逻辑回归模型——python代码实现

• 逻辑回归的推导过程：https://blog.csdn.net/ACM_hades/article/details/90448785
• 代码主要实现了下面公式：$$W^{k+1}=W^k+\lambda X(Y-f_{W^k}(X^T))$$
• 数据集：我们选择MNIST数据集进行实验，它包含各种手写数字(0-9)图片，图片大小28*28。MNIST数据集本身有10个类别，为了将其变成二分类问题我们进行如下处理：label等于0的继续等于0，label大于0改为1。这样就将十分类的数据改为二分类的数据。
• 特征选择：可选择的特征有很多，包括：
  • 自己提取特征
  • 将整个图片作为特征向量
  • HOG特征
• 我们将整个图片作为特征(784=28×28)。

import time
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score


class Logistic:
    def __init__(self,feature_len):
        self.weights = np.ones((feature_len, 1))


    def model_function(self, X):
        W_X=np.matmul(X, self.weights)
        temp_1=(W_X>=0).astype(np.float)
        temp_0 = (W_X < 0).astype(np.float)
        resut_1=1.0 / (1 + np.exp(-temp_1*W_X))*temp_1
        #W_X为负数是，因为参数值inx很大时，exp(inx)可能会发生溢出，所以修改计算方式
        resut_0 = np.exp(temp_0*W_X) / (1 + np.exp(temp_0*W_X))*temp_0
        return resut_1+resut_0

    def train(self, Data, label):   #训练
        label = label.reshape((-1,1))
        alpha = 0.01
        max_iter = 500
        for i in range(max_iter):    #迭代
            pres = self.model_function(Data)
            error = label-pres    #预测值和标签值所形成的误差
            self.weights = self.weights +  alpha * np.matmul(Data.T , error)   #权重的更新

    def predict(self, Data):
        return self.model_function(Data).reshape(-1)

if __name__ == '__main__':
    print('Start read data')
    S = time.time()
    raw_data = pd.read_csv('./lihang_book_algorithm-master/data/train_binary.csv')  # 读取数据
    data = raw_data.values  # 获取数据
    print("data shape:", data.shape)
    imgs = data[:, 1:]
    labels = data[:, 0]
    print("imgs shape:", imgs.shape)
    imgs = np.concatenate((imgs, np.ones((imgs.shape[0], 1))), axis=1)#拼接常数项
    print("imgs shape:", imgs.shape)
    print("labels shape:", labels.shape)
    print("label:",list(set(labels)))
    Model = Logistic(imgs.shape[-1])

    # 选取 2/3 数据作为训练集， 1/3 数据作为测试集
    train_features, test_features, train_labels, test_labels = train_test_split(
        imgs, labels, test_size=0.33, random_state=23323)
    print("train data count ：%d" % len(train_labels))
    print("test data count ：%d" % len(test_labels))
    print('read data cost ', time.time() - S, ' second')

    print('Start training')
    S = time.time()
    Model.train(train_features, train_labels)
    print('training cost ', time.time() - S, ' second')

    print('Start predicting')
    S = time.time()
    test_predict = Model.predict(test_features)
    print('predicting cost ', time.time() - S, ' second')

    score = accuracy_score(test_labels, test_predict)
    print("The accruacy socre is ", score)

结果：
	Start read data
	data shape: (42000, 785)
	imgs_origin shape: (42000, 784)
	imgs shape: (42000, 785)
	labels shape: (42000,)
	label: [0, 1]
	train data count ：28140
	test data count ：13860
	read data cost  4.148890018463135  second
	Start training
	training cost  15.161401748657227  second
	Start predicting
	predicting cost  0.007978200912475586  second
	The accruacy socre is  0.9892496392496393