Abstract This paper presents a robust and comprehensive graph-based rank aggregation approach, used to combine results of isolated ranker models in retrieval tasks. The method follows an unsupervised scheme, which is independent of how the isolated ranks are formulated. Our approach is able to combine arbitrary models, defined in terms of different ranking criteria, such as those based on textual, image or hybrid content representations. We reformulate the ad-hoc retrieval problem as a document retrieval based on fusion graphs , which we propose as a new unified representation model capable of merging multiple ranks and expressing inter-relationships of retrieval results automatically. By doing so, we claim that the retrieval system can benefit from learning the manifold structure of datasets, thus leading to more effective results. Another contribution is that our graph-based aggregation formulation, unlike existing approaches, allows for encapsulating contextual information encoded from multiple ranks, which can be directly used for ranking, without further computations and post-processing steps over the graphs. Based on the graphs, a novel similarity retrieval score is formulated using an efficient computation of minimum common subgraphs. Finally, another benefit over existing approaches is the absence of hyperparameters. A comprehensive experimental evaluation was conducted considering diverse well-known public datasets, composed of textual, image, and multimodal documents. Performed experiments demonstrate that our method reaches top performance, yielding better effectiveness scores than state-of-the-art baseline methods and promoting large gains over the rankers being fused, thus demonstrating the successful capability of the proposal in representing queries based on a unified graph-based model of rank fusions.
Rank aggregation can be seen as the task of finding a good permutation of retrieved objects obtained from different input ranks. The Kemeny rank aggregation problem consists of finding the optimal permutation. It is an NP-hard problem for more than three input ranks @cite_12 . In practice, rank aggregation methods compose inexact solutions that intend to promote better results than the isolated input ranks.
@cite_12
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Kemeny Rank Aggregation is a consensus finding problem important in many areas ranging from classical voting over web search and databases to bioinformatics. The underlying decision problem Kemeny Score is NP-complete even in case of four input rankings to be aggregated into a "median ranking". We analyze efficient polynomial-time data reduction rules with provable performance bounds that allow us to find even all optimal median rankings. We show that our reduced instances contain at most [InlineEquation not available: see fulltext.] candidates where @math d a denotes the average Kendall's tau distance between the input votes. On the theoretical side, this improves a corresponding result for a "partial problem kernel" from quadratic to linear size. In this context we provide a theoretical analysis of a commonly used data reduction. On the practical side, we provide experimental results with data based on web search and sport competitions, e.g., computing optimal median rankings for real-world instances with more than 100 candidates within milliseconds. Moreover, we perform experiments with randomly generated data based on two random distribution models for permutations. We consider the problem of finding a ranking of a set of elements that is "closest to" a given set of input rankings of the elements; more precisely, we want to find a permutation that minimizes the Kendall-tau distance to the input rankings, where the Kendall-tau distance is defined as the sum over all input rankings of the number of pairs of elements that are in a different order in the input ranking than in the output ranking. If the input rankings are permutations, this problem is known as the Kemeny rank aggregation problem. This problem arises for example in building meta-search engines for Web search, aggregating viewers' rankings of movies, or giving recommendations to a user based on several different criteria, where we can think of having one ranking of the alternatives for each criterion. Many of the approximation algorithms and heuristics that have been proposed in the literature are either positional, comparison sort or local search algorithms. The rank aggregation problem is a special case of the (weighted) feedback arc set problem, but in the feedback arc set problem we use only information about the preferred relative ordering of pairs of elements to find a ranking of the elements, whereas in the case of the rank aggregation problem, we have additional information in the form of the complete input rankings. The positional methods are the only algorithms that use this additional information. Since the rank aggregation problem is NP-hard, none of these algorithms is guaranteed to find the optimal solution, and different algorithms will provide different solutions. We give theoretical and practical evidence that a combination of these different approaches gives algorithms that are superior to the individual algorithms. Theoretically, we give lower bounds on the performance for many of the "pure" methods. Practically, we perform an extensive evaluation of the "pure" algorithms and combinations of different approaches. We give three recommendations for which (combination of) methods to use based on whether a user wants to have a very fast, fast or reasonably fast algorithm. The Kemeny Score problem is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a "consensus permutation" that is "closest" to the given set of permutations. Computing an optimal consensus permutation is NP-hard. We provide first, encouraging fixed-parameter tractability results for computing optimal scores (that is, the overall distance of an optimal consensus permutation). Our fixed-parameter algorithms employ the parameters "score of the consensus", "maximum distance between two input permutations", and "number of candidates". We extend our results to votes with ties and incomplete votes, thus, in both cases having no longer permutations as input. This paper is concerned with rank aggregation, which aims to combine multiple input rankings to get a better ranking. A popular approach to rank aggregation is based on probabilistic models on permutations, e.g., the Luce model and the Mallows model. However, these models have their limitations in either poor expressiveness or high computational complexity. To avoid these limitations, in this paper, we propose a new model, which is defined with a coset-permutation distance, and models the generation of a permutation as a stagewise process. We refer to the new model as coset-permutation distance based stagewise (CPS) model. The CPS model has rich expressiveness and can therefore be used in versatile applications, because many different permutation distances can be used to induce the coset-permutation distance. The complexity of the CPS model is low because of the stagewise decomposition of the permutation probability and the efficient computation of most coset-permutation distances. We apply the CPS model to supervised rank aggregation, derive the learning and inference algorithms, and empirically study their effectiveness and efficiency. Experiments on public datasets show that the derived algorithms based on the CPS model can achieve state-of-the-art ranking accuracy, and are much more efficient than previous algorithms.