Unlabelled Principal Component Analysis

Abstract: This talk will consider the problem of recovering a matrix of bounded rank from a corrupted version of it, where the corruption consists of an unknown permutation of the matrix entries. Exploiting the theory of Groebner bases for determinantal ideals, recovery theorems will be given. For a special instance of the problem, an algorithmic pipeline will be demonstrated, which employs methods for robust principal component analysis with respect to outliers and methods for linear regression without correspondences.

machine learningalgebraic geometry

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html