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A similarity measure between unordered vector sets with application to image categorization

Yan Liu, Florent Perronnin
We present a novel approach to compute the similarity between two unordered variable-sized vector sets. To solve this problem, several authors have proposed to model each vector set with a Gaussian mixture model (GMM) and to compute a probabilistic measure of similarity between the GMMs. The main contribution of this paper is a model each vector set with a GMM adapted from a common universal GMM using the maximum a posteriori (MAP) criterion. The advantages of this approach are twofold. MAP provides a more accurate estimate of the GMM parameters compared to standard maximum likelihood estimation (MLE) in the challenging case where the cardinality of the vector set is small. Moreover, there is a correspondence between the Gaussians of two GMMs adapted from a common distribution and one can take advantage of this fact to compute efficiently the probabilistic similarity. This work is applied to the image categorization problem: images are modeled as bags of low-level features and classification is performed using a kernel classifier based on the proposed similarity measure. Experimental results on the PASCAL VOC 2006 and VOC 2007 databases show the excellent performance of our approach.
IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Egan Convention Center, Anchorage, Alaska, June 24-26, 2008.