【机器学习】PyTorch手动实现Logistic算法

news2024/11/26 12:51:37

参考地址：点击打开

计算较为繁琐，需要用到sigmoid函数和梯度下降算法，步骤主要如下：

二项分布概率公式表示
最大似然估计和对数化计算
求道
带入梯度下降算法计算和优化

在这里插入图片描述

代码：

import numpy as np
import matplotlib.pyplot as plt

def sigmoid(z):
    return 1.0/(1+np.exp(-z))


# datas NxD
# labs Nx1
# w    Dx1

def weight_update(datas,labs,w,alpha=0.01):
    z = np.dot(datas,w) # Nx1
    h = sigmoid(z)        # Nx1
    Error = labs-h        # Nx1 
    w = w + alpha*np.dot(datas.T,Error)
    return w
    
def train_LR(datas,labs,n_epoch=2,alpha=0.005):
    N,D = np.shape(datas)   
    w = np.ones([D,1])  # Dx1
    # 进行n_epoch轮迭代
    for i in range(n_epoch):
        w = weight_update(datas,labs,w,alpha)
        error_rate=test_accuracy(datas,labs,w)
        print("epoch %d error %.3f%%"%(i,error_rate*100))
    return w
    
def test_accuracy(datas,labs,w):
    N,D = np.shape(datas)
    z = np.dot(datas,w) # Nx1
    h = sigmoid(z)        # Nx1
    lab_det = (h>0.5).astype(np.float)
    error_rate=np.sum(np.abs(labs-lab_det))/N
    return error_rate
    
def draw_desion_line(datas,labs,w,name="0.jpg"):
    dic_colors={0:(.8,0,0),1:(0,.8,0)}
  
    # 画数据点
    for i in range(2):
        index = np.where(labs==i)[0]
        sub_datas = datas[index]
        plt.scatter(sub_datas[:,1],sub_datas[:,2],s=16.,color=dic_colors[i])
    
    # 画判决线
    min_x = np.min(datas[:,1])
    max_x = np.max(datas[:,1])
    w = w[:,0]
    x = np.arange(min_x,max_x,0.01)
    y = -(x*w[1]+w[0])/w[2]
    plt.plot(x,y)
    
    plt.savefig(name)
    
def load_dataset(file):    
    with open(file,"r",encoding="utf-8") as f:
        lines = f.read().splitlines()
    
    # 取 lab 维度为 N x 1
    labs = [line.split("\t")[-1] for line in lines]
    labs = np.array(labs).astype(np.float32)
    labs= np.expand_dims(labs,axis=-1) # Nx1
    
    # 取数据 增加 一维全是1的特征
    datas = [line.split("\t")[:-1] for line in lines]
    datas = np.array(datas).astype(np.float32)
    N,D = np.shape(datas)
    # 增加一个维度
    datas = np.c_[np.ones([N,1]),datas]
    return datas,labs
    
if __name__ == "__main__":
    ''' 实验1 基础测试数据'''
    # 加载数据
    file = "testset.txt"
    datas,labs = load_dataset(file)
    
    weights = train_LR(datas,labs,alpha=0.001,n_epoch=800)
    print(weights)
    draw_desion_line(datas,labs,weights,name="test_1.jpg")

训练需要的数据集testset.txt文件：

-0.017612	14.053064	0
-1.395634	4.662541	1
-0.752157	6.538620	0
-1.322371	7.152853	0
0.423363	11.054677	0
0.406704	7.067335	1
0.667394	12.741452	0
-2.460150	6.866805	1
0.569411	9.548755	0
-0.026632	10.427743	0
0.850433	6.920334	1
1.347183	13.175500	0
1.176813	3.167020	1
-1.781871	9.097953	0
-0.566606	5.749003	1
0.931635	1.589505	1
-0.024205	6.151823	1
-0.036453	2.690988	1
-0.196949	0.444165	1
1.014459	5.754399	1
1.985298	3.230619	1
-1.693453	-0.557540	1
-0.576525	11.778922	0
-0.346811	-1.678730	1
-2.124484	2.672471	1
1.217916	9.597015	0
-0.733928	9.098687	0
-3.642001	-1.618087	1
0.315985	3.523953	1
1.416614	9.619232	0
-0.386323	3.989286	1
0.556921	8.294984	1
1.224863	11.587360	0
-1.347803	-2.406051	1
1.196604	4.951851	1
0.275221	9.543647	0
0.470575	9.332488	0
-1.889567	9.542662	0
-1.527893	12.150579	0
-1.185247	11.309318	0
-0.445678	3.297303	1
1.042222	6.105155	1
-0.618787	10.320986	0
1.152083	0.548467	1
0.828534	2.676045	1
-1.237728	10.549033	0
-0.683565	-2.166125	1
0.229456	5.921938	1
-0.959885	11.555336	0
0.492911	10.993324	0
0.184992	8.721488	0
-0.355715	10.325976	0
-0.397822	8.058397	0
0.824839	13.730343	0
1.507278	5.027866	1
0.099671	6.835839	1
-0.344008	10.717485	0
1.785928	7.718645	1
-0.918801	11.560217	0
-0.364009	4.747300	1
-0.841722	4.119083	1
0.490426	1.960539	1
-0.007194	9.075792	0
0.356107	12.447863	0
0.342578	12.281162	0
-0.810823	-1.466018	1
2.530777	6.476801	1
1.296683	11.607559	0
0.475487	12.040035	0
-0.783277	11.009725	0
0.074798	11.023650	0
-1.337472	0.468339	1
-0.102781	13.763651	0
-0.147324	2.874846	1
0.518389	9.887035	0
1.015399	7.571882	0
-1.658086	-0.027255	1
1.319944	2.171228	1
2.056216	5.019981	1
-0.851633	4.375691	1
-1.510047	6.061992	0
-1.076637	-3.181888	1
1.821096	10.283990	0
3.010150	8.401766	1
-1.099458	1.688274	1
-0.834872	-1.733869	1
-0.846637	3.849075	1
1.400102	12.628781	0
1.752842	5.468166	1
0.078557	0.059736	1
0.089392	-0.715300	1
1.825662	12.693808	0
0.197445	9.744638	0
0.126117	0.922311	1
-0.679797	1.220530	1
0.677983	2.556666	1
0.761349	10.693862	0
-2.168791	0.143632	1
1.388610	9.341997	0
0.317029	14.739025	0