A Geometric Perspective on Machine Learning and Data Mining

Increasingly, we face machine learning problems in very high dimensional spaces. We proceed with the intuition that although
natural data lives in very high dimensions, they have relatively few degrees of freedom. One way to formalize this intuition is to model
the data as lying on or near a low dimensional manifold embedded in the high dimensional space. This point of view leads to a
new class of algorithms that are "manifold motivated" and a new set of theoretical questions that surround their analysis.
A central construction in these algorithms is a graph or simplicial complex that is data-derived and we will relate the geometry
of these to the geometry of the underlying manifold. Applications to embedding, clustering, classification, and
semi-supervised learning will be considered.

Partha Niyogi, University of Chicago

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