Isometric Multi-manifold Learning for Feature Extraction

Manifold learning is an important topic in pattern recognition and computer vision. However, most manifold learning algorithms implicitly assume the data are aligned on a single manifold, which is too strict in actual applications. Isometric feature mapping (Isomap), as a promising manifold learning method, fails to work on data which distribute on clusters in a single manifold or manifolds. In this paper, we propose a new multi-manifold learning algorithm (M-Isomap). The algorithm first discovers the data manifolds and then reduces the dimensionality of the manifolds separately. Meanwhile, a skeleton representing the global structure of whole data set is built and kept in low-dimensional space. Secondly, by referring to the low-dimensional representation of the skeleton, the embeddings of the manifolds are relocated to a global coordinate system. Compared with previous methods, these algorithms can keep both of the intra and inter manifolds geodesics faithfully. The features and effectiveness of the proposed multi-manifold learning algorithms are demonstrated and compared through experiments.