Local Convex Representation with Pruning for Manifold Clustering

High-dimensional data in many applications can be considered as samples drawn from a union of multiple lowdimensional manifolds. Assigning data points into their own manifolds is referred to manifold clustering. Inspired by recent advances in subspace clustering, in this paper, we present an efficient approach for manifold clustering, called Local Convex Representation (LCR), in which each data point is represented as a convex combination of other points in the local neighborhood and under some mild conditions the nonzero coefficients are guaranteed to correspond to the data points lying on the same manifold. Moreover, we incorporate the estimated intrinsic dimension of the manifold to prune the minor nonzero coefficients and validate that the pruning step helps LCR yield remarkable improvements. Experiments on synthetic data as well as real world data demonstrate promising performance.