Geometric Tools for Algorithms.
Abstract
Our thesis is that a geometric perspective yields insights into the structure of fundamental problems, and thereby suggests efficient algorithms for them. As evidence we develop new geometric models and general-purpose tools for removing outliers from numeric data, reducing dimensionality, and counting combinatorial sets. Then we apply these techniques to a set of old problems to obtain polynomial-time algorithms. These include: (1) learning noisy linear-threshold functions (half-spaces), (2) learning the intersection of halfspaces, (3) clustering text corpora, and (4) counting lattice points in a convex body. We supplement some of our theorems with experimental studies.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1997
- Accession Number
- ADA329831
Entities
People
- Santosh Vempala
Organizations
- Carnegie Mellon University