Robust spectral clustering using LASSO regularization
This work addresses the need for more robust clustering methods in graph analysis, though it appears incremental as it builds on existing spectral clustering with a new regularization approach.
The paper tackles the problem of improving spectral clustering's theoretical guarantees for graph partition recovery by introducing a variant called 1-spectral clustering, which uses LASSO regularization to promote sparsity, and demonstrates its effectiveness and robustness in simulated and real data examples.
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is currently one of the most widely used due to its speed and simplicity. Yet, there are few theoretical guarantee to recover the underlying partitions of the graph for general models. This paper therefore presents a variant of spectral clustering, called 1-spectral clustering, performed on a new random model closely related to stochastic block model. Its goal is to promote a sparse eigenbasis solution of a 1 minimization problem revealing the natural structure of the graph. The effectiveness and the robustness to small noise perturbations of our technique is confirmed through a collection of simulated and real data examples.