Curve Registered Coupled Low Rank Factorization
This work addresses a specific challenge in tensor analysis for researchers in signal processing or data science, but it appears incremental as it extends an existing model with constrained variations.
The authors tackled the problem of tensor decomposition when latent factors vary across data slices via unknown diffeomorphisms, proposing a registered CP model that merges curve registration and tensor decomposition, and demonstrated its performance through simulation comparisons with other models.
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.