Accession Number : ADA329831
Title : Geometric Tools for Algorithms.
Descriptive Note : Doctoral thesis,
Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Vempala, Santosh
PDF Url : ADA329831
Report Date : AUG 1997
Pagination or Media Count : 85
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.
Descriptors : *ALGORITHMS, *NUMERICAL ANALYSIS, MODELS, COUNTING METHODS, THESES, SAMPLING, INFORMATION RETRIEVAL, GEOMETRY.
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE