  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.
