# Orthogonal Inductive Matrix Completion

arXiv: https://arxiv.org/abs/2004.01653 · HTML: https://mlsanity.com/paper/2004.01653/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Localization from structured distance matrices via low-rank matrix recovery](https://mlsanity.com/paper/2311.18076/) (2023)
- [Generalization Bounds for Inductive Matrix Completion in Low-noise Settings](https://mlsanity.com/paper/2212.08339/) (2022)
- [Bridging Offline-Online Evaluation with a Time-dependent and Popularity Bias-free Offline Metric for Recommenders](https://mlsanity.com/paper/2308.06885/) (2023)
- [Conv4Rec: A 1-by-1 Convolutional AutoEncoder for User Profiling through Joint Analysis of Implicit and Explicit Feedbacks](https://mlsanity.com/paper/2509.07499/) (2025)
- [Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information](https://mlsanity.com/paper/2511.13049/) (2025)

## Abstract (arXiv)

We propose orthogonal inductive matrix completion (OMIC), an interpretable approach to matrix completion based on a sum of multiple orthonormal side information terms, together with nuclear-norm regularization. The approach allows us to inject prior knowledge about the singular vectors of the ground truth matrix. We optimize the approach by a provably converging algorithm, which optimizes all components of the model simultaneously. We study the generalization capabilities of our method in both the distribution-free setting and in the case where the sampling distribution admits uniform marginals, yielding learning guarantees that improve with the quality of the injected knowledge in both cases. As particular cases of our framework, we present models which can incorporate user and item biases or community information in a joint and additive fashion. We analyse the performance of OMIC on several synthetic and real datasets. On synthetic datasets with a sliding scale of user bias relevance, we show that OMIC better adapts to different regimes than other methods. On real-life datasets containing user/items recommendations and relevant side information, we find that OMIC surpasses the state-of-the-art, with the added benefit of greater interpretability.