无监督--聚类算法

聚类算法

概述: 训练数据不存在类别标签信息，而且我们又需要根据数据特征将数据分成不同的类别， 聚类有时也被分为无监督分类，

和监督分类区别在于，聚类的训练数据没有对应的y值，而监督算法的数据有对应y值。

经典算法：K-均值聚类

K-均值聚类算法

优点：容易实现；

缺点：可能收敛到局部最小值，在大规模数据集上收敛较慢

适用数据类型： 数值型数据

思想：给定数据集k个簇的算法，簇的个数由用户给定，每个簇通过其质心，即簇中所有点的中心描述。

1、随机确定k个初始点作为质心；
2、为数据集中的每一个点找其最近的质心，并将其分配给该质心对应的簇

K-均值效果差的原因：

k-均值算法收敛到了局部最小值，而非全局最小值

思考：K-均值聚类中的簇的数目如何来定？

SSE（Sum of Squared Error, 误差平方和），度量聚类效果的指标

SSE越小表越接近他们的质心，聚类效果越好

改进方法：

二分k-均值算法：

场景：克服K-均值算法收敛于局部最小问题

思想：

1、首先将所有点作为一个簇，然后将该簇一分为二，之后选择其中一个继续划分，其选择哪一个划分

取决于是否可以最大程度降低SSE值，不断重复直到得到用户指定的簇数目为止

2、另一种做法，选择最大的簇进行划分，直到簇数目达到用户指定数目为止

代码实践

#!/usr/bin/env python3
# -*- coding:utf-8 -*-
"""
K-均值聚类
"""
from numpy import *
import matplotlib
from matplotlib import pyplot as plt


def loadDataSet(fileName):
    """
    加载数据
    :param fileName: 问价路径
    :return: 数据组
    """
    dataMat = []
    with open(fileName) as fr:
        for line in fr.readlines():
            curLine = line.strip().split('\t')
            fltLine = [float(i) for i in curLine]
            dataMat.append(fltLine)
    return dataMat

def distEclud(vecA, vecB):
    """
    计算欧式距离
    :param vecA:
    :param vecB:
    :return:
    """
    return sqrt(sum(power(vecA - vecB, 2)))

def randCent(dataSet, k):
    n = shape(dataSet)[1]
    centroids = mat(zeros((k, n)))
    for j in range(n):
        minJ = min(dataSet[:, j])
        rangeJ = float(max(dataSet[:, j]) - minJ)
        centroids[:, j] = minJ + rangeJ * random.rand(k, 1)
    return centroids

def kMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
    """
    K-均值算法
    :param dataSet:
    :param k:
    :param distMeas:
    :param createCent:
    :return:
    """
    m = shape(dataSet)[0]
    clusterAssment = mat(zeros((m, 2)))
    centroids = createCent(dataSet, k)
    clusterChanged = True
    while clusterChanged:
        clusterChanged = False
        for i in range(m):
            minDist = inf
            minIndex = -1
            for j in range(k):
                distJI = distMeas(centroids[j, :], dataSet[i, :])
                if distJI < minDist:
                    minDist = distJI
                    minIndex = j
            if clusterAssment[i, 0] != minIndex:
                clusterChanged = True
            clusterAssment[i, :] = minIndex, minDist**2
        # print(centroids)
        for cent in range(k):
            ptsInClust = dataSet[nonzero(clusterAssment[:, 0].A == cent)[0]]
            centroids[cent, :] = mean(ptsInClust, axis=0)
    return centroids, clusterAssment


def biKMeans(dataSet, k, distMeas=distEclud):
    """
    二分k-均值
    :param dataSet:
    :param k:
    :param distMeas:
    :return:
    """
    m = shape(dataSet)[0]
    clusterAssment = mat(zeros((m, 2)))
    centroid0 = mean(dataSet, axis=0).tolist()[0]
    centList = [centroid0]
    for j in range(m):
        clusterAssment[j, 1] = distMeas(mat(centroid0), dataSet[j, :])**2
    while len(centList) < k:
        lowestSSE = inf
        for i in range(len(centList)):
            ptsInCurrCluster = dataSet[nonzero(clusterAssment[:, 0].A == i)[0], :]
            centroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)
            sseSplit = sum(splitClustAss[:, 1])
            sseNotSplit = sum(clusterAssment[nonzero(clusterAssment[:, 0].A != i)[0],1])
            print(f'sseSplit: {sseSplit}, and notSplit: {sseNotSplit}')
            if sseSplit + sseNotSplit < lowestSSE:
                bestCentToSplit = i
                bestNewCents = centroidMat
                bestClustAss = splitClustAss.copy()
                lowestSSE = sseSplit + sseNotSplit
        bestClustAss[nonzero(bestClustAss[:, 0].A == 1)[0], 0] = len(centList)  # change 1 to 3,4, or whatever
        bestClustAss[nonzero(bestClustAss[:, 0].A == 0)[0], 0] = bestCentToSplit
        print(f'the bestCentToSplit is: {bestCentToSplit}')
        print(f'the len of bestClustAss is: {len(bestClustAss)}')
        centList[bestCentToSplit] = bestNewCents[0, :].tolist()[0]  # replace a centroid with two best centroids
        centList.append(bestNewCents[1, :].tolist()[0])
        clusterAssment[nonzero(clusterAssment[:, 0].A == bestCentToSplit)[0], :] = bestClustAss  # reassign new clusters, and SSE
    return mat(centList), clusterAssment


# 对地理坐标进行聚类

def distSlC(vecA, vecB):
    """
    计算球面距离
    :param vecA:
    :param vecB:
    :return:
    """
    a = sin(vecA[0, 1] * pi / 180) * sin(vecB[0, 1] * pi / 180)
    b = cos(vecA[0, 1] * pi / 180) * cos(vecB[0, 1] * pi / 180) * cos(pi * (vecB[0, 0] - vecA[0, 0]) / 180)
    return arccos(a + b) * 6371.0

def clusterClubs(fileName, numClust=5):
    datList = []
    with open(fileName) as fr:
        for line in fr.readlines():
            lineArr = line.split('\t')
            datList.append([float(lineArr[4]), float(lineArr[3])])
    datMat = mat(datList)
    myCentroids, clustAssing = biKMeans(datMat, numClust, distMeas=distSlC)
    fig = plt.figure()
    rect = [0.1, 0.1, 0.8, 0.8]
    scatterMarkers = ['s', 'o', '^', '8', 'p', 'd', 'v', 'h', '>', '<']
    axprops = dict(xticks=[], yticks=[])
    ax0 = fig.add_axes(rect, label='ax0', **axprops)
    imgP = plt.imread(r"D:\ml_source_code\machinelearninginaction\Ch10\Portland.png")
    ax0.imshow(imgP)
    ax1 = fig.add_axes(rect, label='ax1', frameon=False)
    for i in range(numClust):
        ptsInCurrCluster = datMat[nonzero(clustAssing[:, 0].A == i)[0], :]
        markerStyle = scatterMarkers[i % len(scatterMarkers)]
        ax1.scatter(ptsInCurrCluster[:, 0].flatten().A[0], ptsInCurrCluster[:, 1].flatten().A[0], marker=markerStyle,
                    s=90)
    ax1.scatter(myCentroids[:, 0].flatten().A[0], myCentroids[:, 1].flatten().A[0], marker='+', s=300)
    plt.show()



if __name__ == '__main__':
    filePath = r"D:\ml_source_code\machinelearninginaction\Ch10\places.txt"
    # datMat = mat(loadDataSet(filePath))
    # centList, myNewAssments = biKMeans(datMat, 3)
    # print(centList)
    # print(myNewAssments)
    clusterClubs(filePath, numClust=5)