# Regularized Projection Matrix Approximation with Applications to Community Detection

arXiv: https://arxiv.org/abs/2405.16598 · HTML: https://mlsanity.com/paper/2405.16598/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 26 May 2024.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Adaptive Huber Regression](https://mlsanity.com/paper/1706.06991/) (2017)
- [Statistical-Computational Tradeoffs in Planted Problems and Submatrix Localization with a Growing Number of Clusters and Submatrices](https://mlsanity.com/paper/1402.1267/) (2014)
- [On semidefinite relaxations for the block model](https://mlsanity.com/paper/1406.5647/) (2014)
- [Simplex-Structured Matrix Factorization: Sparsity-based Identifiability and Provably Correct Algorithms](https://mlsanity.com/paper/2007.11446/) (2020)
- [Generalized Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/1905.12995/) (2019)
- [Quadratic Matrix Factorization with Applications to Manifold Learning](https://mlsanity.com/paper/2301.12965/) (2023)
- [An efficient approach for nonconvex semidefinite optimization via customized alternating direction method of multipliers](https://mlsanity.com/paper/2209.03437/) (2022)
- [Bounded Projection Matrix Approximation with Applications to Community Detection](https://mlsanity.com/paper/2305.15430/) (2023)

## Abstract (arXiv)

This paper introduces a regularized projection matrix approximation framework designed to recover cluster information from the affinity matrix. The model is formulated as a projection approximation problem, incorporating an entry-wise penalty function. We investigate three distinct penalty functions, each specifically tailored to address bounded, positive, and sparse scenarios. To solve this problem, we propose direct optimization on the Stiefel manifold, utilizing the Cayley transformation along with the Alternating Direction Method of Multipliers (ADMM) algorithm. Additionally, we provide a theoretical analysis that establishes the convergence properties of ADMM, demonstrating that the convergence point satisfies the KKT conditions of the original problem. Numerical experiments conducted on both synthetic and real-world datasets reveal that our regularized projection matrix approximation approach significantly outperforms state-of-the-art methods in clustering performance.