Latent Space Perspicacity and Interpretation Enhancement (LS-PIE)
  Framework
Jesse Stevens Daniel N. Wilke Itumeleng Setshedi
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.