数据挖掘第三次课

笔记三：感知器算法原理和步骤。

 

程序实现：手撕感知机算法

函数1--训练样本数据：

# 创建训练样本数据,第一个1为阈值对应的w0,即b
def createTrainDataSet():
    trainData = [[1, 1, 4],
                 [1, 2, 3],
                 [1, -2, 3],
                 [1, -2, 2],
                 [1, 0, 1],
                 [1, 1, 2]]
    label = [1, 1, -1, -1, -1, -1]
    return trainData, label

函数2--测试样本数据：

# 创建测试样本数据
def createTestDataSet():
    testData = [[1, 1, 1],
                [1, 2, 0],
                [1, 1, 4],
                [1, 1, 3],
                [1, 3, 5],
                [1, 7, 2]]
    return testData

类3--感知器算法（该类包括初始化、sigmoid函数、PLA、测试分类函数、画图函数）：

# 感知机分类算法
class Perceptron_self():
    def __init__(self):  # 初始化函数
        self.traindataIn, self.trainlabelIn = createTrainDataSet()
        self.train_data = np.mat(self.traindataIn)  # 将特征数据列表转换成矩阵
        self.train_label = np.mat(self.trainlabelIn).transpose()  # 将标签数据列表转化为矩阵并进行转置
        self.testdata = createTestDataSet()         # 获取测试集样本数据
        self.m, self.n = np.shape(self.train_data)  # 获取矩阵的行和列，行m用来更新每一个W值，列n用来形成全1数组
        self.w = np.ones((self.n, 1))               # numpy中的ones函数是用于生成一个全1的数组

    def sigmoid(self, X):  # 定义激活函数--sigmoid()
        X = float(X)
        if X > 0:
            return 1
        elif X < 0:
            return -1
        else:
            return 0

    def pla(self):  # 感知机学习算法--PLA
        while True:
            iscompleted = True                 # 作为判断是否更新W的标志
            for i in range(self.m):
                if (self.sigmoid(np.dot(self.train_data[i], self.w)) == self.train_label[i]):  # 正确继续循环
                    continue
                else:
                    iscompleted = False
                    # 当WT+b>0,且y=-1:W=W-X;当WT+b<0,且y=+1:W=W+X. 即：[W=W+y*X]进行更新
                    self.w += (self.train_label[i] * self.train_data[i]).transpose()
            if iscompleted:
                break  # 判读全部样本均符合条件，循环退出
        return self.w

    def classify(self, inX, w):
        result = self.sigmoid(np.dot(np.mat(inX), w))
        if result > 0:
            return 1
        else:
            return -1

    def classifyall(self, datatest):
        predict = []
        for data in datatest:
            result = self.classify(data, self.w)
            predict.append(result)
        return predict

    def plotBestFit(self, traindata, label):
        dataArr = np.array(traindata)
        n = np.shape(dataArr)[0]
        xcord1 = []
        ycord1 = []
        xcord2 = []
        ycord2 = []
        for i in range(n):
            if int(label[i]) == 1:
                xcord1.append(dataArr[i, 1])
                ycord1.append(dataArr[i, 2])
            else:
                xcord2.append(dataArr[i, 1])
                ycord2.append(dataArr[i, 2])
        fig = plt.figure()
        ax = fig.add_subplot(111)
        ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
        ax.scatter(xcord2, ycord2, s=30, c='green')
        x = np.arange(-3.0, 3.0, 0.1)
        y = (-self.w[0] - self.w[1] * x) / self.w[2]
        ax.plot(x, y)
        plt.xlabel('X1')
        plt.ylabel('X2')
        plt.show()

训练结果展示：

测试结果展示：

 测试结果为：

完整代码为：

import numpy as np
import matplotlib.pyplot as plt

# 创建训练样本数据,第一个1为阈值对应的w0,即b
def createTrainDataSet():
    trainData = [[1, 1, 4],
                 [1, 2, 3],
                 [1, -2, 3],
                 [1, -2, 2],
                 [1, 0, 1],
                 [1, 1, 2]]
    label = [1, 1, -1, -1, -1, -1]
    return trainData, label


# 创建测试样本数据
def createTestDataSet():
    testData = [[1, 1, 1],
                [1, 2, 0],
                [1, 1, 4],
                [1, 1, 3],
                [1, 3, 5],
                [1, 7, 2]]
    return testData


# 感知机分类算法
class Perceptron_self():
    def __init__(self):  # 初始化函数
        self.traindataIn, self.trainlabelIn = createTrainDataSet()
        self.train_data = np.mat(self.traindataIn)  # 将特征数据列表转换成矩阵
        self.train_label = np.mat(self.trainlabelIn).transpose()  # 将标签数据列表转化为矩阵并进行转置
        self.testdata = createTestDataSet()         # 获取测试集样本数据
        self.m, self.n = np.shape(self.train_data)  # 获取矩阵的行和列，行m用来更新每一个W值，列n用来形成全1数组
        self.w = np.ones((self.n, 1))               # numpy中的ones函数是用于生成一个全1的数组

    def sigmoid(self, X):  # 定义激活函数--sigmoid()
        X = float(X)
        if X > 0:
            return 1
        elif X < 0:
            return -1
        else:
            return 0

    def pla(self):  # 感知机学习算法--PLA
        while True:
            iscompleted = True                 # 作为判断是否更新W的标志
            for i in range(self.m):
                if (self.sigmoid(np.dot(self.train_data[i], self.w)) == self.train_label[i]):  # 正确继续循环
                    continue
                else:
                    iscompleted = False
                    # 当WT+b>0,且y=-1:W=W-X;当WT+b<0,且y=+1:W=W+X. 即：[W=W+y*X]进行更新
                    self.w += (self.train_label[i] * self.train_data[i]).transpose()
            if iscompleted:
                break  # 判读全部样本均符合条件，循环退出
        return self.w

    def classify(self, inX, w):
        result = self.sigmoid(np.dot(np.mat(inX), w))
        if result > 0:
            return 1
        else:
            return -1

    def classifyall(self, datatest):
        predict = []
        for data in datatest:
            result = self.classify(data, self.w)
            predict.append(result)
        return predict

    def plotBestFit(self, traindata, label):
        dataArr = np.array(traindata)
        n = np.shape(dataArr)[0]
        xcord1 = []
        ycord1 = []
        xcord2 = []
        ycord2 = []
        for i in range(n):
            if int(label[i]) == 1:
                xcord1.append(dataArr[i, 1])
                ycord1.append(dataArr[i, 2])
            else:
                xcord2.append(dataArr[i, 1])
                ycord2.append(dataArr[i, 2])
        fig = plt.figure()
        ax = fig.add_subplot(111)
        ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
        ax.scatter(xcord2, ycord2, s=30, c='green')
        x = np.arange(-3.0, 3.0, 0.1)
        y = (-self.w[0] - self.w[1] * x) / self.w[2]
        ax.plot(x, y)
        plt.xlabel('X1')
        plt.ylabel('X2')
        plt.show()


if __name__ == '__main__':
    per = Perceptron_self()
    per.pla()

    # 训练
    traindata, label = createTrainDataSet()
    per.plotBestFit(traindata, label)

    # 测试
    testdata = createTestDataSet()
    predict = per.classifyall(testdata)
    per.plotBestFit(testdata, predict)

    # print(testdata, "\n", predict)
    # print("y={}x0+{}x1+{}x2".format(w[0],w[1],w[2]))