Abstract:

Recently, nonlinear dimensionality reduction has attracted extensive interests of researchers in the machine learning community. The techniques for nonlinear dimensionality reduction can be divided into two categories: kernelbased methods and manifold learning. These two methods have different motivations and derivations. This paper interprets the wellknown manifold learning algorithm LTSA as a kernel method. We show that LTSA can be described as the kernel PCA, and LTSA utilizes the local neighborhood information to construct a special kernel matrix, and the global embedding obtained by LTSA with modified constraints is equivalent to principal coordinates by the kernel PCA with this special kernel.

Key words: dimensionality reduction;manifold learning;kernel method;kernel principal component analysis;local tangent space alignment