机器学习导论（附录）–LDA之Python代码

附上 LDA 的 python 代码实现，后期在补充上基于西瓜数据的分类效果

#!/usr/bin/env python
#-*- coding: utf-8 -*-

'''
LDA 算法实现
'''

import os
import sys
import numpy as np
from numpy import *
import operator
import matplotlib
import matplotlib.pyplot as plt


def createDataSet():
	#group=array([[1.0,1.1], [1.0,1.0], [0,0], [0,0.1], [1.1, 1.2], [0.1, 0.2]])
	#labels=['A','A','B','B']
	#group1=mat([[x for x in range(1,6)], [x for x in range(1,6)]])
	#group2=mat([[x for x in range(10,15)], [x for x in range(15, 20)]])	
	group1=mat(random.random((2,8))*5+20)
	group2=mat(random.random((2,8))*5+2)
	return group1, group2
#end of createDataSet

def draw(group):
	fig=plt.figure()
	plt.ylim(0, 30)
	plt.xlim(0, 30)
	ax=fig.add_subplot(111)
	ax.scatter(group[0,:], group[1,:])
	plt.show()
#end of draw

#计算样本均值 
#参数 samples 为 nxm 维矩阵，其中 n 表示维数，m 表示样本个数
def compute_mean(samples):
	mean_mat=mean(samples, axis=1)
	return mean_mat
#end of compute_mean

#计算样本类内离散度
#参数 samples 表示样本向量矩阵，大小为 nxm，其中 n 表示维数，m 表示样本个数
#参数 mean 表示均值向量，大小为 1xd，d 表示维数，大小与样本维数相同，即 d=m
def compute_withinclass_scatter(samples, mean):
	#获取样本维数，样本个数	
	dimens,nums=samples.shape[:2]
	#将所有样本向量减去均值向量
	samples_mean=samples-mean
	#初始化类内离散度矩阵	
	s_in=0	
	for i in range(nums):
		x=samples_mean[:,i]
		s_in+=dot(x,x.T)
	#endfor
	return s_in
#end of compute_mean


if __name__=='__main__':
	group1,group2=createDataSet()
	print "group1 :\n",group1
	print "group2 :\n",group2
	draw(hstack((group1, group2)))
	mean1=compute_mean(group1)
	print "mean1 :\n",mean1
	mean2=compute_mean(group2)
	print "mean2 :\n",mean2
	s_in1=compute_withinclass_scatter(group1, mean1)
	print "s_in1 :\n",s_in1
	s_in2=compute_withinclass_scatter(group2, mean2)
	print "s_in2 :\n",s_in2
	#求总类内离散度矩阵
	s=s_in1+s_in2
	print "s :\n",s	
	#求 s 的逆矩阵
	s_t=s.I
	print "s_t :\n",s_t
	#求解权向量
	w=dot(s_t, mean1-mean2)
	print "w :\n",w
	#判断(2,3)是在哪一类
	test1=mat([1,1])
	g=dot(w.T, test1.T-0.5*(mean1-mean2))
	print "g(x) :",g
	#判断(4,5)是在哪一类
	test2=mat([10,10])
	g=dot(w.T, test2.T-0.5*(mean1-mean2))
	print "g(x) :",g
#endif