Curve Registered Coupled Low Rank Factorization

TL;DR

This paper introduces registered CP, a novel tensor decomposition model that simultaneously estimates latent factors and unknown diffeomorphisms across data slices, merging curve registration with tensor factorization.

Contribution

It extends the canonical polyadic tensor model by incorporating unknown diffeomorphisms, enabling joint estimation of latent factors and their transformations.

Findings

Registered CP outperforms existing models in simulations.

The algorithm effectively estimates both factors and diffeomorphisms.

Simulation results demonstrate improved accuracy over traditional methods.

Abstract

We propose an extension of the canonical polyadic (CP) tensor model where one of the latent factors is allowed to vary through data slices in a constrained way. The components of the latent factors, which we want to retrieve from data, can vary from one slice to another up to a diffeomorphism. We suppose that the diffeomorphisms are also unknown, thus merging curve registration and tensor decomposition in one model, which we call registered CP. We present an algorithm to retrieve both the latent factors and the diffeomorphism, which is assumed to be in a parametrized form. At the end of the paper, we show simulation results comparing registered CP with other models from the literature.