# The Minority Matters: A Diversity-Promoting Collaborative Metric Learning Algorithm

arXiv: https://arxiv.org/abs/2209.15292 · HTML: https://mlsanity.com/paper/2209.15292/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 67 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Learning Disentangled Representations for Recommendation](https://mlsanity.com/paper/1910.14238/) (2019)
- [Fast Matrix Factorization for Online Recommendation with Implicit Feedback](https://mlsanity.com/paper/1708.05024/) (2017)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Denoising Implicit Feedback for Recommendation](https://mlsanity.com/paper/2006.04153/) (2020)
- [Understanding Negative Sampling in Graph Representation Learning](https://mlsanity.com/paper/2005.09863/) (2020)
- [Generalization bounds for deep convolutional neural networks](https://mlsanity.com/paper/1905.12600/) (2019)
- [A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning](https://mlsanity.com/paper/2109.02355/) (2021)
- [Outer Product-based Neural Collaborative Filtering](https://mlsanity.com/paper/1808.03912/) (2018)
- [Latent Relational Metric Learning via Memory-based Attention for Collaborative Ranking](https://mlsanity.com/paper/1707.05176/) (2017)
- [A Neural Autoregressive Approach to Collaborative Filtering](https://mlsanity.com/paper/1605.09477/) (2016)
- [Bootstrapping User and Item Representations for One-Class Collaborative Filtering](https://mlsanity.com/paper/2105.06323/) (2021)
- [Recommendations and User Agency: The Reachability of Collaboratively-Filtered Information](https://mlsanity.com/paper/1912.10068/) (2019)
- [Towards Open-World Recommendation: An Inductive Model-based Collaborative Filtering Approach](https://mlsanity.com/paper/2007.04833/) (2020)
- [Multi-Component Graph Convolutional Collaborative Filtering](https://mlsanity.com/paper/1911.10699/) (2019)
- [Collaborative Translational Metric Learning](https://mlsanity.com/paper/1906.01637/) (2019)
- [Improving Collaborative Metric Learning with Efficient Negative Sampling](https://mlsanity.com/paper/1909.10912/) (2019)
- [Local Rademacher Complexity Bounds based on Covering Numbers](https://mlsanity.com/paper/1510.01463/) (2015)
- [The Stereotyping Problem in Collaboratively Filtered Recommender Systems](https://mlsanity.com/paper/2106.12622/) (2021)
- [The Sample Complexity of Online One-Class Collaborative Filtering](https://mlsanity.com/paper/1706.00061/) (2017)
- [Quantifying Availability and Discovery in Recommender Systems via Stochastic Reachability](https://mlsanity.com/paper/2107.00833/) (2021)
- [Rethinking Neural vs. Matrix-Factorization Collaborative Filtering: the Theoretical Perspectives](https://mlsanity.com/paper/2110.12141/) (2021)
- [Collaborative Metric Learning with Memory Network for Multi-Relational Recommender Systems](https://mlsanity.com/paper/1906.09882/) (2019)
- [Hierarchical Latent Relation Modeling for Collaborative Metric Learning](https://mlsanity.com/paper/2108.04655/) (2021)
- [Density-Ratio Based Personalised Ranking from Implicit Feedback](https://mlsanity.com/paper/2101.07481/) (2021)

## Built on by (most cited first, 9 of 9)

- [AUCSeg: AUC-oriented Pixel-level Long-tail Semantic Segmentation](https://mlsanity.com/paper/2409.20398/) (2024)
- [One Image is Worth a Thousand Words: A Usability Preservable Text-Image Collaborative Erasing Framework](https://mlsanity.com/paper/2505.11131/) (2025)
- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [adSformers: Personalization from Short-Term Sequences and Diversity of Representations in Etsy Ads](https://mlsanity.com/paper/2302.01255/) (2023)
- [Break Out of a Pigeonhole: A Unified Framework for Examining Miscalibration, Bias, and Stereotype in Recommender Systems](https://mlsanity.com/paper/2312.17443/) (2023)
- [Tree of Preferences for Diversified Recommendation](https://mlsanity.com/paper/2601.02386/) (2025)
- [Geometric Collaborative Filtering with Convergence](https://mlsanity.com/paper/2410.03064/) (2024)
- [Towards a Theoretical Understanding of Two Tower Recommendation Models](https://mlsanity.com/paper/2403.00802/) (2024)
- [Cross-Temporal 3D Gaussian Splatting for Sparse-View Guided Scene Update](https://mlsanity.com/paper/2512.00534/) (2025)

## Abstract (arXiv)

Collaborative Metric Learning (CML) has recently emerged as a popular method in recommendation systems (RS), closing the gap between metric learning and Collaborative Filtering. Following the convention of RS, existing methods exploit unique user representation in their model design. This paper focuses on a challenging scenario where a user has multiple categories of interests. Under this setting, we argue that the unique user representation might induce preference bias, especially when the item category distribution is imbalanced. To address this issue, we propose a novel method called textitDiversity-Promoting Collaborative Metric Learning (DPCML), with the hope of considering the commonly ignored minority interest of the user. The key idea behind DPCML is to include a multiple set of representations for each user in the system. Based on this embedding paradigm, user preference toward an item is aggregated from different embeddings by taking the minimum item-user distance among the user embedding set. Furthermore, we observe that the diversity of the embeddings for the same user also plays an essential role in the model. To this end, we propose a textitdiversity control regularization term to accommodate the multi-vector representation strategy better. Theoretically, we show that DPCML could generalize well to unseen test data by tackling the challenge of the annoying operation that comes from the minimum value. Experiments over a range of benchmark datasets speak to the efficacy of DPCML.