THE CATHOLIC UNIVERSITY OF AMERICA
Washington, DC 20064
SEMINAR IN FUNCTIONAL ANALYSIS
AND RELATED AREAS
Wednesday, February 18, 2026
5:15 p.m. - 6:15 p.m. 

 SPEAKER : Professor Reza Modarres
                    George Washington University

TITLE: High Dimensional Data Analysis: An Interpoint Distance Approach

ABSTRACT: High-dimensional data, where the number of features p far exceeds the number of observations n, has become increasingly prevalent in modern science and technology. From microarrays and fMRI to network traffic analysis, researchers are confronted with datasets consisting of millions of variables measured on only a few dozen samples. Classical multivariate methods, which assume n >> p, can lose effectiveness or even fail entirely when dealing with high-dimensional, low-sample-size (HDLSS) settings. In this context, interpoint distances play a crucial role, providing a way to reduce complex multivariate relationships into simpler one-dimensional summaries. By focusing on distances and dissimilarities, we avoid reliance on distributional assumptions and use the concentration of measure phenomenon to our advantage. We explore two high-dimensional dissimilarity measures and their convergence as p → ∞. Using these measures, we introduce new statistics for testing the equality of high-dimensional distributions, and we propose novel methods for classification, clustering, and change-point detection. Distance matrices serve as key representations in settings where direct access to data is impractical, or the data is inherently relational, such as in social networks or transportation systems. We investigate the connection between the eigenstructure of distance matrices and the presence of outliers. Furthermore, we establish an equivalence between constant distance matrices and distributional equality, and present tests for determining whether a distance matrix exhibits constant structure. We also study the eigenvalues of k distance matrices for testing distributional equality and further explore the spectral properties of dissimilarity matrices under HDLSS conditions.

 PLACE:  Aquinas Hall, Room 108. The talk will also be held on Zoom from 5:15 p.m. to 6:15 p.m. (ET). See the information about the corresponding link below.

ORGANIZERS: V. Bogdan (The Catholic University of America), P. Kainen (Georgetown University), R. Kalpathy (The Catholic University of America), and A. Levin (The Catholic University of America).

Tel: 202-319-5221  E-mail:levin@cua.edu

Web page:  https://mathematics.catholic.edu/faculty-and-research/mathematics-seminar/index.html

The talk will be on Zoom as well (from 5:15 p.m. to 6:15 p.m. ET).   The following is the information about the corresponding link.