Mini-Batch Spectral Clustering

TL;DR

This paper introduces a scalable spectral clustering method using adaptive stochastic gradient optimization that accurately recovers the Laplacian spectrum and outperforms existing approximate methods on large datasets.

Contribution

It presents a novel stochastic gradient approach for spectral clustering that guarantees exact spectrum recovery in the limit and is computationally efficient for large data sets.

Findings

Method scales to half a million samples

Outperforms state-of-the-art approximate methods

Recovers exact Laplacian spectrum asymptotically

Abstract

The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This paper proposes a practical approach to learn spectral clustering based on adaptive stochastic gradient optimization. Crucially, the proposed approach recovers the exact spectrum of Laplacian matrices in the limit of the iterations, and the cost of each iteration is linear in the number of samples. Extensive experimental validation on data sets with up to half a million samples demonstrate its scalability and its ability to outperform state-of-the-art approximate methods to learn spectral clustering for a given computational budget.