Constraining Non-Negative Matrix Factorization to Improve Signature Learning

Aldo Galeano, Suzana Santos, Ruben Jimenez, Alberto Paccanaro

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Keywords: Representation Learning, Colaborative Filtering (CF), Recommender Systems, Link Prediction

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TL;DR: We present a novel constrained non-negative matrix factorization model capable of learning meaningful representations by effectively harnessing the patterns within the observed association data.

Abstract:

Collaborative filtering approaches are fundamental for learning meaningful low-dimensional representations when only association data is available. Among these methods, Non-negative Matrix Factorization (NMF) has gained prominence due to its capability to yield interpretable and meaningful low-dimensional representations. However, one significant challenge for NMF is the vast number of solutions for the same problem instance, making the selection of high-quality signatures a complex task. In response to this challenge, our work introduces a novel approach, Self-Matrix Factorization (SMF), which leverages NMF by incorporating constraints that preserve the relationships inherent in the original data. This is achieved by drawing inspiration from a distinct family of matrix decomposition methods, known as Self-Expressive Models (SEM).
In our experimental analyses, conducted on two diverse benchmark datasets, our findings present a compelling narrative. SMF consistently delivers competitive or even superior performance when compared to NMF in predictive tasks. However, what truly sets SMF apart, as validated by our empirical results, is its remarkable ability to consistently generate significantly more meaningful object representations.

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Submission Number: 8304