图文详解牛顿迭代算法原理及Python实现

import pandas as pd
import numpy as np
import os
import matplotlib.pyplot as plt
import matplotlib as mpl
from Logit import Logit

'''
* @breif: 从CSV中加载指定数据
* @param[in]: file -> 文件名
* @param[in]: colName -> 要加载的列名
* @param[in]: mode -> 加载模式, set: 列名与该列数据组成的字典, df: df类型
* @retval: mode模式下的返回值
'''
def loadCsvData(file, colName, mode='df'):
    assert mode in ('set', 'df')
    df = pd.read_csv(file, encoding='utf-8-sig', usecols=colName)
    if mode == 'df':
        return df
    if mode == 'set':
        res = {}
        for col in colName:
            res[col] = df[col].values
        return res

if __name__ == '__main__':
    # ============================
    # 读取CSV数据
    # ============================
    csvPath = os.path.abspath(os.path.join(__file__, "../../data/dataset3.0alpha.csv"))
    dataX = loadCsvData(csvPath, ["含糖率", "密度"], 'df')
    dataY = loadCsvData(csvPath, ["好瓜"], 'df')
    label = np.array([
        1 if i == "是" else 0
        for i in list(map(lambda s: s.strip(), list(dataY['好瓜'])))
    ])

    # ============================
    # 绘制样本点
    # ============================
    line_x = np.array([np.min(dataX['密度']), np.max(dataX['密度'])])
    mpl.rcParams['font.sans-serif'] = [u'SimHei']
    plt.title('对数几率回归模拟\nLogistic Regression Simulation')
    plt.xlabel('density')
    plt.ylabel('sugarRate')
    plt.scatter(dataX['密度'][label==0],
                dataX['含糖率'][label==0],
                marker='^',
                color='k',
                s=100,
                label='坏瓜')
    plt.scatter(dataX['密度'][label==1],
                dataX['含糖率'][label==1],
                marker='^',
                color='r',
                s=100,
                label='好瓜')

    # ============================
    # 实例化对数几率回归模型
    # ============================
    logit = Logit(dataX, label)

    # 采用牛顿迭代法
    logit.logitRegression(logit.newtomMethod)
    line_y = -logit.w[0, 0] / logit.w[1, 0] * line_x - logit.w[2, 0] / logit.w[1, 0]
    plt.plot(line_x, line_y, 'g-', label="牛顿迭代法")

    # 绘图
    plt.legend(loc='upper left')
    plt.show()

    '''
    * @breif: 牛顿迭代法更新权重
    * @param[in]: None
    * @retval: 优化参数的增量dw
    '''
    def newtomMethod(self):
        wTx = np.dot(self.w.T, self.X).reshape(-1, 1)
        p = Logit.sigmod(wTx)
        dw_1 = -self.X.dot(self.y - p)
        dw_2 = self.X.dot(np.diag((p * (1 - p)).reshape(self.N))).dot(self.X.T)
        dw = np.linalg.inv(dw_2).dot(dw_1)
        return dw