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X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences
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DTSTART:20210314T100000
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DTSTART;TZID=America/Los_Angeles:20210426T150000
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DTSTAMP:20210509T044624
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SUMMARY:Applied Math. Talk: Balancing Geometry and Density: Path Distances on High-Dimensional Data by Anna Little\, University of Utah
DESCRIPTION: Abstract: This talk discusses multiple methods for clustering\nhigh-dimensional data\, and explores the delicate balance between utilizing\ndata density and data geometry. I will first present path-based spectral\nclustering\, a novel approach which combines a density-based metric with\ngraph-based clustering. This density-based path metric allows for fast\nalgorithms and strong theoretical guarantees when clusters concentrate\naround low-dimensional sets. However\, the method suffers from a loss of\ngeometric information\, information which is preserved by simple linear\ndimension reduction methods such as classic multidimensional scaling\n(CMDS). The second part of the talk will explore when CMDS followed by a\nsimple clustering algorithm can exactly recover all cluster labels with\nhigh probability. However\, scaling conditions become increasingly\nrestrictive as the ambient dimension increases\, and the method will fail\nfor irregularly shaped clusters. Finally\, I will discuss how a more\ngeneral family of path metrics\, when combined with CMDS\, give\nlow-dimensional embeddings which respect both data density and data\ngeometry. This new method exhibits promising performance on single cell\nRNA sequence data and can be computed efficiently by restriction to a\nsparse graph. \n
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-anna-little-university-of-utah/
LOCATION:Zoom meeting\, United States
CATEGORIES:Applied Math Seminar
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