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局部加权线性回归

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# -*- codeing = utf-8 -*-
# @Time : 2022/4/29 17:01
# @Author :
# @File : bao_1.py
# @Software : PyCharm
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import csv

from numpy import linalg


def multiplyList(myList) :
    for x in myList:
         if x == 0:
             return True
    return False;
def loadDataSet(fileName):
    dataMat = [];
    labelMat = []
    with open(fileName, 'r') as f:
        reader = csv.reader(f, delimiter='\t')
        for row in reader:
            row = [float(x) for x in row]
            dataMat.append(row[:-1])     #特征数据
            labelMat.append(row[-1])     #年龄数据
        for i in dataMat:
            if i[0]==0:
                i[0]=2
            elif i[0]==-1:
                i[0]=3
    return dataMat, labelMat
def get_w(X, Y):#普通的线性回归求解参数方法
    # 用普通最小二乘法求解，知道X,Y,求参数w   w=(X.T*X)(-1)*X.T*Y
    X_I = np.linalg.inv(np.dot(X.T, X))  # 返回矩阵的逆
    w = np.dot(np.dot(X_I, X.T), Y)  #矩阵乘法
    return w
def get_w_lwlr(X, Y, x_test):
    m = X.shape[0]
    # k = 0.01  #可变参数,衰减因子，即权重衰减的速率
    k=0.02
    weight = np.eye(m)   #生成对角矩阵
    for j in range(m):
        # 对于预测点，根据预测点与每一个样本点之间的接近程度，更新每一个样本点的权重
        diff = x_test - X[j, :]
        weight[j, j] = np.exp(np.dot(diff.T, diff) / (-2 * k ** 2))  #e的x幂次方,权重值大小以指数级衰减
    # 局部加权之后，重新计算得到新的参数w_lwlr
    X_w = np.linalg.inv(np.dot(np.dot(X.T, weight), X))
    w = np.dot(np.dot(np.dot(X_w, X.T), weight), Y)
    return w

def score(X,Y,testx,testy):
    num = 0
    sum1 = 0
    sum2 = 0
    sum4 = 0
    sum5 = 0
    sum3 = sum(testy[0:1000])-testy[165]-testy[276]-testy[277]-testy[355]-testy[762]-testy[999]-testy[510]
    sum3 = sum3/993
    mse = 0
    mae = 0
    for i in range(1000):
        if multiplyList(testx[i]) or i==165 or i==276 or i==277 or i==355 or i==762 or i==999 or i==510:
            continue
        w_lwlr = get_w_lwlr(X, Y, testx[i])
        y2 = np.dot(np.array(testx[i]), w_lwlr.T)
        if (testy[i]-0.5)<=y2<=(testy[i]+0.5):
            num = num +1
        print(testx[i],i)
        print("真实值：",testy[i])
        w = get_w(X, Y)
        y1 = np.dot(np.array(testx[i]), w.T)
        sum1 = (y2-testy[i])**2+sum1
        sum4 = (y1-testy[i])**2+sum4
        sum2 = (sum3-testy[i])**2+sum2
        sum5 = abs(y2-testy[i])+sum5
        print("局部加权预测值：", y2)
        print("普通线性回归预测值：", y1)
    print("局部加权线性回归R^2分析:",1-sum1/sum2)
    print("普通线性回归R^2分析:", 1 - sum4/sum2)
    print("mae平均绝对误差:",sum1/993)
    print("mse均方误差：",sum5/993)

def main():
    dataMat, labelMat = loadDataSet('abalone.txt')
    print(dataMat)
    X = np.array(dataMat)
    Y = np.array(labelMat).T
    score(X,Y,dataMat,labelMat);

if __name__ == '__main__':
    main()