Persistent Clustering and a Theorem of J. Kleinberg Export

@article{citeulike:3157932, abstract = {We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorem analogous to one of J. Kleinberg, in which one obtains an existence and uniqueness theorem instead of a non-existence result. We explore further properties of this unique scheme, stability and convergence are established.}, archivePrefix = {arXiv}, author = {Carlsson, Gunnar and Memoli, Facundo}, citeulike-article-id = {3157932}, citeulike-linkout-0 = {http://arxiv.org/abs/0808.2241}, citeulike-linkout-1 = {http://arxiv.org/pdf/0808.2241}, day = {16}, eprint = {0808.2241}, keywords = {category\_theory, clustering, theory, trees}, month = {Aug}, posted-at = {2008-08-27 09:13:53}, priority = {4}, title = {Persistent Clustering and a Theorem of J. Kleinberg}, url = {http://arxiv.org/abs/0808.2241}, year = {2008} }

TY - JOUR ID - citeulike:3157932 L3 - citeulike-article-id:3157932 N2 - We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorem analogous to one of J. Kleinberg, in which one obtains an existence and uniqueness theorem instead of a non-existence result. We explore further properties of this unique scheme, stability and convergence are established. TI - Persistent Clustering and a Theorem of J. Kleinberg KW - category_theory KW - clustering KW - theory KW - trees AU - Carlsson, Gunnar AU - Memoli, Facundo PY - 2008/Aug/16/ UR - http://arxiv.org/abs/0808.2241 ER -