Kernel Spectral Clustering and applications

TL;DR

This paper reviews kernel spectral clustering (KSC), a kernel-based optimization approach that improves clustering by model-based parameter tuning, scalability, and applications in various real-world domains.

Contribution

It introduces a comprehensive review of KSC, including sparse algorithms, hierarchical and soft clustering methods, and demonstrates its effectiveness in large-scale and real-world applications.

Findings

KSC enables effective multi-way clustering using ECOC encoding.

Sparse KSC algorithms improve scalability for large datasets.

KSC demonstrates strong performance in image, time-series, and document clustering.

Abstract

In this chapter we review the main literature related to kernel spectral clustering (KSC), an approach to clustering cast within a kernel-based optimization setting. KSC represents a least-squares support vector machine based formulation of spectral clustering described by a weighted kernel PCA objective. Just as in the classifier case, the binary clustering model is expressed by a hyperplane in a high dimensional space induced by a kernel. In addition, the multi-way clustering can be obtained by combining a set of binary decision functions via an Error Correcting Output Codes (ECOC) encoding scheme. Because of its model-based nature, the KSC method encompasses three main steps: training, validation, testing. In the validation stage model selection is performed to obtain tuning parameters, like the number of clusters present in the data. This is a major advantage compared to classical spectral clustering where the determination of the clustering parameters is unclear and relies on heuristics. Once a KSC model is trained on a small subset of the entire data, it is able to generalize well to unseen test points. Beyond the basic formulation, sparse KSC algorithms based on the Incomplete Cholesky Decomposition (ICD) and $L_0$, $L_1, L_0 + L_1$, Group Lasso regularization are reviewed. In that respect, we show how it is possible to handle large scale data. Also, two possible ways to perform hierarchical clustering and a soft clustering method are presented. Finally, real-world applications such as image segmentation, power load time-series clustering, document clustering and big data learning are considered.