Latent Space Perspicacity and Interpretation Enhancement (LS-PIE) Framework

Abstract

Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or unordered. The data is then projected onto the latent directions to obtain their projected representations (or scores). For example, PCA solvers usually rank the principal directions by explaining the most to least variance, while ICA solvers usually return independent directions unordered and often with single sources spread across multiple directions as multiple sub-sources, which is of severe detriment to their usability and interpretability. This paper proposes a general framework to enhance latent space representations for improving the interpretability of linear latent spaces. Although the concepts in this paper are language agnostic, the framework is written in Python. This framework automates the clustering and ranking of latent vectors to enhance the latent information per latent vector, as well as, the interpretation of latent vectors. Several innovative enhancements are incorporated including latent ranking (LR), latent scaling (LS), latent clustering (LC), and latent condensing (LCON). For a specified linear latent variable model, LR ranks latent directions according to a specified metric, LS scales latent directions according to a specified metric, LC automatically clusters latent directions into a specified number of clusters, while, LCON automatically determines an appropriate number of clusters into which to condense the latent directions for a given metric. Additional functionality of the framework includes single-channel and multi-channel data sources, data preprocessing strategies such as Hankelisation to seamlessly expand the applicability of linear latent variable models (LLVMs) to a wider variety of data. The effectiveness of LR, LS, and LCON are showcased on two crafted foundational problems with two applied latent variable models, namely, PCA and ICA.