Outlier Cluster Formation in Spectral Clustering

Outlier detection and cluster number estimation is an important issue for clustering real data. This paper focuses on spectral clustering, a time-tested clustering method, and reveals its important properties related to outliers. The highlights of this paper are the following two mathematical observations: first, spectral clustering's intrinsic property of an outlier cluster formation, and second, the singularity of an outlier cluster with a valid cluster number. Based on these observations, we designed a function that evaluates clustering and outlier detection results. In experiments, we prepared two scenarios, face clustering in photo album and person re-identification in a camera network. We confirmed that the proposed method detects outliers and estimates the number of clusters properly in both problems. Our method outperforms state-of-the-art methods in both the 128-dimensional sparse space for face clustering and the 4,096-dimensional non-sparse space for person re-identification.