Modified Kernel Functions by Geodesic Distance

Kernel Isomap

Isomap [4] is a manifold learning algorithm, which extends classical multidimensional scaling (MDS) 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 ...

Geodesic Distance-based Kernel Construction for Gaussian Process Value Function Approximation

Finding accurate approximations to state and action value functions is essential in Reinforcement learning tasks on continuous Markov Decision Processes. Using Gaussian processes as function approximators we can simultaneously represent model confidence and generalize to unvisited states. To improve the accuracy of the value function approximation in this article I present a new method of const...

Project: Heat kernel construction on cortical surface using geodesic distance

Open problem : kernel methods on manifolds and metric spaces

Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong linear properties. This negative result hints that radial kernel are perhaps not suitable over geo...

یادگیری نیمه نظارتی کرنل مرکب با استفاده از تکنیک‌های یادگیری معیار فاصله

Distance metric has a key role in many machine learning and computer vision algorithms so that choosing an appropriate distance metric has a direct effect on the performance of such algorithms. Recently, distance metric learning using labeled data or other available supervisory information has become a very active research area in machine learning applications. Studies in this area have shown t...