Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

Direct Optimization of Ranking Measures

Abstract: Web page ranking and collaborative filtering require the optimization of sophisticated performance measures. Current Support Vector approaches are unable to optimize them directly and focus on pairwise comparisons instead. We present a new approach which allows direct optimization of the relevant loss functions. This is achieved via structured estimation in Hilbert spaces. It is most related to Max-Margin-Markov networks optimization of multivariate performance measures. Key to our approach is that during training the ranking problem can be viewed as a linear assignment problem, which can be solved by the Hungarian Marriage algorithm. At test time, a sort operation is sufficient, as our algorithm assigns a relevance score to every (document, query) pair. Experiments show that the our algorithm is fast and that it works very well.

Graph Matching: Relax at Your Own Risk

Abstract: Graph matching—aligning a pair of graphs to minimize their edge disagreements—has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.