Reliability-Aware and Graph-Based Approach for Rank Aggregation of Biological Data

Abstract

Massive biological datasets are available in public databases and can be queried using portals with keyword queries. Ranked lists of answers are obtained by users. However, properly querying such portals remains difficult since various formulations of the same query can be considered (e.g., using synonyms). Consequently, users have to manually combine several lists of hundreds of answers into one list. Rank aggregation techniques are particularly well-fitted to this context as they take in a set of ranked elements (rankings) and provide a consensus, that is, a single ranking which is the "closest" to the input rankings. However, the problem of rank aggregation is NP-hard in most cases. Using an exact algorithm is currently not possible for more than a few dozens of elements. A plethora of heuristics have thus been proposed which behaviour are, by essence, difficult to anticipate: given a set of input rankings, one cannot guarantee how far from an exact solution the consensus ranking provided by an heuristic will be. The two challenges we want to tackle in this paper are the following: (i) providing an approach based on a pre-process to decompose large data sets into smaller ones where high-quality algorithms can be run and (ii) providing information to users on the robustness of the positions of elements in the consensus ranking produced. Our approach not only lies in mathematical bases, offering guarantees on the result computed but it has also been implemented in a real system available to life science community and tested on various real use cases.

Efficient, robust and effective rank aggregation for massive biological datasets

“…Interestingly, this new algorithm not only finds (much) more frontiers than in our previous work [16] (as shown in Figure 9, section 7), but it also subsumes the two major following previous works: the non-dirty elements [3] and the Extended Condorcet Criterion [19].…”

“…Remark. In a previous work [16], we used a slightly different notion: we did not define robust arcs but we defined a second graph G r named the robust graph of elements. Information provided by G r and R e are equivalent: it can be seen from Table 3 and the similar Table in [16] that G r is the oriented graph on U whose arcs are all (x, y) such that (y, x) / ∈ R e .…”

“…In a previous work [16], we defined the robust graph G r to compute frontiers: G r = (V r , E r ) is the directed graph such that…”

“…Experiment 5: Ability of computing new frontiers of interest. In this second part of experiments dedicated to frontiers, we consider all the datasets and compare the number of frontiers obtained by ParFront with the number of frontiers obtained by the non-dirty elements (NDE) [3], the Extended Condorcet Criterion (ECC) [19] and the robust graph of elements (RGE) [16], as introduced in Section 5. To be fair towards all methods, we considered unified rankings: if a gene x is present in a ranking r whereas another gene y is missing in r, we considered that x is before y in r. This consideration increases the number of frontiers found using ECC and NDE methods.…”

“…Our second contribution allows to provide a robust solution. Here we tackle the problem of multiple optimal solutions to the rank aggregation problem by exploring further the concept of frontier defined in [16].…”