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Activity Number: 544
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #310000
Title: Branching Out with Level Set Trees: Generalizing Beyond Densities and Enabling Interactive Data Analysis
Author(s): Brian P. Kent*+ and Alessandro Rinaldo and Timothy Verstynen
Companies: Carnegie Mellon University Department of Statistics and Carnegie Mellon University and Carnegie Mellon University Dept of Psychology and Ctr for the Neural Basis of Cognition
Keywords: nonparametric density estimation ; level set trees ; clustering ; functional data analysis
Abstract:

Level set trees provide a statistically principled framework for visualizing and clustering high-dimensional and complex data. We improve and generalize level set trees in a traditional probability density-based setting by showing how to use them interactively for data analysis and by indexing the tree height by the empirical probability content rather than level values. Next we extend the applicability of level set trees by generalizing the method to data sets that lack bona fide probability densities. In functional data analysis for example, we use pseudo-densities to construct level set trees for infinite-dimensional data and show that this technique produces reliable and accurate clustering results. Level set trees can also be used to construct hierarchical groupings of lattice points based on an arbitrary function evaluated on the lattice. Finally, we explore the use of level set trees for statistical inference, proposing simple methods based on repeated subsampling to describe the stochastic fluctuations in tree features. We use the new python toolbox DEnsity-BAsed CLustering (DeBaCl) to illustrate our methods on several simulated and neuroimaging data sets.


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