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# Drs. Huang, Kovalsky, and Marzuola, UNC – Mathematical and Statistical Analysis of Compressible Data on Compressive Network

## February 2, 2023 @ 3:30 pm - 4:30 pm

Mode: In-Person

Title: **Mathematical and Statistical Analysis of Compressible Data on Compressive Network**

Abstract:

We present an overview of the FRG project on the “Mathematical and Statistical Analysis of Compressible Data on Compressive Networks”.

Compressible features of data include the low-rank, low-dimension, sparsity, and features from the classification/categorization/clustering process.

Discovering such compressible features is a major challenge in data analysis, which we will address using hierarchical decompositions derived from

spectral, statistical, and algebraic geometric analysis of data. We also study how to construct optimally defined compressive networks, specifically tailored

to the discovered compressible features, to enable an accurate and efficient extraction and manipulation of sparse representations in complex and

high dimensional systems in an inherently interpretable manner. Sample ongoing projects include the accurate and efficient representation of layer

potential using algebraic variety, spectral flow and fast computation of the eigensystems, frequency domain based statistical analysis, fast algorithms

for high dimensional truncated multivariate Gaussian expectations, and recursive tree algorithms for orthogonal matrix generation and matrix-vector

multiplications in rigid body Brownian dynamics simulations.