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

TL;DR

This paper introduces a multi-metric latent factor model that employs multiple vector spaces and norms to better analyze high-dimensional, sparse data, outperforming existing methods.

Contribution

It proposes a novel multi-metric approach with ensemble strategy for latent factor analysis on heterogeneous high-dimensional sparse matrices.

Findings

MMLF outperforms 10 state-of-the-art models on eight real-world datasets.

Theoretical analysis confirms performance gains.

Ensemble of multiple metric spaces enhances representation quality.

Abstract

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.