# Matrix Completion with Hierarchical Graph Side Information

@article{Elmahdy2020MatrixCW, title={Matrix Completion with Hierarchical Graph Side Information}, author={Adel M. Elmahdy and Junhyung Ahn and Changho Suh and Soheil Mohajer}, journal={ArXiv}, year={2020}, volume={abs/2201.01728} }

We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clustering and matrix ratings. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model (to be detailed), we demonstrate that our…

## 8 Citations

### When to Use Graph Side Information in Matrix Completion

- Computer Science2021 IEEE International Symposium on Information Theory (ISIT)
- 2021

The key idea is to make a careful selection for the information employed in the first clustering step, between two types of given information: graph & matrix ratings.

### The Optimal Sample Complexity of Matrix Completion with Hierarchical Similarity Graphs

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

The information-theoretic limit on the number of observed matrix entries is characterized as a function of the quality of graph side information by proving sharp upper and lower bounds on the sample complexity.

### On the Fundamental Limits of Matrix Completion: Leveraging Hierarchical Similarity Graphs

- Computer ScienceArXiv
- 2021

The optimal sample complexity is analyzed and different regimes whose characteristics rely on quality metrics of side information of the hierarchical similarity graph are identified and it is shown that the characterized information-theoretic limit can be asymptotically achieved.

### Graph-assisted Matrix Completion in a Multi-clustered Graph Model

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

A computationally efficient algorithm is developed that achieves the optimal sample complexity for the entire regime of graph information under the multiple cluster setting and outperforms prior algorithms that leverage graph side information.

### Community Detection and Matrix Completion With Social and Item Similarity Graphs

- Computer ScienceIEEE Transactions on Signal Processing
- 2021

This work considers the problem of recovering a binary rating matrix as well as clusters of users and items based on a partially observed matrix together with side-information in the form of social and item similarity graphs together with lower and upper bounds on sample complexity that match for various scenarios.

### Discrete-Valued Latent Preference Matrix Estimation with Graph Side Information

- Computer ScienceICML
- 2021

A new model is proposed in which 1) the unknown latent preference matrix can have any discrete values, and 2) users can be clustered into multiple clusters, thereby relaxing the assumptions made in prior work.

### Online Low Rank Matrix Completion

- Computer Science
- 2022

A novel algorithm OCTAL (Online Collaborative ﬁlTering using iterAtive user cLustering) that ensures nearly optimal regret bound of O ( polylog ( M + N ) T 1 / 2 ) .

### Nonparametric Matrix Estimation with One-Sided Covariates

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

This work provides an algorithm and accompanying analysis which shows that the algorithm improves upon naively estimating each row separately when the number of rows is not too small and achieves the minimax optimal nonparametric rate of an oracle algorithm that knows the row covariates.

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