Kernel Isomap

Abstract

Isomap is a manifold learning algorithm, which extends classical multidimensional scaling by considering approximate geodesic distance instead of Euclidean distance. The approximate geodesic distance matrix can be interpreted as a kernel matrix, which implies that Isomap can be solved by a kernel eigenvalue problem. However, the geodesic distance kernel matrix is not guaranteed to be positive semi-definite. A constant-adding method is employed, which leads to the Mercer kernel-based Isomap algorithm. Numerical experimental results with noisy. ‘Swiss roll’ data, confirm the validity and high performance of the kernel Isomap algorithm.