Finding Rule-Interpretable Non-Negative Data Representation

TL;DR

This paper introduces a novel NMF-based method that integrates rule-based descriptions to produce interpretable, part-based, lower-dimensional representations of non-negative data, enhancing interpretability and focus on specific labels.

Contribution

The proposed approach merges rule-based descriptions with NMF to generate interpretable, rule-described latent factors in non-negative data, improving interpretability over traditional NMF.

Findings

Creates rule-described non-negative data representations

Reveals attribute importance and interactions

Enables focused embedding with multiple labels

Abstract

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other dimensionality reduction approaches (such as PCA) because the non-negativity of the approach naturally fits the characteristics of the domain problem and its results are easier to analyze and understand. Despite these advantages, obtaining exact characterization and interpretation of the NMF's latent factors can still be difficult due to their numerical nature. Rule-based approaches, such as rule mining, conceptual clustering, subgroup discovery and redescription mining, are often considered more interpretable but lack lower-dimensional representation of the data. We present a version of the NMF approach that merges rule-based descriptions with advantages of part-based representation offered by the NMF. Given the numerical input data with non-negative entries and a set of rules with high entity coverage, the approach creates the lower-dimensional non-negative representation of the input data in such a way that its factors are described by the appropriate subset of the input rules. In addition to revealing important attributes for latent factors, their interaction and value ranges, this approach allows performing focused embedding potentially using multiple overlapping target labels.