Pairwise comparison

About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.

Winner determination in sequential majority voting

Abstract: Preferences can be aggregated using voting rules We consider here the family of rules which perform a sequence of pairwise majority comparisons between two candidates The winner thus depends on the chosen sequence of comparisons, which can be represented by a binary tree We address the difficulty of computing candidates that win for some trees, and then introduce and study the notion of fair winner, ie candidates who win in a balanced tree We then consider the situation where we lack complete informations about preferences, and determine the computational complexity of computing winners in this case

An improved method for solving multiple criteria problems involving discrete alternatives

Abstract: An approach is presented for solving a discrete-multiple-criteria problem The approach asks pairwise comparisons of a decision-maker Under mild assumptions, the method obtains the most preferred alternative The required number of pairwise comparisons is generally modest The authors' experience with the method indicates that for reasonable underlying utility functions, a heuristic stopping rule generally yields the most preferred alternative after several comparisons, usually fewer than 20

Constrained spectral clustering via exhaustive and efficient constraint propagation

Abstract: This paper presents an exhaustive and efficient constraint propagation approach to exploiting pairwise constraints for spectral clustering. Since traditional label propagation techniques cannot be readily generalized to propagate pairwise constraints, we tackle the constraint propagation problem inversely by decomposing it to a set of independent label propagation subproblems which are further solved in quadratic time using semi-supervised learning based on k-nearest neighbors graphs. Since this time complexity is proportional to the number of all possible pairwise constraints, our approach gives a computationally efficient solution for exhaustively propagating pairwise constraint throughout the entire dataset. The resulting exhaustive set of propagated pairwise constraints are then used to adjust the weight (or similarity) matrix for spectral clustering. It is worth noting that this paper first clearly shows how pairwise constraints are propagated independently and then accumulated into a conciliatory closed-form solution. Experimental results on real-life datasets demonstrate that our approach to constrained spectral clustering outperforms the state-of-the-art techniques.

Active Ranking from Pairwise Comparisons and when Parametric Assumptions Don't Help

Abstract: We consider sequential or active ranking of a set of $n$ items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of prespecified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-$k$ items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, chosen based on confidence intervals specified by the data collected up to that point. We prove that this algorithm succeeds in recovering the ranking using a number of comparisons that is optimal up to logarithmic factors. This guarantee does depend on whether or not the underlying pairwise probability matrix, satisfies a particular structural property, unlike a significant body of past work on pairwise ranking based on parametric models such as the Thurstone or Bradley–Terry–Luce models. It has been a long-standing open question as to whether or not imposing these parametric assumptions allows for improved ranking algorithms. For stochastic comparison models, in which the pairwise probabilities are bounded away from zero, our second contribution is to resolve this issue by proving a lower bound for parametric models. This shows, perhaps surprisingly, that these popular parametric modeling choices offer at most logarithmic gains for stochastic comparisons.