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