Submanifold decomposition

Extracting low-dimensional structures from high-dimensional space through spectral analysis has been prevalent in the fields of machine learning and computer vision. However, most manifold learning methods assume that there is a dominant low-dimensional manifold, while other variations are usually considered as noise or even ignored. This paper proposes a novel submanifold decomposition (SMD) algorithm, which simultaneously considers multiple submanifolds intertwined in the same high-dimensional space for decomposition. It makes full use of multi-category labels of a dataset to improve the modeling of manifolds of each label. In order to applied the proposed method to practical applications, the linear version of SMD is developed subsequently. Comparative experiments demonstrate that the proposed method not only effectively extracts submanifolds by subspace learning, but also outperforms traditional manifold and subspace learning methods for visual recognition tasks.