高斯判别分析（GDA）Python代码---AI那点小事

概要

本篇博客主要是高斯判别分析（GDA）的Python代码。对于GDA的理论讲解请移步我的另一篇博客：斯坦福机器学习笔记（三）—— 高斯判别分析。高斯判别分析的PDF资源请移步：斯坦福机器学习笔记（三）—— 高斯判别分析（GDA）

GDA Python代码#!/usr/bin/env python # -*- coding: utf-8 -*- # @Time : 2018/8/812:56 # @Author : DaiPuWei # E-Mail : 771830171@qq.com # @Site : 湖北省荆州市公安县自强中学 # @File : GDA.py # @Software: PyCharm import numpy as np from sklearn.model_selection import train_test_split from sklearn.datasets import load_breast_cancer from sklearn.preprocessing import MinMaxScaler from sklearn.metrics import accuracy_score from sklearn.linear_model import LogisticRegression import matplotlib as mpl import matplotlib.pyplot as plt class GDA: def __init__(self,train_data,train_label): """ 这是GDA算法构造函数 :param train_data: 训练数据 :param train_label: 训练数据标签 """ self.Train_Data = train_data self.Train_Label = train_label self.postive_num = 0 # 正样本个数 self.negetive_num = 0 # 负样本个数 postive_data = [] # 正样本数组 negetive_data = [] # 负样本数组 for (data,label) in zip(self.Train_Data,self.Train_Label): if label == 1: # 正样本 self.postive_num += 1 postive_data.append(list(data)) else: # 负样本 self.negetive_num += 1 negetive_data.append(list(data)) # 计算正负样本的二项分布的概率 row,col = np.shape(train_data) self.postive = self.postive_num*1.0/row # 正样本的二项分布概率 self.negetive = 1-self.postive # 负样本的二项分布概率 # 计算正负样本的高斯分布的均值向量 postive_data = np.array(postive_data) negetive_data = np.array(negetive_data) postive_data_sum = np.sum(postive_data, 0) negetive_data_sum = np.sum(negetive_data, 0) self.mu_positive = postive_data_sum*1.0/self.postive_num # 正样本的高斯分布的均值向量 self.mu_negetive = negetive_data_sum*1.0/self.negetive_num # 负样本的高斯分布的均值向量 # 计算高斯分布的协方差矩阵 positive_deta = postive_data-self.mu_positive negetive_deta = negetive_data-self.mu_negetive self.sigma = [] for deta in positive_deta: deta = deta.reshape(1,col) ans = deta.T.dot(deta) self.sigma.append(ans) for deta in negetive_deta: deta = deta.reshape(1,col) ans = deta.T.dot(deta) self.sigma.append(ans) self.sigma = np.array(self.sigma) #print(np.shape(self.sigma)) self.sigma = np.sum(self.sigma,0) self.sigma = self.sigma/row self.mu_positive = self.mu_positive.reshape(1,col) self.mu_negetive = self.mu_negetive.reshape(1,col) def Gaussian(self, x, mean, cov): """ 这是自定义的高斯分布概率密度函数 :param x: 输入数据 :param mean: 均值向量 :param cov: 协方差矩阵 :return: x的概率 """ dim = np.shape(cov)[0] # cov的行列式为零时的措施 covdet = np.linalg.det(cov + np.eye(dim) * 0.001) covinv = np.linalg.inv(cov + np.eye(dim) * 0.001) xdiff = (x - mean).reshape((1, dim)) # 概率密度 prob = 1.0 / (np.power(np.power(2 * np.pi, dim) * np.abs(covdet), 0.5)) * np.exp(-0.5 * xdiff.dot(covinv).dot(xdiff.T))[0][0] return prob def predict(self,test_data): predict_label = [] for data in test_data: positive_pro = self.Gaussian(data,self.mu_positive,self.sigma) negetive_pro = self.Gaussian(data,self.mu_negetive,self.sigma) if positive_pro >= negetive_pro: predict_label.append(1) else: predict_label.append(0) return predict_label def run_main(): """ 这是主函数 """ # 导入乳腺癌数据 breast_cancer = load_breast_cancer() data = np.array(breast_cancer.data) label = np.array(breast_cancer.target) data = MinMaxScaler().fit_transform(data) # 解决画图是的中文乱码问题 mpl.rcParams['font.sans-serif'] = [u'simHei'] mpl.rcParams['axes.unicode_minus'] = False # 分割训练集与测试集 train_data,test_data,train_label,test_label = train_test_split(data,label,test_size=1/4) # 数据可视化 plt.scatter(test_data[:,0],test_data[:,1],c = test_label) plt.title("乳腺癌数据集显示") plt.show() # GDA结果 gda = GDA(train_data,train_label) test_predict = gda.predict(test_data) print("GDA的正确率为：",accuracy_score(test_label,test_predict)) # 数据可视化 plt.scatter(test_data[:,0],test_data[:,1],c = test_predict) plt.title("GDA分类结果显示") plt.show() # Logistic回归结果 lr = LogisticRegression() lr.fit(train_data,train_label) test_predict = lr.predict(test_data) print("Logistic回归的正确率为：",accuracy_score(test_label,test_predict)) # 数据可视化 plt.scatter(test_data[:,0],test_data[:,1],c = test_predict) plt.title("Logistic回归分类结果显示") plt.show() if __name__ == '__main__': run_main()结果分析

以下是上述程序的结果截图：

明显看到，GDA的效果略微差于Logistic回归，这也证实了GDA的模型假设更强，当数据不是特别服从高斯分布时，效果略差于LR。LR更具备鲁棒性，实用性更强

---来自腾讯云社区的---AI那点小事