  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.
