# Cluster Developing 1-Bit Matrix Completion

## TL;DR

This paper introduces Cluster Developing 1-Bit Matrix Completion methods that incorporate group-specific effects and clustering to improve recommender systems, especially when grouping information is unavailable.

## Contribution

It proposes GS1MC to include group effects in 1-bit matrix completion and CDMC to cluster users/items without prior grouping, integrating sparse subspace clustering.

## Key findings

- GS1MC outperforms existing 1-bit matrix completion methods.
- CDMC effectively captures item features from sparse binary data.
- Clustering enhances the interpretability and accuracy of recommender systems.

## Abstract

Matrix completion has a long-time history of usage as the core technique of recommender systems. In particular, 1-bit matrix completion, which considers the prediction as a ``Recommended'' or ``Not Recommended'' question, has proved its significance and validity in the field. However, while customers and products aggregate into interacted clusters, state-of-the-art model-based 1-bit recommender systems do not take the consideration of grouping bias. To tackle the gap, this paper introduced Group-Specific 1-bit Matrix Completion (GS1MC) by first-time consolidating group-specific effects into 1-bit recommender systems under the low-rank latent variable framework. Additionally, to empower GS1MC even when grouping information is unobtainable, Cluster Developing Matrix Completion (CDMC) was proposed by integrating the sparse subspace clustering technique into GS1MC. Namely, CDMC allows clustering users/items and to leverage their group effects into matrix completion at the same time. Experiments on synthetic and real-world data show that GS1MC outperforms the current 1-bit matrix completion methods. Meanwhile, it is compelling that CDMC can successfully capture items' genre features only based on sparse binary user-item interactive data. Notably, GS1MC provides a new insight to incorporate and evaluate the efficacy of clustering methods while CDMC can be served as a new tool to explore unrevealed social behavior or market phenomenon.