softmax回归

基本知识

Softmax 回归是一种多分类模型，也称做多类Logistic回归；

模型假设

代价函数

梯度计算

代码实现

import numpy as np
import math
import matplotlib.pyplot as plt
import random

#获取数据
def getData():
    X=[]
    Y=[]
    X0=[]
    X1=[]
    X2=[]
    Y0=[]
    with open("./ex4Data/ex4x.dat") as f:
        for line in f.readlines():
            data =line.split('\n\t')
            for str0 in data:
                sub_str = str0.split(' ')
            if sub_str:
                X.append(sub_str)
    for i in range(0,80):
        X0.append(float(1))
        X1.append(float(X[i][3]))
        X2.append(float(X[i][6]))
    X=[X0,X1,X2]
    with open("./ex4Data/ex4y.dat") as f2:
        for line in f2.readlines():
            data =line.split('\n\t')
            for str0 in data:
                sub_str=str0.split(' ')
            if sub_str:
                Y0.append(sub_str)
    for i in range(0,80):
        Y.append(float(Y0[i][3]))

    xMat=np.mat(X).T
    yMat=np.mat(Y).T
    x0Mat=np.mat(X0)
    return xMat,yMat,x0Mat

xMat,yMat,x0Mat=getData()

#softmax函数
def softMax(x):
    return np.exp(x)/np.sum(np.exp(x),axis=0)
#损失函数
def cost(x,y,weights):
    m,n=x.shape
    hypothesis=softMax( np.dot(weights,x.T) )
    cost=(-1/m)*np.sum(np.diagonal(np.dot(y,np.log(hypothesis))))
    return cost

#one_hot编码
def one_hot(y):
    m,n=y.shape  #80*1
    for i in range(0,m):
        if i<40:
            y[i]=[0,1]
        else:
            y[i]=[1,0]
    return y
#批处理梯度下降
def Training(x,y,alpha=0.001,maxepoch=3000):

    x_m,x_n=x.shape#80*3
    y_m,y_n=y.shape#80*2
    y=one_hot(y)
    weights=np.zeros((y_n,x_n)) #2*3
    
    epoch=0
    loss_list=[]
    while epoch<maxepoch:
        loss=cost(x,y,weights)
        hypothesis=softMax( np.dot(weights,x.T) )#80*3
        grad=(-y.T+hypothesis)*x 
        weights=weights-alpha*grad
        loss_list.append(loss)
        epoch+=1
        print("这是第"+str(epoch)+"次迭代")
    plt.plot(loss_list)
    plt.show()
    return weights
#随机梯度下降
def SGD_Training(x,y,alpha=0.001,maxepoch=10000):
    x_m,x_n=x.shape#80*3
    y_m,y_n=y.shape#80*2
    y=one_hot(y)
    weights=np.zeros((y_n,x_n)) #2*3
    
    weights[0]=[0.2,-1.13,0.5]
    weights[1]=[-0.2,1.13,0.5]
    epoch=0
    loss_list=[]
    while epoch<maxepoch:
        i=random.randint(0,x_m-1)
        data_x=x[i]
        data_y=y[i]
        loss=cost(x,y,weights)
        hypothesis=softMax( np.dot(weights,data_x.T) )#80*3
        grad=(-data_y.T+hypothesis)*data_x
        weights=weights-alpha*grad
        loss_new=cost(x,y,weights)
        if abs(loss_new-loss)<0.000001:
            break
        loss_list.append(loss)
        epoch+=1
        print("这是第"+str(epoch)+"次迭代")
    plt.plot(loss_list)
    plt.show()
    return weights
    
weights=SGD_Training(xMat,yMat)
print(weights)