A Multi-Metric Latent Factor Model for Analyzing High-Dimensional and Sparse data

High-dimensional and sparse (HiDS) matrices are omnipresent in a variety of big data-related applications. Latent factor analysis (LFA) is a typical representation learning method that extracts useful yet latent knowledge from HiDS matrices via low-rank approximation. Current LFA-based models mainly focus on a single-metric representation, where the representation strategy designed for the approximation Loss function, is fixed and exclusive. However, real-world HiDS matrices are commonly heterogeneous and inclusive and have diverse underlying patterns, such that a single-metric representation is most likely to yield inferior performance. Motivated by this, we in this paper propose a multi-metric latent factor (MMLF) model. Its main idea is two-fold: 1) two vector spaces and three Lp-norms are simultaneously employed to develop six variants of LFA model, each of which resides in a unique metric representation space, and 2) all the variants are ensembled with a tailored, self-adaptive weighting strategy. As such, our proposed MMLF enjoys the merits originated from a set of disparate metric spaces all at once, achieving the comprehensive and unbiased representation of HiDS matrices. Theoretical study guarantees that MMLF attains a performance gain. Extensive experiments on eight real-world HiDS datasets, spanning a wide range of industrial and science domains, verify that our MMLF significantly outperforms ten state-of-the-art, shallow and deep counterparts.