University of Kentucky
Lexington, Kentucky, U. S. A.
In object recognition, each image is represented by a vector of very high dimension, and a large collection of images is then represented by a (tall and dense) matrix $X$ whose columns represent images. To recognize an unknown image against the collection, the distance between the vector for the unknown image to $X$'s column space is computed. To do so efficiently, one of the standard practices, among others, is to compress the large image set first to a low-dimensional subspace by computing the outstanding eigenspace of $X^TX$ and to compute the distance between the vector and the eigenspace. In this talk, we shall first review various current methods in the area and show how they can be improved with recent developments in numerical linear algebra.