Tangent space intrinsic manifold regularization for data representation

A new regularization method called tangent space intrinsic manifold regularization is presented, which is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in its formulation are local tangent space representations which we estimate by local principal component analysis, and the connections which relate adjacent tangent spaces. We exhibit its application to data representation where a nonlinear embedding in a low-dimensional space is found by solving an eigen-decomposition problem. Experimental results including comparisons with state-of-the-art techniques show the effectiveness of the proposed method.