Spectrally regularised LVMs : a spectral regularisation framework for latent variable models designed for single-channel applications

Abstract

Latent variable models (LVMs) are commonly used to capture the underlying dependencies, patterns, and hidden structures in observed data. Source duplication is a by-product of the data Hankelisation pre-processing step common to single-channel LVM applications, which hinders practical LVM utilisation. In this article, a Python package titled spectrally-regularised-LVMs is presented. The proposed package addresses the source duplication issue by adding a novel spectral regularisation term. This package provides a framework for spectral regularisation in single-channel LVM applications, thereby making it easier to investigate and utilise LVMs with spectral regularisation. This is achieved via symbolic or explicit representations of potential LVM objective functions, which are incorporated into a framework that uses spectral regularisation during the LVM parameter estimation process. This package aims to provide a consistent linear LVM optimisation framework incorporating spectral regularisation and caters to single-channel time-series applications.