A spectral technique for image clustering

Given an image i* and an image database V containing and unknown number of image classes, in this paper we propose a technique for finding the class A of V that contains i*. To solve this (1+x)-class clustering problem a novel spectral ¿asymmetric¿ formulation of the problem is introduced: The Asymmetric Cut. It permits the extraction of the required class regardless other classes in the data base. The actual goal is to find a spectral formulation of the (1+x)-class clustering problem and to propose an efficient numerical implementation of the approach for large image database. The proposed method finds a subset A that maximizes the similarities within the chosen cluster but it does not involve affinities or dissimilarities among remaining unknown clusters in the database. Asymmetric cuts seamlessly lead to a spectral representation which can be solved by finding the critical points of the corresponding Rayleigh quotient. Following the underlying spectral theoretical approach the critical points correspond to the eigenvectors of an affinity matrix derived from pair-wise similarities involving information related to a single image i* representing the image class of concern. Selected results from experimental evaluation are presented.