Orthogonal Isometric Projection

In contrast with Isomap, which learns the low-dimension embedding, and solves problem under the classic Multi-dimension Scaling (MDS) framework, we propose a dimensionality reduction technique, called Orthogonal Isometric Projection (OIP), in this paper. We consider an explicit orthogonal linear projection by capturing the geodesic distance, which is able to handle new data straightforward, and leads to a standard eigenvalue problem. And we extend our method to Sparse Orthogonal Isometric Projection (SOIP), which can be solved efficiently using LARS. Numerical experiments are reported to demonstrate the performance of OIP by comparing with a few competing methods.