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

arXiv: https://arxiv.org/abs/2204.07819 · HTML: https://mlsanity.com/paper/2204.07819/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 16 Apr 2022.

## Builds on (most cited first, 18 of 18)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [Neural Factorization Machines for Sparse Predictive Analytics](https://mlsanity.com/paper/1708.05027/) (2017)
- [Deep Learning based Recommender System: A Survey and New Perspectives](https://mlsanity.com/paper/1707.07435/) (2017)
- [Neural Collaborative Filtering vs. Matrix Factorization Revisited](https://mlsanity.com/paper/2005.09683/) (2020)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [Neural Rating Regression with Abstractive Tips Generation for Recommendation](https://mlsanity.com/paper/1708.00154/) (2017)
- [Meta Matrix Factorization for Federated Rating Predictions](https://mlsanity.com/paper/1910.10086/) (2019)
- [Latent Relational Metric Learning via Memory-based Attention for Collaborative Ranking](https://mlsanity.com/paper/1707.05176/) (2017)
- [Federated Multi-view Matrix Factorization for Personalized Recommendations](https://mlsanity.com/paper/2004.04256/) (2020)
- [Multi-Component Graph Convolutional Collaborative Filtering](https://mlsanity.com/paper/1911.10699/) (2019)
- [Fast Matrix Factorization with Non-Uniform Weights on Missing Data](https://mlsanity.com/paper/1811.04411/) (2018)

## Built on by (most cited first, 1 of 1)

- [High Order Collaboration-Oriented Federated Graph Neural Network for Accurate QoS Prediction](https://mlsanity.com/paper/2507.05308/) (2025)

## Abstract (arXiv)

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.