Devina Shiwlochan, University of Central Florida


Study of Diffusion Maps and the Mystery Behind it

Abstract: Diffusion Maps is a method of representing higher dimensional data in lower dimensions. It is also used as a method of sorting two dimensional images. In multiple numerical experiments it has been seen that diffusion maps can sort two dimensional images that have been rotated horizontally. However, how diffusion maps can determine the angle from the image and sort them has not been analytically proven. In our case we have derived a simplified Gaussian kernel that shows that the angle is being directed calculated from the kernel, hence diffusion maps sorts the images correctly. It has been seen countless times that numerically the second eigen component is the only component that correctly sorts rotated images. Analytically it has yet to be proven that the second eigen component sorts correctly, another aspect of my research.

Advisor: Xin Li (University Central Florida)