435
14

Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian

Abstract

The extraction of clusters from a dataset which includes multiple clusters and another significant portion of "background" samples is a task of practical importance. The traditional spectral clustering algorithm, relying on the leading KK eigenvectors to detect the KK clusters, fails in such cases. This paper proposes the spectral embedding norm which sums the squared values of the first II (normalized) eigenvectors, where II can be larger than KK. We prove that the quantity can be used to separate clusters from the background under generic conditions motivated by applications such as anomaly detection. The performance of the algorithm is not sensitive to the choice of II, and we present experiments on synthetic and real-world datasets.

View on arXiv
Comments on this paper