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.

翻译：线性潜变量模型（如主成分分析PCA、独立成分分析ICA、典型相关分析CCA和因子分析FA）能够识别有序或无序的潜在方向（或载荷）。数据通过投影至这些潜在方向获取其投影表示（或得分）。例如，PCA求解器通常按方差从大到小排序主方向，而ICA求解器通常返回无序的独立方向，且常常将单一源信号分散到多个方向形成多个子源，严重损害了其可用性与可解释性。本文提出一个通用框架以增强线性潜空间的表示能力，从而提升其可解释性。尽管本文概念与语言无关，但该框架采用Python实现。该框架通过自动化潜向量的聚类与排序，增强每个潜向量的信息含量及其可解释性。框架集成了多项创新性增强技术，包括：潜向量排序（LR）、潜向量缩放（LS）、潜向量聚类（LC）及潜向量浓缩（LCON）。对于指定的线性潜变量模型，LR根据指定度量标准对潜方向进行排序；LS根据指定度量标准缩放潜方向；LC自动将潜方向聚类至指定数量的簇；而LCON则针对给定度量标准，自动确定将潜方向浓缩至适当数量的簇。框架的附加功能包括：支持单通道与多通道数据源，以及数据预处理策略（如Hankel化），以无缝扩展线性潜变量模型（LLVM）对更广泛数据类型的适用性。本文通过两个基础性问题案例（分别应用PCA和ICA两种潜变量模型）展示了LR、LS及LCON的有效性。