Digital Signal Processing with Kernel Methods

11 Clustering and Anomaly Detection with Kernels

Many problems in signal processing deal with the identification of the right subspace where signals can be better represented. Finding good and representative groups or clusters in the data is of course the main venue. We will find many kernel algorithms to approach the problem, by ‘kernelizing’ either the metric or the algorithm. When there is just one class of interest, alternative methods exist under the framework of one‐class detection or anomaly detection. The field of anomaly detection has the challenge of finding the anomalous patterns in the data. Anomaly detection from data has many practical implications, such as the classification of rare events in time series, the identification of target signals buried in noise, or the online identification of changes and anomalies in the wild.

The problem of defining regularity, cluster, membership, and abnormality is a conceptually challenging one, for which there exist many lines of attack and assumptions involved. This chapter will review the recent advances of kernel methods in the fields of clustering, domain description (also known as outlier identification or one‐class classification) and subspace detectors. It goes without saying that all these methods are unsupervised or weakly supervised, so the challenge is even bigger. The chapter will present examples dealing with synthetic data as well as real problems in all these domains.

11.1 Introduction

Detecting patterns ...