#### Conference abstracts

Session A4 - Computational Geometry and Topology

July 10, 15:00 ~ 15:25

## Supervised Learning of Labeled Pointcloud Differences via Cover-Tree Entropy Reduction

### Paul Bendich

### Duke University, and Geometric Data Analytics, United States of America - bendich@math.duke.edu

We introduce a new algorithm, called CDER, for supervised machine learning that merges the multi-scale geometric properties of Cover Trees with the information-theoretic properties of entropy. CDER applies to a training set of labeled pointclouds embedded in a common Euclidean space. If typical pointclouds corresponding to distinct labels tend to differ at any scale in any sub-region, CDER can identify these differences in (typically) linear time, creating a set of distributional coordinates which act as a feature extraction mechanism for supervised learning. We describe theoretical properties and implementation details of CDER, and illustrate its benefits on several synthetic examples

Joint work with Abraham Smith (University of Wisconsin-Stout, Geometric Data Analytics), John Harer (Duke University, Geometric Data Analytics) and Jay Hineman (Geometric Data Analytics).