Work

Scattering Statistics of Generalized Spatial Poisson Point Processes

Year: 2022

Type: conference-paper

Abstract: We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples the roles of scale and frequency, replacing wavelets with Gabor-type measurements. We show that, with suitable nonlinearities, our measurements distinguish Poisson point processes from common self-similar processes, and separate different types of Poisson point processes.

Source: IEEE International Conference on Acoustics Speech and Signal Processing

DOI: 10.1109/icassp43922.2022.9746382

Authors: Michael Perlmutter, Jieqian He, Matthew Hirn

Institutions: University of California, Los Angeles, Michigan State University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Institute of General Medical Sciences

Award: Finding emergent structure in multi-sample biological data with the dual geometry of cells and features