模糊聚类分析2012-7-22.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,模糊聚类分析,Fuzzy Clustering Analysis,零、关系与经典等价关系,方以類聚，物以群分，吉凶生矣。,易,繫辭上,聚类是一个古老的问题，它伴随着人类社会的产生和发展而不断深化。人类要认识世界就必须区别不同的事物并认识事物间的相似性。,按确定的标准对客观事物进行分类的数学方法称为聚类分析。,聚类分析的应用,市场营销，金融业（客户分类）,生物学（物种分类，种子筛选，,DNA,分类）,图像处理（）,模式识别（地质勘探，医疗诊断（中医），军事领域）,聚类关系,以木橫持門戶也。,说文,从門，聲。古還切。,關,闭，合拢：闭。,园日涉以成趣,门虽设而常关。,晋,陶渊明,归去来兮辞,2.,拘禁：押。禁。,3.,古代在险要地方或国界设立的守卫处所：卡,qi,，嘉峪。,尝以十倍之地,百万之师,叩关而攻秦。,汉,贾谊,过秦论,4.,征收进出口货税的机构：海。税。,5.,重要的转折点，不易度过的时机：节。难。年。,6.,牵连，联属：连。联。心。注。于。有。,7.,旧指发给或支领薪饷：饷。,8.,姓。,行隔一路曰关,林应龙,适情录,1.,有联属关系的：数，世。,2.,高等学校中教学单位：中文,department,。,3.,关联：干。关,relate to,。,4.,联结，栓：名誉所。,5.,牵挂：恋念。,6.,是：确实情。,7.,从井下把土上来。,8.,约束,;,羁绊,restrain,愚士系俗兮,窘若囚拘。,汉,贾谊,鹏鸟赋,9.,（,j,）结，扣。,tie;fasten,Claudius Ptolemy,（约,85165,）,Optics,公元,140,年。,Willebrord,Snell,（,15801626,）,公元,1621,年。,An object(in this case a pencil)part immersed in water looks bent due to refraction:the light waves from X change direction and so seem to originate at Y.,,en.wikipedia.org/wiki/Refraction,食物链构成的“关系”。,水葫芦原产于南美，在原产地巴西由于受生物天敌的控制，仅以一种观赏性,种群,零散分布于水体，,1844,年在美国的博览会上曾被喻为“美化,世界的淡紫色花冠”。,19,世纪期间引入,东南亚,，,1901,年作为花卉引入中国，,30,年代作为畜禽饲料引入中国内地各省，并作为观赏和净化水质的植物推广种植，后逃逸为野生。,2012,年,1,月,31,日，福建宁德市古田县水口镇湾口村段,2012,年,7,月,7,日,广西柳州的张先生在柳江河遭遇,3,条食人鱼袭击,食人鱼（又名食人鲳）栖息在主流、较大支流，河宽甚广、水流较湍急处。在巴西的亚马逊河流域，食人鱼被列入当地最危险的四种水族,生物,之首。,经典分类等价关系,Mona Lisa,or,La,Gioconda,(15031505/1507),Louvre,Paris,France,孔子,公元前,551479,爱因斯坦,1879-1955,老子,公元前,571471,武则天,624,年,705,年,居里夫人,1867-1934,阿基米德,约前,287212,年,达,芬奇,1452-1519,伽利略,1564-1642,牛顿,1643-1727,吴文俊,1919,吾未见好德如好色者也。,天下皆知美之为美，斯恶已；皆知上之为善，斯不善已。,给我一个支点和一根足够长的杠杆，我就能撬动整个地球。,勤劳一日，可得一夜安眠，勤劳一生，可得幸福长眠。,欲安其家，先安其国。,弱者坐待时机；强者制造时机。,追求科学需要特殊的勇敢。,我不知道世人怎样看我，但我自己以为我不过像一个在海边玩耍的孩子，不时为发现比寻常更为美丽的一块卵石或一片贝壳而沾沾自喜，至于展现在我面前的浩翰的真理海洋，却全然没有发现,我没有什么特别的才能，不过喜欢寻根刨底地追究问题罢了。,孔子、老子、,阿基米德,公元前生,11500,生,1500,后生,达,.,芬奇 武则天,伽利略、牛顿、居里夫人、爱因斯坦、吴文俊,Art-model-data,1.aggcacggaaaaacgggaataacggaggaggacttggcacggcattacacggaggacgaggtaaaggaggcttgtctacggccggaagtgaagggggatatgaccgcttgg,2.cggaggacaaacgggatggcggtattggaggtggcggactgttcggggaattattcggtttaaacgggacaaggaaggcggctggaacaaccggacggtggcagcaaagga,3.gggacggatacggattctggccacggacggaaaggaggacacggcggacatacacggcggcaacggacggaacggaggaaggagggcggcaatcggtacggaggcggcgga,4.atggataacggaaacaaaccagacaaacttcggtagaaatacagaagcttagatgcatatgttttttaaataaaatttgtattattatggtatcataaaaaaaggttgcga,5.cggctggcggacaacggactggcggattccaaaaacggaggaggcggacggaggctacaccaccgtttcggcggaaaggcggagggctggcaggaggctcattacggggag,6.atggaaaattttcggaaaggcggcaggcaggaggcaaaggcggaaaggaaggaaacggcggatatttcggaagtggatattaggagggcggaataaaggaacggcggcaca,7.atgggattattgaatggcggaggaagatccggaataaaatatggcggaaagaacttgttttcggaaatggaaaaaggactaggaatcggcggcaggaaggatatggaggcg,8.atggccgatcggcttaggctggaaggaacaaataggcggaattaaggaaggcgttctcgcttttcgacaaggaggcggaccataggaggcggattaggaacggttatgagg,9.atggcggaaaaaggaaatgtttggcatcggcgggctccggcaactggaggttcggccatggaggcgaaaatcgtgggcggcggcagcgctggccggagtttgaggagcgcg,10.tggccgcggaggggcccgtcgggcgcggatttctacaagggcttcctgttaaggaggtggcatccaggcgtcgcacgctcggcgcggcaggaggcacgcgggaaaaaacg,11.gttagatttaacgttttttatggaatttatggaattataaatttaaaaatttatattttttaggtaagtaatccaacgtttttattactttttaaaattaaatatttatt,12.gtttaattactttatcatttaatttaggttttaattttaaatttaatttaggtaagatgaatttggttttttttaaggtagttatttaattatcgttaaggaaagttaaa,13.gtattacaggcagaccttatttaggttattattattatttggattttttttttttttttttttaagttaaccgaattattttctttaaagacgttacttaatgtcaatgc,14.gttagtcttttttagattaaattattagattatgcagtttttttacataagaaaatttttttttcggagttcatattctaatctgtctttattaaatcttagagatatta,15.gtattatatttttttatttttattattttagaatataatttgaggtatgtgtttaaaaaaaatttttttttttttttttttttttttttttttaaaatttataaatttaa,16.gttatttttaaatttaattttaattttaaaatacaaaatttttactttctaaaattggtctctggatcgataatgtaaacttattgaatctatagaattacattattgat,17.gtatgtctatttcacggaagaatgcaccactatatgatttgaaattatctatggctaaaaaccctcagtaaaatcaatccctaaacccttaaaaaacggcggcctatccc,18.gttaattatttattccttacgggcaattaattatttattacggttttatttacaattttttttttttgtcctatagagaaattacttacaaaacgttattttacatactt,19.gttacattatttattattatccgttatcgataattttttacctcttttttcgctgagtttttattcttactttttttcttctttatataggatctcatttaatatcttaa,20.gtatttaactctctttactttttttttcactctctacattttcatcttctaaaactgtttgatttaaacttttgtttctttaaggattttttttacttatcctctgttat,11:,agatctggaaatggaccccaactgctcctgctccaccggtaagagaatacccagttaggaccgcagagacttcccgcagttgtagaggatgtagtgtagaatcttcgcgggaataatgccttcgttggggattcattctagttctttttagcgtccccctttgcaagcacctccatctattcttgcagtattaatattgtccgaacgatcctttgtcggggttgagggcagtatttaggcgcacaaatgtcccgctcctgatcaaccaggtagtgaggacatctgggtcgagctccaggcactactaaacttttatgaattgcctagactaggagagaagtgagggacttctgtgtcttggaccaaagaccaagccctaccctaccccgtgagaagtgggggctaggcttcctggaatcctgagcaggatttagtgaactgagctcggcacgtgtgtgggcctgtgatcttgcaagtctctctactgtcttctttctcctccgcagcagcacctgcacctgctccagttcctgtggctgcaaagactgcaagtgcacctcctgcaagaagagtgagtgtggagggatacctggggtggtggctaaggtttggcgggaacacccacaggcccgacagatcccagggccctcccttgtaacgtgtcaggccagagctgttctaagacacacacacccccgcttgttggggcaagaaacaggtcttccgtcaggtctgtgtgacaggtcttaggactccagctttgacctcttcctctccctgttctagctgctgctcctgctgcccagtgggctgctccaagtgtgcccagggctgcgtctgcaaaggggcatcggacaagtgcacgtgctgtgcctaatgggaggacgatgccgcctcccacgtgtaaatagtgcccggagctctaccctgtttactaagtccccttttctacgaaatatgtgaataaaaaaccaatgtgattctaactttggttttctttgtgtgacttggaaataaggaagtggggtgacagattgacttaatgagattgcaaggattggttctggagttgttggtccctttacctcttcaccctctgccccagaggagggggaagtgtcttagggaaagatcaattatgtcatgagcttcctcttaatggaagacgagcagctgtgtgccggatcagactctctctctctctctctctctctctctctctctctctctctctgtgtgtgtgtgtgtgtgtgtgtgtgtgtgcgcgcgcgcgcgcgcggccatgcgtgcgtgtgcagagctctagcaagtgctcacatttgcttggcatgtggaggctgagatggacattgggaatcttcctctttcactttctgccccccaccttgagacaggtttatctgtgtagctttggaggctgtcttgaaactgactctgtagaccagactggcctcagactcacagagatccgcttgcttctgccctacaaatgctgggattaaaggcttgcaccaccattgactgggcctctaatcttactttttgaaatgagatct,数学,上，,二元关系,（或简称,关系,）用于讨论两种物件的连系。诸如,算术,中的,大于,及,等于,，,几何学,中的,相似,，或,集合论,中的,为,.,之元素,或,为,.,之子集,。,集合,到集合 上的,二元关系,是 的一个子集 。,若（,x,y,）属于,R,，则称,x,与,y,有关系,R,，记作,xRy,。,特别地，,X,到,X,的关系,R,称为是,X,上的关系,。,X,上的关系,R,称为是,等价关系,，若他它满足：,（,1,）（,自反性，,Reflectivity,）对于任何,x,，有,xRx,；,（,2,）（,对称性，,Symmetry,）对于任何,x,，,y,若,xRy,，则,yRx,；,（,3,）（,传递性，,Transitivity,）若,xRy,且,yRz,，则,xRz,。,设,X上的关系,R,称为是,等价关系，,则对应划分,20,年后的今天是星期几？,关系的矩阵,孔 老 阿 达 吴 武 居里 伽 牛顿 爱,关系的复合,祖孙,=,父子,父子；婆媳,=,母子,夫妻。,R,为,X,到,Y,的关系，,Q,为,Y,到,Z,的关系，则,Q,R,定义为,X,到,Z,的关系：,一、模糊集与模糊等价关系,模糊集的概念（,Zadeh,，,1965,）起源。,X,是一个集合，称之为论域。考虑下列命题：,是一个大数；,这朵玫瑰是红的；,所有鸟都会飞。,第一个断言，预先需假设存在一个大数集合。问题是，边界放于何处。,三分法：成员可能是一个成员，非成员或,边界成员,。,例如，断定红，就不得不在下述意义的基础上进行定义：“在波长为,580.27mu,和,702.35mu,之间的单色关照射下，从均匀的反射面上，一个红色物体是不可区分的。”,Zadeh,引入了从非隶属到隶属的逐渐过渡来取代一个分明边界。诸如“大”这样一个不精确的、模糊断言的物体，被认为在论域（自然数集合）上构成了一个模糊集合；从非隶属到隶属的过渡是渐渐的，而不是突然的。表明某个数比另一个数更优先具有“大数”的标签是有意义的。,2.,关于隶属函数,于内容有关；,与不同观测者有关；,一个绝对，确切的隶属函数并不存在。,3.,模糊等价关系,寒,热,虚,实,自汗 恶寒 咳嗽 喘,自汗,恶寒,咳嗽,喘,肺 心,模糊关系的复合,寒,热,虚,实,自汗 恶寒 咳嗽 喘,自汗,恶寒,咳嗽,喘,肺 心,寒,自汗,恶寒,咳嗽,喘,肺,寒,热,虚,实,肺 心,称,R,是,X,上的,模糊等价关系（,相应的矩阵,称为,Fuzzy,等价矩阵）,，若,模糊等价关系的定义,二、基于,Fuzzy,等价关系的,Fuzzy,聚类,必为,Fuzzy,等价矩阵，依它为基础聚类即可！,性味归经：苦，寒。归肺、胆、脾、大肠、小肠经。,清肌退热，柴胡最佳，然无黄芩不能凉肌达表。,本草汇言,性味归经：性微寒、味苦、辛、归,肝经,、,胆经,。,功能：透表泄热，疏肝解郁，升举阳气。,0.8,1,0,0,0,0,0,0,0,0.5,0,0,0.5,0.5,-1,0,1,0,0,-1,0,1,1,0,0,0,0,0,0.5,0.5,0,1,1,0,1,0.5,-1,1,0.5,0.5,1,0.5,0.5,0,0.5,-1,-1,0.5,-1,0,1.5,1,1,1,1,0,0,1.5,0.5,0.5,0.5,0.5,0,0,0.5,0,1,1,0,1,0,1,0,0.5,0.5,0,0.5,0,1.5,1.5,1,1.5,1.5,1.5,0,1.5,1.5,0.5,1.5,1.5,1.5,1.5,0.5,0,1,0,0,0,1.5,1,0,0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0.6667,0.908,0.7161,0.6262,0.5611,0.0687,0.6667,1,0.7515,0.5371,0.9393,0.6099,0.1374,0.908,0.7515,1,0.8408,0.7059,0.7334,0.0645,0.7161,0.5371,0.8408,1,0.5045,0.7076,0.4059,0.6262,0.9393,0.7059,0.5045,1,0.5729,0.1291,0.5611,0.6099,0.7334,0.7076,0.5729,1,0.4023,0.0687,0.1374,0.0645,0.4059,0.1291,0.4023,1,1,0.4059,0.4059,0.4059,0.4059,0.4059,0.4059,0.4059,1,0.7334,0.7334,0.7334,0.7334,0.7334,0.4059,0.7334,1,0.7515,0.7515,0.9393,0.7515,0.4059,0.7334,0.7515,1,0.8408,0.7515,0.8408,0.4059,0.7334,0.7515,0.8408,1,0.7515,0.908,0.4059,0.7334,0.9393,0.7515,0.7515,1,0.7515,0.4059,0.7334,0.7515,0.8408,0.908,0.7515,1,为,Fuzzy,等价矩阵（称为,R,的,传递闭包,），据此聚类！,1,0.4059,0.4059,0.4059,0.4059,0.4059,0.4059,0.4059,1,0.7334,0.7334,0.7334,0.7334,0.7334,0.4059,0.7334,1,0.7515,0.7515,0.9393,0.7515,0.4059,0.7334,0.7515,1,0.8408,0.7515,0.8408,0.4059,0.7334,0.7515,0.8408,1,0.7515,0.908,0.4059,0.7334,0.9393,0.7515,0.7515,1,0.7515,0.4059,0.7334,0.7515,0.8408,0.908,0.7515,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,1,0,1,柴胡,黄岑,半夏、生姜,人参，甘草、大枣,动态聚类图,三、基于,Fuzzy,划分的,Fuzzy,聚类分析（,FCM,）,孔子、老子、,阿基米德,公元前生,11500,生,1500,后生,达,.,芬奇 武则天,伽利略、牛顿、居里夫人、爱因斯坦、吴文俊,1.crisp c-partitions and fuzzy c-partitions,欲将数据集,分为,c,类，使得,X,中的任意样本,必须完全属,于某一类，以及每一类至少包含一个样本。这种问题的结果可由下列矩阵表示，称,矩阵,D,其为,X,的,硬,c-,划分,（,crisp c-partitions,）,.,孔 老 阿 达 吴 武 居里 伽 牛顿 爱,Fuzzy c-partitions,称矩阵,D,其为,X,的,模糊,c-,划分,（,fuzzy c-partitions,）,.,给定,c,和,n,两个正整数，,cn,。矩阵,满足,X,的,模糊,c-,划分,（,fuzzy c-partitions给出,X,上的,c,个模糊集,.,X,的,模糊,c-,划分,（,fuzzy c-partitions,）给出,X,上的,c,个模糊集,.,2.,基于,fuzzy c-partitions,的聚类,孔 老 阿 达 吴 武 居里 伽 牛顿 爱,类 聚类中心,95,89,87,80,82,79,73,65,86,76,90,86,76,90,83,96,98,90,87,86,68,71,89,58,79,75,67,52,74,73,97,90,98,97,92,100,92,95,99,85,82,84,93,75,87,85,76,70,70,76,ISODATA,Iterative Self-Organizing Data Analysis Technique,考虑（,lagrange,乘子法）,求偏导数，有,取得最小值的必要条件,ISODATA,算法设计,U0=,rand(C,N,);,%,随机矩阵,U0=U0./(ones(C,1)*sum(U0);,%,随机矩阵列归一，可得初始化划分矩阵,步骤,1,任意指定,Fuzzy,划分矩阵,U0,步骤,2,根据上式计算,c,个聚类中心,Um=U0.M;P=Um*Data./(ones(S,1)*,sum(Um,);,步骤,3,计算目标函数的值,J,（,D,V,）,步骤,4,计算新的,U,并返回步骤,2,