The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering Export

@article{citeulike:2815369, abstract = {An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.}, archivePrefix = {arXiv}, author = {Murtagh, Fionn}, citeulike-article-id = {2815369}, citeulike-linkout-0 = {http://arxiv.org/abs/0805.2756}, citeulike-linkout-1 = {http://arxiv.org/pdf/0805.2756}, day = {16}, eprint = {0805.2756}, keywords = {clustering, high-dimensional, simplex}, month = {Nov}, posted-at = {2009-07-28 06:21:18}, priority = {1}, title = {The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering}, url = {http://arxiv.org/abs/0805.2756}, year = {2008} }

TY - JOUR ID - citeulike:2815369 L3 - citeulike-article-id:2815369 N2 - An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling. TI - The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering KW - clustering KW - high-dimensional KW - simplex AU - Murtagh, Fionn PY - 2008/Nov/16/ UR - http://arxiv.org/abs/0805.2756 ER -