Compressed Locally Embedding

The common strategy of Spectral manifold learning algorithms, e.g., Locally Linear Embedding (LLE) and Laplacian Eigenmap (LE), facilitates neighborhood relationships which can be constructed by $knn$ or $\epsilon$ criterion. This paper presents a simple technique for constructing the nearest neighborhood based on the combination of $\ell_{2}$ and $\ell_{1}$ norm. The proposed criterion, called Locally Compressive Preserving (CLE), gives rise to a modified spectral manifold learning technique. Illuminated by the validated discriminating power of sparse representation, we additionally formulate the semi-supervised learning variation of CLE, SCLE for short, based on the proposed criterion to utilize both labeled and unlabeled data for inference on a graph. Extensive experiments on both manifold visualization and semi-supervised classification demonstrate the superiority of the proposed algorithm.