A novel conformal deformation based sparse subspace clustering

Sparse Subspace Clustering (SSC) methods based on variant norms have attracted significant attention due to their empirical success. However, SSC methods presume that data points are embedded in a linear space and use the linear structure to find the sparse representation of data. Unfortunately, real-world datasets usually reside on a special manifold where linear geometry reduces the efficiency of clustering methods. This paper extends Sparse Subspace Clustering with l_1 -norm and Entropy norm to cluster data points that lie in submanifolds of an unknown manifold. The key idea is to provide a novel feature space by conformal mapping the original intrinsic manifolds with unknown structures to n-spheres such that angles and sparse similarities of the original manifold data are preserved. The proposed method finds an appropriate distance instead of the Euclidean distance for the Kernel SSC algorithm and the SSC algorithm with Entropy norm. Finally, we provide the experimental analysis to compare the efficiency of stereographic sparse subspace clustering with l_1 -norm, Entropy norm, and kernel on several data sets.