Project: Large scale applications of principal angles in Statistics, Information Retrieval and Data Mining

MATH 6664 and C SC 5646: Numerical Linear Algebra

Fall 2001. University of Colorado at Denver

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: by appointment
WWW: http://www-math.cudenver.edu/~aknyazev/
Email: aknyazev@math.cudenver.edu

The Background:
A paper A. V. Knyazev, Merico E. Argentati, An Effective and Robust Algorithm for Finding Principal Angles Between Subspaces Using An A-Based Scalar Product; a revised version submitted to SISC, 2000, describes algorithms of computing principal angles between subspaces. These algorithms are implemented in a MATLAB code SUBSPACEA.m. The code accurately and relatively efficiently computes principal angles between subspaces given by dense matrices of the size n-by-p and n-by-q when n >> p and n >> q. A similar code for subspaces given by sparse matrices is a work in progress.

The Ultimate Goal:
Finding possible applications of principal angles in Statistics, Information Retrieval and Data Mining, providing small- and large-scale test problems for the code, and analyzing the numerical results of the tests.

The Project Stages:
1. Browsing the web, reading the literature and gathering other intelligence on Statistics, Information Retrieval and Data Mining, identifying applications of principal angles between subspaces. Tentative Due Date: November 6.
2. Formulating and testing small-scale problems using the existing MATLAB code SUBSPACEA.m. Tentative Due Date: November 13.
3. Formulating and testing large-scale problems for upcoming MATLAB and parallel codes for subspaces given by sparse matrices. Tentative Due Date: December 10.

Starting points on Information Retrieval and Data Mining: