In this paper, we present a novel low rank representation (LRR) algorithm for data lying on the manifold of square root densities. Unlike traditional LRR methods which rely on the assumption that the data points are vectors in the Euclidean space, our new algorithm is designed to incorporate the intrinsic geometric structure and geodesic distance of the manifold. Experiments on several computer...

Emerging high-dimensional data mining applications needs to find interesting clusters embeded in arbitrarily aligned subspaces of lower dimensionality. It is difficult to cluster high-dimensional data objects, when they are sparse and skewed. Updations are quite common in dynamic databases and they are usually processed in batch mode. In very large dynamic databases, it is necessary to perform ...

Sparse Subspace Clustering (SSC) has been used extensively for subspace iden-tification tasks due to its theoretical guarantees and relative ease of implemen-tation. However SSC has quadratic computation and memory requirementswith respect to the number of input data points. This burden has prohibitedSSCs use for all but the smallest datasets. To overcome this we propose a n...

Clustering techniques often define the similarity between instances using distance measures over the various dimensions of the data [12, 14]. Subspace clustering is an extension of traditional clustering that seeks to find clusters in different subspaces within a dataset. Traditional clustering algorithms consider all of the dimensions of an input dataset in an attempt to learn as much as possi...

AMS subject classifications: 62H10 62H15 Keywords: Covariance matrix Hypothesis testing High-dimensional data analysis a b s t r a c t In this paper we propose a new test procedure for sphericity of the covariance matrix when the dimensionality, p, exceeds that of the sample size, N = n + 1. Under the assumptions that (A) 0 < trΣ the concentration, a new statistic is developed utilizing the rat...

This paper addresses the subspace properties and the recovery of articulated motion. We point out that the nature of the motion subspace of an articulated object is a combination of a number of intersecting rigid motion subspaces. The rank of that motion subspace is less than that of each articulated part combined, depending on the connection between every two linked parts, either a rotation ax...

Traditional clustering algorithms consider all of the dimensions of an input data set equally. However, in the high dimensional data, a common property is that data points are highly clustered in subspaces, which means classes of objects are categorized in subspaces rather than the entire space. Subspace clustering is an extension of traditional clustering that seeks to find clusters in differe...

We consider the problem of clustering incomplete data drawn from a union of subspaces. Classical subspace clustering methods are not applicable to this problem because the data are incomplete, while classical low-rank matrix completion methods may not be applicable because data in multiple subspaces may not be low rank. This paper proposes and evaluates two new approaches for subspace clusterin...

Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is n...