A General Framework for Manifold Alignment

Manifold alignment has been found to be useful in many elds of machine learning and data mining. In this paper we summarize our work in this area and introduce a general framework for manifold alignment. This framework gener-ates a family of approaches to align manifolds by simulta-neously matching the corresponding instances and preserv-ing the local geometry of each given manifold. Some ap-proaches like semi-supervised alignment and manifold pro-jections can be obtained as special cases. Our framework can also solve multiple manifold alignment problems and be adapted to handle the situation when no correspondence in-formation is available. The approaches are described and evaluated both theoretically and experimentally, providing re-sults showing useful knowledge transfer from one domain to another. Novel applications of our methods including iden-tication of topics shared by multiple document collections, and biological structure alignment are discussed in the paper.