Parameter Estimation for Manifold Learning, Through Density Estimation

Manifold learning turns out to be a very useful tool for many applications of machine learning, such as classification. Unfortunately the existing algorithms use ad hoc selection of the parameters that define the geometry of the manifold. The parameter choice affects significantly the performance of manifold learning algorithms. Recent theoretical work has proven the equivalence between the Mercer kernel learning methods and the kernel in kernel density estimation. Based on this fact the problem of kernel parameter estimation for manifold learning is addressed based on the nonparametric statistical theory estimation. An automatic way of determining the local bandwidths that define the geometry is introduced. The results show that the automatic bandwidth selection leads to improved clustering performance and reduces the computational load versus ad hoc selection.