浅谈谱聚类算法及应用摘要在这个大数据时代，数据分析是一个很重要的问题，聚类技术的发展，大大缓解了这种情况。所以谱聚类算法的研究得到很多学者的参与和关注，尤其在模式识别方面。本文首先对谱聚类算法做了一个简单介绍，然后说明了在中国以及其他国家的一个发展情况，接着介绍了一些理论基础，图的表示，引出了相似矩阵和拉普拉斯矩阵的概念以及图的划分原则。再深入介绍了谱聚类算法的主流算法以及每一种算法具体实现的操作步骤并应用于实例来说明；最后也讲述了谱聚类算法的一个应用--图像分割，也指出了一些不足，同时也通过实例图分析了谱聚类算法在图像分割上的应用。关键词：谱聚类；拉普拉斯矩阵；图像分割AbriefdiscussiononspectralclusteringalgorithmanditsapplicationAbstractInthisageofbigdata,dataanalysisisaveryimportantproblem,andthedevelopmentofclusteringtechnologygreatlyalleviatesthissituation.Inthefieldofpatternrecognition,theemergenceofspectralclusteringhasbecomethefocusofscholars.Thispaperpresentsanoverviewofspectralclusteringalgorithmanditsresearchstatusathomeandabroad.Thenitintroducesthatsometheoreticalbasis,therepresentationofgraph,theconceptofsimilaritymatrixandLaplacianmatrixandthedivisionprincipleofgraph.Thenitintroducesthatthemainstreamalgorithmandrealizationstepofspectralclusteringalgorithm,andanalyzesitbyexample.Finally,theapplicationofspectralclusteringalgorithminimagesegmentationisalsodiscussed,andsomeshortcomingsarepointedout.Meanwhile,theapplicationofspectralclusteringalgorithminimagesegmentationisalsoanalyzedbyexamplegraph.Keywords:Spectralclustering;Laplacematrix;Imagesegmentation目录目录摘要....................................................................................................................................IAbstract..................................................................................................................................II第1章绪论...........................................................................................................................11.1谱聚类算法概述....................................................................................................11.2国内外研究状况....................................................................................................11.3论文结构............................................................................................................2第2章理论基础..................................................................................................................42.1聚类分析概述及分类..........................................................................................42.1.1聚类分析.....................................................................................................42.2图和矩阵的表示..................................................................................................42.2.1图的基本知识.............................................................................................42.2.2图的矩阵表示.............................................................................................52.2.3相似性测度....................................................................错误!未定义书签。2.2.4拉普拉斯矩阵及其性质.............................................................................72.3相似图的构造方法.................................................................................................82.4谱图划分准则..........................................
