "different rows,can not merge matrix"
            return;
        mergMat = zeros((m1, n1 + n2))
        mergMat[:, 0:n1] = matrix1[:, 0:n1]
        mergMat[:, n1:(n1 + n2)] = matrix2[:, 0:n2]
        return mergMat

    # 隐藏层初始化
    def init_hiddenWB(self):
        self.hi_w = 2.0 * (random.rand(self.nHidden, self.nSampDim) - 0.5)
        self.hi_b = 2.0 * (random.rand(self.nHidden, 1) - 0.5)
        self.hi_wb = mat(self.addcol(mat(self.hi_w), mat(self.hi_b)))

    # 输出层初始化
    def init_OutputWB(self):
        self.out_w = 2.0 * (random.rand(self.nOut, self.nHidden) - 0.5)
        self.out_b = 2.0 * (random.rand(self.nOut, 1) - 0.5)
        self.out_wb = mat(self.addcol(mat(self.out_w), mat(self.out_b)))

    # bp网主程序
    def bpTrain(self):
        # 数据集矩阵化
        SampIn = self.dataMat.T
        expected = mat(self.classLabels)
        self.init_hiddenWB()
        self.init_OutputWB()
        # 默认旧权值
        dout_wbOld = 0.0;
        dhi_wbOld = 0.0

        for i in range(self.maxiter):
            # 1. 工作信号正向传播

            # 1.1 输入层到隐含层
            hi_input = self.hi_wb * SampIn
            hi_output = self.logistic(hi_input)
            hi2out = self.addcol(hi_output.T, ones((self.nSampNum, 1))).T
            # 1.2 隐含层到输出层
            out_input = self.out_wb * hi2out
            out_output = self.logistic(out_input)

            # 2. 误差计算
            err = expected - out_output
            sse = self.errorfunc(err)
            self.errlist.append(sse);
            # 2.1 判断是否收敛至最优
            if sse <= self.eb:
                self.iterator = i + 1
                break;

            # 3.误差信号反向传播
            # 3.1 DELTA为输出层梯度
            DELTA = multiply(err, self.dlogit(out_output))
            # 3.2 delta为隐含层梯度
            delta = multiply(self.out_wb[:, :-1].T * DELTA, self.dlogit(hi_output))
            # 3.3 输出层权值微分
            dout_wb = DELTA * hi2out.T
            # 3.4 隐含层权值微分
            dhi_wb = delta * SampIn.T
            # 3.5 更新输出层和隐含层权值
            if i == 0:
                self.out_wb = self.out_wb + self.eta * dout_wb
                self.hi_wb = self.hi_wb + self.eta * dhi_wb
            else:
                self.out_wb = self.out_wb + (1.0 - self.mc) * self.eta * dout_wb + self.mc * dout_wbOld
                self.hi_wb = self.hi_wb + (1.0 - self.mc) * self.eta * dhi_wb + self.mc * dhi_wbOld
            dout_wbOld = dout_wb
            dhi_wbOld = dhi_wb

    # bp网分类器
    def BPClassfier(self, start, end, steps=30):
        x = linspace(start, end, steps)
        xx = mat(ones((steps, steps)))
        xx[:, 0:steps] = x
        yy = xx.T
        z = ones((len(xx), len(yy)));
        for i in range(len(xx)):
            for j in range(len(yy)):
                xi = [];
                tauex = [];
                tautemp = []
                mat(xi.append([xx[i, j], yy[i, j], 1]))
                hi_input = self.hi_wb * (mat(xi).T)
                hi_out = self.logistic(hi_input)
                taumrow, taucol = shape(hi_out)
                tauex = mat(ones((1, taumrow + 1)))
                tauex[:, 0:taumrow] = (hi_out.T)[:, 0:taumrow]
                out_input = self.out_wb * (mat(tauex).T)
                out = self.logistic(out_input)
                z[i, j] = out
        return x, z

    # 绘制分类线
    def classfyLine(self, plt, x, z):
        plt.contour(x, x, z, 1, colors='black')

    # 绘制趋势线: 可调整颜色
    def TrendLine(self, plt, color='r'):
        X = linspace(0, self.maxiter, self.maxiter)
        Y = log2(self.errlist)
        plt.plot(X, Y, color)

    # 绘制分类点
    def drawClassScatter(self, plt):
        i = 0
        for mydata in self.dataMat:
            if self.classLabels[i] == 0:
                plt.scatter(mydata[0, 0], mydata[0, 1], c='blue', marker='o')
            else:
                plt.scatter(mydata[0, 0], mydata[0, 1], c='red', marker='s')
            i += 1



bpnet = BPNet()
bpnet.loadDataSet(r"D:BPNet	estSet2.txt")
bpnet.dataMat = bpnet.normalize(bpnet.dataMat)

#绘制数据散点图
bpnet.drawClassScatter(plt)

#BP神经网络进行数据分类
bpnet.bpTrain()

print(bpnet.out_wb)
print(bpnet.hi_wb)

#计算和绘制分类线
x,z = bpnet.BPClassfier(-3.0,3.0)
bpnet.classfyLine(plt,x,z)
plt.show()

#绘制误差曲线
bpnet.TrendLine(plt)
plt.show()

 

误差曲线