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

Abstract

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.