Modified Kernel Functions by Geodesic Distance

Modified Kernel Functions by Geodesic Distance

When dealing with pattern recognition problems one encounters different types of prior knowledge. It is important to incorporate such knowledge into the classification method at hand. A common prior knowledge is that many datasets are on some kinds of manifolds. Distance-based classification methods can make use of this by a modified distance measure called geodesic distance. We introduce a new...

Project: Heat kernel construction on cortical surface using geodesic distance

Absolute Orientation Based on Distance Kernel Functions

The classical absolute orientation method is capable of transforming tie points (TPs) from a local coordinate system to a global (geodetic) coordinate system. The method is based only on a unique set of similarity transformation parameters estimated by minimizing the total difference between all ground control points (GCPs) and the fitted points. Nevertheless, it often yields a transformation w...

Distance Functions for Reproducing Kernel Hilbert Spaces

Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also present some computational properties and examples.

Approximating geodesic tree distance

Billera, Holmes, and Vogtmann introduced an intriguing new phylogenetic tree metric for weighted trees with useful properties related to statistical analysis. However, the best known algorithm for calculating this distance is exponential in the number of leaves of the trees compared. We point out that lower and upper bounds for this distance, which can be calculated in linear time, can differ b...