（一），KMeans聚类
k均值算法的计算过程非常直观：
1、从D中随机取k个元素，作为k个簇的各自的中心。
2、分别计算剩下的元素到k个簇中心的相异度，将这些元素分别划归到相异度最低的簇。
3、根据聚类结果，重新计算k个簇各自的中心，计算方法是取簇中所有元素各自维度的算术平均数。
4、将D中全部元素按照新的中心重新聚类。
5、重复第4步，直到聚类结果不再变化。
6、将结果输出。
（二），Spark下KMeans的应用
1，数据集下载：数据来源电影集ml-100k，解压后内容如下：
2，加载数据集（u.data,u.item,u.user,u.genre）
import breeze.numerics.pow
import breeze.linalg.{DenseVector, sum}
import org.apache.log4j.{Level, Logger}
import org.apache.spark.mllib.clustering.KMeans
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.linalg.distributed.RowMatrix
import org.apache.spark.mllib.recommendation.{ALS, Rating}
import org.apache.spark.{SparkConf, SparkContext}
/**
* Created by hadoop on 17-5-25.
*/
object Clustering {
def main(args: Array[String]): Unit = {
Logger.getLogger("org.apache.spark").setLevel(Level.WARN)
Logger.getLogger("org.eclipse.jetty.server").setLevel(Level.OFF)
val conf = new SparkConf().setMaster("local[4]").setAppName("Clustering")
val sc = new SparkContext(conf)
/*加载电影信息*/
val file_item=sc.textFile("ml-100k/u.item")
println(file_item.first())
/* 1|Toy Story (1995)|01-Jan-1995
||http://us.imdb.com/M/title-exact?Toy%20Story%20(1995)|0|0|0|1|1|1|0|0|0|0|0|0|0|0|0|0|0|0|0*/
/*加载电影类别信息*/
val file_genre=sc.textFile("ml-100k/u.genre")
println(file_genre.first())
/*加载评论人的信息*/
val file_user=sc.textFile("ml-100k/u.user")
/*加载评论人的评论信息*/
val file_data=sc.textFile("ml-100k/u.data")
3，获取用户相似度和商品相似度的特征
/*训练推荐模型*/
val data_vector=file_data.map(_.split("\t")).map{
x =>
Rating(x(0).toInt,x(1).toInt,x(2).toDouble)
}.cache()
val aslModel=ALS.train(data_vector,50,10,0.1)
/*获取用户相似特征*/
val userFactors=aslModel.userFeatures
/*用户特征向量化*/
val userVectors=userFactors.map(x =>Vectors.dense(x._2))
/*获取商品相似特征*/
val movieFactors=aslModel.productFeatures
/*商品相似特征向量化*/
val movieVectors=movieFactors .map(x => Vectors.dense(x._2))
4，对特征向量进行归一化判断（相差性不大，不需要归一化处理）
/*归一化判断*/
val movieMatrix=new RowMatrix(movieVectors)
val movieMatrix_Summary=movieMatrix.computeColumnSummaryStatistics()
println(movieMatrix_Summary.mean)//每列的平均值
println(movieMatrix_Summary.variance)//每列的方差
val userMatrix=new RowMatrix(userVectors)
val userMatrix_Summary=userMatrix.computeColumnSummaryStatistics()
println(userMatrix_Summary.mean)//每列的平均值
println(userMatrix_Summary.variance)//每列的方差
/*
[-0.13008311396438857,0.31661349981643944,0.04176194036295573,-0.17211569215642514,-0.4497891125174345,0.09243001925706192,-0.2755917868411943,-0.19225727923869668,-0.018074178428278184,0.043485409688419366,-0.06171785901744992,-0.02591447976817197,0.19002821603433132,-0.05013381354161954,0.15294254500299065,-0.08252016445098687,-0.0057098213683935105,-0.13747174430426554,0.05802203164542926,0.033331425727203726,0.13930257786165984,-0.2941097050176434,-0.19734704657277818,0.1793645468213842,0.1858669768823329,-0.08710850192711901,-0.3094421959292386,-0.2548794820483227,0.05249494735633076,-0.3562774572049559,0.015031007230226604,-0.18366799252050295,-0.08052010999605276,0.23969935994832287,-0.15085203866404293,-0.0266082986122826,0.48041088915071206,0.3819342264520057,0.10262863779907039,0.3689219391143156,0.21978187693621526,-0.04213238444149567,-0.05693009052711689,-0.04565851868781088,0.1643780671247495,-0.05540201890562131,-0.05187046972756212,-0.060050296088081975,-0.021567585541199932,0.4901373003250682]
[0.03743475409539939,0.031032747373518976,0.029213407748178235,0.03226267596613916,0.040257690707209866,0.034539707321632425,0.027611845740142894,0.028509309121624964,0.025440295510889853,0.02511832158923448,0.03080754975061996,0.03201104062279273,0.02991156881925051,0.0345705916462603,0.035140884173621934,0.031036810909755186,0.03576908913423648,0.03642722793348703,0.029388891832012827,0.02494498821491199,0.03132437145414312,0.0369521012943726,0.02901464695221897,0.027311134522322922,0.02676860109379616,0.032518349865363054,0.028838970048305275,0.0365380120266148,0.04609520070723283,0.05599010197906069,0.03397713010328192,0.029447553057890395,0.028579423940221296,0.030239922213002635,0.03378179513855587,0.02421525892247664,0.046378108876308416,0.03264410698537499,0.03230986943273885,0.051741906473701554,0.035497888204443974,0.02812785680617771,0.025779274246114193,0.031207111744648054,0.03327289703736872,0.028603617535928046,0.040022623716766015,0.029880344948539223,0.02983948000863361,0.04062228040657388]
[-0.2397596338254717,0.4594882978827614,0.05195971267920803,-0.2277342193865653,-0.6149972658209337,0.12565839801843265,-0.3426050112692244,-0.2757319484961794,0.006145707878818492,0.027304305682852706,-0.05091203888118997,-0.02226309713645111,0.2433257826385377,-0.06589234037518484,0.22518879044694215,-0.0852476117191397,-0.03780259258005953,-0.22765740097208045,0.06361867089908667,0.039030569957985047,0.15821200728387022,-0.39808113600175793,-0.24932252666595706,0.22289011456090352,0.22899166768162324,-0.15776169666472803,-0.3765026197540609,-0.3971351730371645,0.07838055551392697,-0.48751263454885346,0.07657040774049793,-0.24468786257011882,-0.1352783094162975,0.3543083916189498,-0.23719722044210134,-0.06395667672598723,0.7071586536245534,0.4900572946816604,0.11565260993463476,0.5059177976591497,0.28435506896522744,-0.04909286770435483,-0.05596895760600775,-0.05533550545287566,0.19748140330452815,-0.04547192154361222,-0.11179801900008168,-0.04702601122332145,-0.04258431545777241,0.6540003003096279]
[0.03569838097111229,0.03249774062792991,0.03737983785495416,0.0450460289446052,0.034109606797398676,0.042907070585855724,0.03783857934270285,0.035853469267097295,0.029187533362003956,0.028232712750621707,0.03850051061674194,0.04163192994799209,0.03882657092942245,0.03887707935487142,0.03728989496029858,0.03378360832995031,0.03714453151827954,0.04825414942767919,0.03232008429647026,0.03364460380334661,0.035709645433473214,0.03413621873837159,0.03864382041647934,0.0322039375743242,0.02840916049694515,0.03770926875822772,0.029974874000465297,0.03927937435771869,0.04622604645998578,0.04328527359957934,0.040115015618337774,0.04423951593706847,0.03177280103515792,0.030474791894718824,0.03700057945320223,0.03050651636255259,0.0332588386775746,0.032796935599422934,0.03211705636393917,0.044225120867550045,0.036286898809297856,0.040310338676373035,0.02899783829803054,0.03521037302334469,0.03950475206010323,0.03683043230289064,0.04654706810054013,0.032119433718304606,0.03213251469574535,0.050332188470470975]
*/
5，对用户因子进行kMeans聚类
/*对用户K-means因子聚类*/
val userClusterModel=KMeans.train(userVectors,5,100)
/*使用聚类模型进行预测*/
val user_predict=userClusterModel.predict(userVectors)
def computeDistance(v1:DenseVector[Double],v2:DenseVector[Double])=sum(pow(v1-v2,2))
user_predict.map(x =>(x,1)).reduceByKey(_+_).collect().foreach(println(_))
/*每个类中的数目
(4,170)
(0,230)
(1,233)
(2,175)
(3,135)
*/
val userInfo=file_user.map(_.split("\\|")).map{
x => (x(0).toInt,(x(1),x(2),x(3),x(4)))
}
/*联合用户信息和特征值*/
val infoAndFactors=userInfo.join(userFactors)
val userAssigned=infoAndFactors.map{
case(userId,((age,sex,title,zip),factors)) =>
val pred=userClusterModel.predict(Vectors.dense(factors))
val center=userClusterModel.clusterCenters(pred)
val dist=computeDistance(DenseVector(factors),DenseVector(center.toArray))
(userId,age,sex,title,zip,dist,pred)
}
val userCluster=userAssigned.groupBy(_._7).collectAsMap()
/*输出每个类中的20个用户分类情况*/
for((k,v) <- userCluster.toSeq.sortBy(_._1)){
println(s"userCluster$k")
val info=v.toSeq.sortBy(_._6)
println(info.take(20).map{
case(userId,age,sex,title,zip,pred,dist) =>
(userId,age,sex,title,zip)
}.mkString("\n"))
println("========================")
}
/*
userCluster0
(757,26,M,student,55104)
(276,21,M,student,95064)
(267,23,M,engineer,83716)
(643,39,M,scientist,55122)
(540,28,M,engineer,91201)
(407,29,M,engineer,03261)
(135,23,M,student,38401)
(429,27,M,student,29205)
(92,32,M,entertainment,80525)
(624,19,M,student,30067)
(650,42,M,engineer,83814)
(70,27,M,engineer,60067)
(625,27,M,programmer,20723)
(748,28,M,administrator,94720)
(292,35,F,programmer,94703)
(10,53,M,lawyer,90703)
(26,49,M,engineer,21044)
(864,27,M,programmer,63021)
(889,24,M,technician,78704)
(457,33,F,salesman,30011)
========================
userCluster1
(916,27,M,engineer,N2L5N)
(94,26,M,student,71457)
(645,27,M,programmer,53211)
(339,35,M,lawyer,37901)
(666,44,M,administrator,61820)
(607,49,F,healthcare,02154)
(85,51,M,educator,20003)
(543,33,M,scientist,95123)
(573,68,M,retired,48911)
(829,48,M,writer,80209)
(766,42,M,other,10960)
(184,37,M,librarian,76013)
(710,19,M,student,92020)
(794,32,M,educator,57197)
(60,50,M,healthcare,06472)
(293,24,M,writer,60804)
(344,30,F,librarian,94117)
(360,51,M,other,98027)
(537,36,M,engineer,22902)
(18,35,F,other,37212)
========================
userCluster2
(275,38,M,engineer,92064)
(554,32,M,scientist,62901)
(694,60,M,programmer,06365)
(455,48,M,administrator,83709)
(178,26,M,other,49512)
(800,25,M,programmer,55337)
(738,35,M,technician,95403)
(488,48,M,technician,21012)
(647,40,M,educator,45810)
(764,27,F,educator,62903)
(87,47,M,administrator,89503)
(298,44,M,executive,01581)
(633,35,M,programmer,55414)
(311,32,M,technician,73071)
(484,27,M,student,21208)
(786,36,F,engineer,01754)
(398,40,M,other,60008)
(290,40,M,engineer,93550)
(749,33,M,other,80919)
(25,39,M,engineer,55107)
========================
userCluster3
(56,25,M,librarian,46260)
(552,45,M,other,68147)
(804,39,M,educator,61820)
(606,28,M,programmer,63044)
(33,23,M,student,27510)
(162,25,M,artist,15610)
(348,24,F,student,45660)
(504,40,F,writer,92115)
(393,19,M,student,83686)
(545,27,M,technician,08052)
(826,28,M,artist,77048)
(396,57,M,engineer,94551)
(728,58,M,executive,94306)
(332,20,M,student,40504)
(320,19,M,student,24060)
(907,25,F,other,80526)
(319,38,M,programmer,22030)
(200,40,M,programmer,93402)
(923,21,M,student,E2E3R)
(596,20,M,artist,77073)
========================
userCluster4
(378,35,M,student,02859)
(591,57,F,librarian,92093)
(345,28,F,librarian,94143)
(106,61,M,retired,55125)
(594,46,M,educator,M4J2K)
(908,44,F,librarian,68504)
(329,48,M,educator,01720)
(450,35,F,educator,11758)
(701,51,F,librarian,56321)
(876,41,M,other,20902)
(530,29,M,engineer,94040)
(376,28,F,other,10010)
(207,39,M,marketing,92037)
(716,36,F,administrator,44265)
(84,32,M,executive,55369)
(271,51,M,engineer,22932)
(144,53,M,programmer,20910)
(328,51,M,administrator,06779)
(297,29,F,educator,98103)
(262,19,F,student,78264)
========================
*/
6，商品因子KMeans聚类
/*对电影K-means因子聚类*/
val movieClusterModel=KMeans.train(movieVectors,5,100)
/*KMeans: KMeans converged in 39 iterations.*/
val movie_predict=movieClusterModel.predict(movieVectors)
movie_predict.map(x =>(x,1)).reduceByKey(_+_).collect.foreach(println(_))
/*result
(4,384)
(0,340)
(1,154)
(2,454)
(3,350)
*/
/*查看及分析商品相似度聚类数据*/
/*提取电影的题材标签*/
val genresMap=file_genre.filter(!_.isEmpty).map(_.split("\\|"))
.map(x => (x(1),x(0))).collectAsMap()
/*为电影数据和题材映射关系创建新的RDD，其中包含电影ID、标题和题材*/
val titlesAndGenres=file_item.map(_.split("\\|")).map{
array =>
val geners=array.slice(5,array.size).zipWithIndex.filter(_._1=="1").map(
x => genresMap(x._2.toString)
)
(array(0).toInt,(array(1),geners))
}
val titlesWithFactors=titlesAndGenres.join(movieFactors)
val movieAssigned=titlesWithFactors.map{
case(id,((movie,genres),factors)) =>
val pred=movieClusterModel.predict(Vectors.dense(factors))
val center=movieClusterModel.clusterCenters(pred)
val dist=computeDistance(DenseVector(factors),DenseVector(center.toArray))
(id,movie,genres.mkString(" "),pred,dist)
}
val clusterAssigned=movieAssigned.groupBy(_._4).collectAsMap()
for((k,v)<- clusterAssigned.toSeq.sortBy(_._1)){
println(s"Cluster$k")
val dist=v.toSeq.sortBy(_._5)
println(dist.take(20).map{
case (id,movie,genres,pred,dist) =>
(id,movie,genres)
}.mkString("\n"))
println("============")
}
/*
Cluster0
(1123,Last Time I Saw Paris, The (1954),Drama)
(1526,Witness (1985),Drama Romance Thriller)
(711,Substance of Fire, The (1996),Drama)
(1674,Mamma Roma (1962),Drama)
(1541,Beans of Egypt, Maine, The (1994),Drama)
(1454,Angel and the Badman (1947),Western)
(1537,Cosi (1996),Comedy)
(1506,Nelly & Monsieur Arnaud (1995),Drama)
(483,Casablanca (1942),Drama Romance War)
(479,Vertigo (1958),Mystery Thriller)
(1627,Wife, The (1995),Comedy Drama)
(513,Third Man, The (1949),Mystery Thriller)
(608,Spellbound (1945),Mystery Romance Thriller)
(1122,They Made Me a Criminal (1939),Crime Drama)
(1124,Farewell to Arms, A (1932),Romance War)
(1525,Object of My Affection, The (1998),Comedy Romance)
(1573,Spirits of the Dead (Tre passi nel delirio) (1968),Horror)
(58,Quiz Show (1994),Drama)
(505,Dial M for Murder (1954),Mystery Thriller)
(1460,Sleepover (1995),Comedy Drama)
============
Cluster1
(1455,Outlaw, The (1943),Western)
(54,Outbreak (1995),Action Drama Thriller)
(281,River Wild, The (1994),Action Thriller)
(1668,Wedding Bell Blues (1996),Comedy)
(1670,Tainted (1998),Comedy Thriller)
(1667,Next Step, The (1995),Drama)
(1657,Target (1995),Action Drama)
(1477,Nightwatch (1997),Horror Thriller)
(870,Touch (1997),Romance)
(1430,Ill Gotten Gains (1997),Drama)
(918,City of Angels (1998),Romance)
(1249,For Love or Money (1993),Comedy)
(801,Air Up There, The (1994),Comedy)
(1519,New Jersey Drive (1995),Crime Drama)
(619,Extreme Measures (1996),Drama Thriller)
(1613,Tokyo Fist (1995),Action Drama)
(1542,Scarlet Letter, The (1926),Drama)
(576,Cliffhanger (1993),Action Adventure Crime)
(808,Program, The (1993),Action Drama)
(471,Courage Under Fire (1996),Drama War)
============
Cluster2
(1539,Being Human (1993),Drama)
(1371,Machine, The (1994),Comedy Horror)
(1365,Johnny 100 Pesos (1993),Action Drama)
(1350,Crows and Sparrows (1949),Drama)
(1676,War at Home, The (1996),Drama)
(1513,Sprung (1997),Comedy)
(1414,Coldblooded (1995),Action)
(1354,Venice/Venice (1992),Drama)
(897,Time Tracers (1995),Action Adventure Sci-Fi)
(1374,Falling in Love Again (1980),Comedy)
(1334,Somebody to Love (1994),Drama)
(1359,Boys in Venice (1996),Drama)
(437,Amityville 1992: It‘s About Time (1992),Horror)
(439,Amityville: A New Generation (1993),Horror)
(1318,Catwalk (1995),Documentary)
(1360,Sexual Life of the Belgians, The (1994),Comedy)
(1320,Homage (1995),Drama)
(1340,Crude Oasis, The (1995),Romance)
(1364,Bird of Prey (1996),Action)
(1352,Shadow of Angels (Schatten der Engel) (1976),Drama)
============
Cluster3
(1223,King of the Hill (1993),Drama)
(1538,All Over Me (1997),Drama)
(1370,I Can‘t Sleep (J‘ai pas sommeil) (1994),Drama Thriller)
(1682,Scream of Stone (Schrei aus Stein) (1991),Drama)
(1632,Land and Freedom (Tierra y libertad) (1995),War)
(1640,Eighth Day, The (1996),Drama)
(1641,Dadetown (1995),Documentary)
(1649,Big One, The (1997),Comedy Documentary)
(1633,? k?ldum klaka (Cold Fever) (1994),Comedy Drama)
(1637,Girls Town (1996),Drama)
(1630,Silence of the Palace, The (Saimt el Qusur) (1994),Drama)
(1638,Normal Life (1996),Crime Drama)
(1635,Two Friends (1986) ,Drama)
(1647,Hana-bi (1997),Comedy Crime Drama)
(1356,Ed‘s Next Move (1996),Comedy)
(1515,Wings of Courage (1995),Adventure Romance)
(1423,Walking Dead, The (1995),Drama War)
(1619,All Things Fair (1996),Drama)
(1482,Gate of Heavenly Peace, The (1995),Documentary)
(1578,Collectionneuse, La (1967),Drama)
============
Cluster4
(1603,Angela (1995),Drama)
(1521,Mr. Wonderful (1993),Comedy Romance)
(1096,Commandments (1997),Romance)
(1441,Moonlight and Valentino (1995),Drama Romance)
(1516,Wedding Gift, The (1994),Drama)
(1543,Johns (1996),Drama)
(1436,Mr. Jones (1993),Drama Romance)
(1611,Intimate Relations (1996),Comedy)
(1673,Mirage (1995),Action Thriller)
(1189,Prefontaine (1997),Drama)
(625,Sword in the Stone, The (1963),Animation Children‘s)
(1285,Princess Caraboo (1994),Drama)
(1145,Blue Chips (1994),Drama)
(28,Apollo 13 (1995),Action Drama Thriller)
(196,Dead Poets Society (1989),Drama)
(167,Private Benjamin (1980),Comedy)
(1248,Blink (1994),Thriller)
(164,Abyss, The (1989),Action Adventure Sci-Fi Thriller)
(732,Dave (1993),Comedy Romance)
(1406,When Night Is Falling (1995),Drama Romance)
*/
7，评估聚类模型的性能
通用的内部评价指标包括WCSS（我们之前提过的K-元件的目标函数）、Davies-Bouldin指数、Dunn指数和轮廓系数（silhouette coefficient）。所有这些度量指标都是使类簇内部的样本距离尽可能接近，不同类簇的样本相对较远。
/*内部评价指标，计算性能*/
val movieCost=movieClusterModel.computeCost(movieVectors)
println(movieCost)
val userCost=movieClusterModel.computeCost(userVectors)
println(userCost)
/*
2296.979970714412
1719.2302334162873
*/
因为聚类被认为是无监督分类，如果有一些带标注的数据，便可以用这些标签来评估聚类模型。可以使用聚类模型预测类簇（类标签），使用分类模型中类似的方法评估预测值和真实标签的误差（即真假阳性率和真假阴性率）。具体方法包括Rand measure、F-measure、雅卡尔系数（Jaccard index）等
（三），模型调优
类似分类和回归模型，我们可以应用交叉验证来选择模型最优的类中心数目。这和监督学习的过程一样。需要将数据集分割为训练集和测试集，然后在训练集上训练模型，在测试集上评估感兴趣的指标的性能。如下代码用80/20划分得到训练集和测试集，并使用MLlib内置的WCSS类
/*调节用户分类数次数*/
val userCosts=Seq(1,3,5,7,10,13,20).map{
param =>
(param,KMeans.train(user_train,param,50).computeCost(user_test))
}
println("User clustering cross-validation:")
userCosts.foreach { case (k, cost) => println(f"WCSS for K=$k id $cost%2.2f") }
/*调节电影分类数次数*/
val movieCosts=Seq(1,3,5,7,10,13,20).map{
param =>
(param,KMeans.train(user_train,param,50).computeCost(user_test))
}
println("Movie clustering cross-validation:")
movieCosts.foreach { case (k, cost) => println(f"WCSS for K=$k id $cost%2.2f") }
/*
User clustering cross-validation:
WCSS for K=1 id 352.37
WCSS for K=3 id 320.03
WCSS for K=5 id 310.81
WCSS for K=7 id 307.31
WCSS for K=10 id 305.70
WCSS for K=13 id 301.75
WCSS for K=20 id 296.57
Movie clustering cross-validation:
WCSS for K=1 id 352.37
WCSS for K=3 id 320.65
WCSS for K=5 id 313.34
WCSS for K=7 id 308.47
WCSS for K=10 id 302.66
WCSS for K=13 id 303.27
WCSS for K=20 id 300.56
*/
从结果可以看出，随着类中心数目增加，WCSS值会出现下降，然后又开始增大。另外一个现象，K-均值在交叉验证的情况，WCSS随着K的增大持续减小，但是达到某个值后，下降的速率突然会变得很平缓。这时的K通常为最优的K值（这称为拐点）。k最佳为10左右，尽管较大的K值从数学的角度可以得到更优的解，但是类簇太多就会变得难以理解和解释
需要说明的是，由于聚类模型随机初始化的原因，你得到的结果可能略有不同。
时间： 2024-10-06 19:21:04