Embedding New Samples via Locality-Constrained Sparse Representation for Nonlinear Manifold Learning

How to embed the new observations (or samples) into the low-dimensional space is a crucial problem in non-linear manifold learning techniques. This issue can be converted into the problem of finding an accurate mapping that transfers the unseen data samples into an existing manifold. In this paper, a locality-constrained sparse representation algorithm is proposed to deal with the out-of-sample embedding problem for manifold learning. Through taking the data locality information into consideration, the local data structure can be well preserved in our proposed algorithm. To justify the superiority of the proposed method, our approach has been tested on several challenging face datasets and compared with other out-of-sample embedding techniques. The experimental results show that the proposed method can not only achieve the competitive recognition rate than the existing methods, but also save more time than the traditional nonlinear dimensionality reduction methods for the out-of-sample problem.