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
