Local Convex Representation with Pruning for Manifold Clustering Highdimensional 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.

Image Recognition Using Manifold Constrained Collaborative Representation Image recognition is still a challenging task due to the existed illumination and view variations. Manifold learning and representation based classifiers (RCs) are two widely utilized methods to treat the image recognition. The common RCs only emphasize the representation by the training samples globally, while the geometric manifold structure of samples is not fully considered. In this letter, a novel manifold constrained collaborative representation is proposed, which aims to make the representation of query sample be similar with the codes of their nearbypoints. Thus, the obtained representations can be more discriminative for recognition. Extensive experiments on several popular databases show that the our proposed method is promising in recognizing various images.