# Stochastic Gradient Descent for Spectral Embedding with Implicit Orthogonality Constraint

arXiv: https://arxiv.org/abs/1812.05721 · HTML: https://mlsanity.com/paper/1812.05721/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Multilayer Graph Clustering with Optimized Node Embedding](https://mlsanity.com/paper/2103.16534/) (2021)

## Abstract (arXiv)

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spectral embedding so that it can be solved via stochastic optimization. The idea is to replace the orthogonality constraint with an orthogonalization matrix injected directly into the criterion. As the gradient can be computed through a Cholesky factorization, our reformulation allows us to develop an efficient algorithm based on mini-batch gradient descent. Experimental results, both on synthetic and real data, confirm the efficiency of the proposed method in term of execution speed with respect to similar existing techniques.