k-means聚类算法： python实现

code

import numpy as np
import matplotlib.pyplot as plt
import random



def kMeans(daSet, K):
    centerPoint = random.sample(daSet, K)

    center_dis = 9999
    iterNum = 0
    while np.mean(center_dis) > 1e-6:
        ind = assignment(daSet, centerPoint)
        newCenterPoint = update(daSet, ind, K)
        center_dis = [calDis(centerPoint[i],newCenterPoint[i]) for i in range(K)]
        centerPoint = newCenterPoint #new iteration
        iterNum += 1
        print("cent Dis: ", center_dis, np.mean(center_dis))
    return newCenterPoint, ind, iterNum


def assignment(daSet, centerPoint):
    dis_all = [[calDis(point, center) for center in centerPoint] for point in daSet]
    ind = np.array(dis_all).argmin(axis=1) #注意不是min或nanmin求极值，而是求极值对应的序号，以后续选择cluster归属

    print(dis_all,"\n ind= ", ind)
    return ind

def update(daSet, ind, K):
    newCenterPoint = []#np.array([[]])
    for i in range(0,K):
        clu_i_ind = np.argwhere(np.array(ind)==i)
        #print(clu_i_ind, clu_i_ind.__class__)
        clu = np.array(daSet)[clu_i_ind]
        newCenterPoint.append((np.mean(clu, axis=0)))
        #newCenterPoint = np.append(newCenterPoint, np.mean(clu, axis=0), axis = 0)
    print("clu", clu, np.array(newCenterPoint).squeeze())
    return np.array(newCenterPoint).squeeze()

def calDis(p1,p2):
    #这里采用欧式距
    return np.sqrt(np.sum(np.power(np.array(p1)-np.array(p2),2)))

def createDataSet():
    return [[1,1], [2,1], [3,1], [2,3], [10,9], [9,9],[7,8],[6,5],[10,11], [3,3],[13,12], [13,10],[-5,-2],[-10,-9],[-8,-7]]


if __name__ == "__main__":
    daSet = createDataSet()
    newCenterPoint, ind, iterNum = kMeans(daSet, 3)
    cl = ['bs','k<','c*','yo']
    print("Final", newCenterPoint, ind, "\n iterative rounds:\n",iterNum)
    plt.figure()
    plt.plot(np.array(newCenterPoint)[:,0], np.array(newCenterPoint)[:,1], 'xr')

    for ii, ele in enumerate(daSet):

        plt.plot(ele[0], ele[1], cl[ ind[ii]]) #ind[ii]指明所属，利用cl[]区分不同属的个体；想要输出clu，可以argwhere查找ind==i
    plt.show()

• 主要函数为：创建数据（也可以用正态分布随机生成，效果更好）、控制流程的k-means、主要的分配assigment和更新update两个迭代步骤；分别负责按照距离最小分类、和计算新的类中心；根据中心点不变来判决收敛了； 最后mian函数里图形输出

results

来源

https://en.wikipedia.org/wiki/K-means_clustering

问题

• 数据存储结构设计为list还是array，有问题；array方便处理，list更方便创建和刷新
• 如何根据索引分类：采用ind = np.argmin, cl_ind = np.argwhere(ind), dataSet(cl_ind)输出每一类

改进生数

import numpy as np
import matplotlib.pyplot as plt
import random

cl = ['bs', 'k<', 'c*', 'yo']

def kMeans(daSet, K):
    centerPoint = random.sample(daSet, K)

    center_dis = 9999
    iterNum = 0
    while np.mean(center_dis) > 1e-6:
        ind = assignment(daSet, centerPoint)
        newCenterPoint = update(daSet, ind, K)
        center_dis = [calDis(centerPoint[i],newCenterPoint[i]) for i in range(K)]
        centerPoint = newCenterPoint #new iteration
        iterNum += 1
        print("cent Dis: ", center_dis, np.mean(center_dis))
    return newCenterPoint, ind, iterNum


def assignment(daSet, centerPoint):
    dis_all = [[calDis(point, center) for center in centerPoint] for point in daSet]
    ind = np.array(dis_all).argmin(axis=1) #注意不是min或nanmin求极值，而是求极值对应的序号，以后续选择cluster归属

    print(dis_all,"\n ind= ", ind)
    return ind

def update(daSet, ind, K):
    newCenterPoint = []#np.array([[]])
    for i in range(0,K):
        clu_i_ind = np.argwhere(np.array(ind)==i)
        #print(clu_i_ind, clu_i_ind.__class__)
        clu = np.array(daSet)[clu_i_ind]
        newCenterPoint.append((np.mean(clu, axis=0)))
        #newCenterPoint = np.append(newCenterPoint, np.mean(clu, axis=0), axis = 0)
    print("clu", clu, np.array(newCenterPoint).squeeze())
    return np.array(newCenterPoint).squeeze()

def calDis(p1,p2):
    #这里采用欧式距
    return np.sqrt(np.sum(np.power(np.array(p1)-np.array(p2),2)))

def createDataSet(flag = "simple"):
    if flag == "norm":
        num = 100
        norm1 = (5 * np.random.randn(num,2) - np.array([10, 0])).tolist()
        norm2 = (10 * np.random.randn(num,2) - np.array([0, 0])).tolist()
        norm3 = (5 * np.random.randn(num,2) - np.array([-10, 0])).tolist()
        norm4 = (20 * np.random.randn(num,2) - np.array([-5, 5])).tolist()
        norm1.extend(norm2)
        norm1.extend(norm3)
        norm1.extend(norm4)
        plt.figure()
        for i in range(4):
            plt.plot(np.array(norm1[100*i:100*(i+1)])[:,0],np.array(norm1[100*i:100*(i+1)])[:,1], cl[i])
        return random.sample(norm1, num*4)
    else:
        return [[1,1], [2,1], [3,1], [2,3], [10,9], [9,9],[7,8],[6,5],[10,11], [3,3],[13,12], [13,10],[-5,-2],[-10,-9],[-8,-7]]


if __name__ == "__main__":
    daSet = createDataSet("norm")
    newCenterPoint, ind, iterNum = kMeans(daSet, 4)
    print("Final: *****", newCenterPoint, ind, "\n\n iterative rounds:",iterNum)
    plt.figure()
    for ii, ele in enumerate(daSet):
        plt.plot(ele[0], ele[1], cl[ ind[ii]]) #ind[ii]指明所属，利用cl[]区分不同属的个体；想要输出clu，可以argwhere查找ind==i

    #lable cental points:
    plt.plot(np.array(newCenterPoint)[:,0], np.array(newCenterPoint)[:,1], 'xr')
    plt.show()