Dept Banner
Dept Banner

Calendar

Download as iCal file

Experimental Mathematics Seminar

Matrix volume and its applications

Adi Ben-Israel: Rutgers University

Location:  Hill 705
Date & time: Thursday, 02 March 2017 at 5:00PM - 5:11PM

The volume vol(A) of an mxn matrix A of rank r is: (a) the product of the r singular values of A, or (b) the square root of the sum of squares of all r x r subdeterminants of A, or (c) the volume of the image under A of a unit cube in the range of A transpose. Definition (b) is applicable to non-numerical matrices, in particular to rectangular Jacobians. Some representative applications will be discussed.

References:

[1] The matrix volume: http://benisrael.net/VOLUME.pdf

[2] Application to change-of-variables in integration: http://benisrael.net/INTEGRAL-AMS.pdf

[3] Application to probability: http://benisrael.net/MADISON-AMS.pdf

[4] Low-rank approximation In this paper we show that the negative sample distance covariance function is a quasiconcave set function of samples of random variables that are not statistically independent. We use these properties to propose greedy algorithms to combinatorially optimize some diversity (low statistical dependence) promoting functions of distance covariance. Our greedy algorithm obtains all the inclusion-minimal maximizers of this diversity promoting objective. Inclusion-minimal maximizers are multiple solution sets of globally optimal maximizers that are not a proper subset of any other maximizing set in the solution set. We present results upon applying this approach to obtain diverse features (covariates/variables/predictors) in a feature selection setting for regression (or classification) problems. We also combine our diverse feature selection algorithm with a distance covariance based relevant feature selection algorithm of [7] to produce subsets of covariates that are both relevant yet ordered in non-increasing levels of diversity of these subsets.of matrices: A. Deshpande, L. Rademacher et al, Matrix Approximation and Projective Clustering via Volume Sampling, Theory of Computing 2(2006), 225-247

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.

Contact Us

HillCenter small

Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530