吴恩达人工智能-python实现逻辑回归

吴恩达人工智能

逻辑回归python代码实现

逐行注释

import numpy as np
import pandas as pd
from matplotlib import pyplot as plt

# 逻辑回归算法实现
# sigmoid函数和初始化数据

# 数组说第几列全是从0开始
def sigmoid(z):
    return 1 / (1 + np.exp(-z))

# 初始化数据，载入新数据
def init_data():
    data = np.loadtxt('data.csv')

    # 截取数据集第0列到第倒数第二列而且是正向的排序，0，1，2...-1
    # 也就是排除分类结果的那些列
    dataMatIn = data[:, 0:-1]

    # dataY是dataMatIn在第0列添加新的一列,全为1
    dataY = np.insert(dataMatIn, 0, 1, axis=1)

    # 第一列平方,构造关于第一列的平方根函数,
    dataMatIn[:, 1] = np.power(dataMatIn[:, 1], 2)

    # dataMatIn[:, 0] = np.power(dataMatIn[:, 0], 2)
    dataMatIn = np.insert(dataMatIn, 0, 1, axis=1)  # 特征数据集，添加1是构造常数项x0

    # 进行特征缩放
    # for i in range(1,3):
    #
    #      dataMatIn[:,i]=(dataMatIn[:,i]-np.mean(dataMatIn[:,i],axis=0))/np.std(dataMatIn[:,i])

    # classLabels是数据集的第1列,也是倒数第二列
    classLabels = data[:, -1]

    return dataY, dataMatIn, classLabels

#   梯度下降
def grad_descent(dataMatIn, classLabels):
    # dataMatrix是矩阵化的dataMatIn
    dataMatrix = np.mat(dataMatIn)  # (m,n)

    # labelMat是矩阵化的classLabels,并转置
    labelMat = np.mat(classLabels).transpose()

    # m是行，即有多少训练数据，n是列，
    m, n = np.shape(dataMatrix)

    # weights即为参数，初始化全为1
    weights = np.ones((n, 1))  # 初始化回归系数（n, 1)

    alpha = 0.01  # 步长

    maxCycle = 5000  # 最大循环次数

    # 进入梯度下降训练循环
    for i in range(maxCycle):
        # h是经过激活函数的 参数乘训练集(假设函数)
        h = sigmoid(dataMatrix * weights)  # sigmoid 函数

        # 精髓的一步
        # 用向量的方法实现梯度下降wj=wj-a/m*(sum(hi-yi)*xj)
        # 此处是没有进行正则化的编码（正则化目的是消除过拟合）
        weights = weights + alpha * dataMatrix.transpose() * (labelMat - h) / m  # 梯度

        # print(weights,'\n+')
        # print(alpha,'\n*')
        # print(dataMatrix.transpose(),'\n*')
        # print(labelMat-h)
        # print("=============================================================")

        # weights = weights - alpha * (1/m) * (h-labelMat) * ( dataMatrix.)
    return weights

# 正则化逻辑回归代码，非向量表示的
"""
def costReg(theta, X, y, learningRate):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)
    first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
    second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
    reg = (learningRate / (2 * len(X)) * np.sum(np.power(theta[:, 1:theta.shape[1]], 2))
    return np.sum(first -second) / (len(X)) + reg

"""

# 绘图

def plotBestFIt(weights):
    dataY, dataMatIn, classLabels = init_data()

    n = np.shape(dataMatIn)[0]

    xcord1 = []
    ycord1 = []
    xcord2 = []
    ycord2 = []
    for i in range(n):
        if classLabels[i] == 1:
            xcord1.append(dataY[i][1])
            ycord1.append(dataY[i][2])
        else:
            xcord2.append(dataY[i][1])
            ycord2.append(dataY[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, 3, 0.1)
    y = np.sqrt(((-weights[0, 0] - weights[1, 0] * x) / weights[2, 0]))  # matix
    ax.plot(x, y)
    plt.xlabel('X1')
    plt.ylabel('X2')
    plt.show()

# 计算结果
if __name__ == '__main__':
    dataY, dataMatIn, classLabels = init_data()
    r = grad_descent(dataMatIn, classLabels)
    print(r)
    plotBestFIt(r)