Robust Subspace Clustering by Combined Use of kNND Metric and SVD Algorithm

Subspace clustering has many applications in computer
vision, such as image/video segmentation and pattern
classification. The major issue in subspace clustering
is to obtain the most appropriate subspace from the given
noisy data. Typical methods (e.g., SVD, PCA, and Eigendecomposition)
use least squares techniques, and are sensitive
to outliers. In this paper, we present the k-th Nearest
Neighbor Distance (kNND) metric, which, without actually
clustering the data, can exploit the intrinsic data cluster
structure to detect and remove influential outliers as well
as small data clusters. The remaining data provide a good
initial inlier data set that resides in a linear subspace whose
rank (dimension) is upper-bounded. Such linear subspace
constraint can then be exploited by simple algorithms, such
as iterative SVD algorithm, to (1) detect the remaining outliers
that violate the correlation structure enforced by the
low rank subspace, and (2) reliably compute the subspace.
As an example, we apply our method to extracting layers
from image sequences containing dynamically moving objects.