Enhancing Non-Negative Matrix Factorization Interpretability with Fuzzy Representations

Although many approaches exist to reduce dimensionality, many of them compromise the explainability of the reasoning. Non-negative Matrix factorization, while interpretable to some degree, returns numerical results that could not be easy to understand. Our goal is to suggest an approach that simplifies computational complexity by reducing dimensionality while preserving the explainability of this process. This work introduces a framework that combines fuzzy representations with Non-negative Matrix Factorization (NMF) to improve its inter-pretability. By fuzzifying the factor matrices, descriptions that use linguistic expressions and their fuzzy values are generated, describing latent factors, samples, and clusters in the reduced space. This approach enhances the semantic understanding of the patterns and groups identified by NMF. The proposed framework is applied to acoustic data from a pilot study on bipolar disorder, a condition characterized by alternating mood states. Acoustic features extracted from patients' voices are analyzed using the proposed method, which describes the semantics of the identified latent factors, the samples, and the clustered data in natural language. This representation makes it easier for domain experts to understand the automatic process.