Sparse Manifold Subspace Learning

Abstract

In this chapter, we introduce a new subspace learning framework called “Sparse Manifold Subspace Learning (SMSL)”. Compared with the conventional methods considering global data structure e.g., PCA, LDA, SMSL aims at preserving the local neighborhood structure on the data manifold and provides a more accurate data representation via locality sparse coding. In addition, it removes the common concerns of many local structure based subspace learning methods e.g., Local Linear Embedding (LLE), Neighborhood Preserving Embedding (NPE), that how to choose appropriate neighbors. SMSL adaptively selects neighbors based on their distances and importance, which is less sensitive to noise than NPE. Moreover, the dual-sparse processes, i.e., the locality sparse coding, and sparse eigen-decomposition in graph embedding yield a noise-tolerant framework. Finally, SMSL is learned in an inductive fashion, and therefore easily extended to different tests. We exhibit experimental results on several databases and demonstrate the effectiveness of the proposed method.