高斯判别分析（GDA）Python代码

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）

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GDA Python代码

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2018/8/812:56
# @Author  : DaiPuWei
# E-Mail   : [email protected]
# @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()

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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