# Bounded Projection Matrix Approximation with Applications to Community Detection

arXiv: https://arxiv.org/abs/2305.15430 · HTML: https://mlsanity.com/paper/2305.15430/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 21 May 2023.

## Builds on (most cited first, 7 of 7)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Understanding graph embedding methods and their applications](https://mlsanity.com/paper/2012.08019/) (2020)
- [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)
- [An efficient approach for nonconvex semidefinite optimization via customized alternating direction method of multipliers](https://mlsanity.com/paper/2209.03437/) (2022)

## Built on by (most cited first, 2 of 2)

- [Regularized Projection Matrix Approximation with Applications to Community Detection](https://mlsanity.com/paper/2405.16598/) (2024)
- [Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications](https://mlsanity.com/paper/2607.21039/) (2026)

## Abstract (arXiv)

Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable convex penalty and derive an alternating direction method of multipliers (ADMM) algorithm. Theoretically, we establish the convergence properties of the proposed algorithm. Numerical experiments demonstrate the superiority of our algorithm over its competitors, such as the semi-definite relaxation method and spectral clustering.