Kernelized Sorting

Abstract

Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the classes. This is achieved by maximizing the dependency between matched pairs of observations by means of the Hilbert-Schmidt Independence Criterion. This problem can be cast as one of maximizing a quadratic assignment problem with special structure and we present a simple algorithm for finding a locally optimal solution.

Beyond 2D-grids

“…Kernelized sorting (KS) [18] is a general technique to perform matching between pairs of objects from different domains which only requires a similarity measure within each of the two domains. Indeed, the virtues of performing matching without the need of a cross-domain similarity measure allow us to organize images into arbitrary structures.…”

“…Arbitrary layout structures make it difficult -if not impossible -to compute cross-similarities between images and structure elements, the basic ingredient of traditional layouting approaches. Therefore, we have to resort to a recently developed machine learning technique called kernelized sorting [18]. Kernelized sorting allows one to perform matching without cross-domain similarity measure by maximizing the dependency between sets of objects, in our case images and layout coordinates.…”

Distributed Flow Algorithms for Scalable Similarity Visualization

“…A recently proposed machine learning technique called kernelized sorting [28] allows, among others, layouting of images into arbitrary structures such as grids or spheres so that images that are visually or semantically similar are placed in proximal locations. This layouting is shown to be advantageous for visualization, web image browsing and photo album summarization [29], [30].…”

Deformable Graph Matching

“…Graph matching (GM) has been widely applied in computer vision to solve a variety of problems such as object categorization [10], feature tracking [13,17], symmetry analysis [12], kernelized sorting [20] and action recognition [3]. From an optimization view-point, the GM problem is typically formulated as a quadratic assignment problem (QAP) [18].…”