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Random projections, the Johnson-Lindenstrauss Lemma, and topological persistence

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David Letscher, Saint Louis University

What
  • Topology Seminar
When Fri, Apr 12, 2013
from 11:00 AM to 11:50 AM
Where Ritter Hall 316
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Abstract:  The Johnson-Lindenstrauss lemma says that you can project sets points in a high dimensional space to a much smaller dimension that roughly preserves pairwise distances.  In fact, with some probability, a random projection will suffice.  We prove a similar result holds when considering topological information.  In particular, with some probability, random projections to a lower dimension does not significantly change the homology of a union of balls in Euclidean space.  This leads to a practical probabilistic algorithm for calculating persistent homology for high dimensional spaces.

 
 
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