On Finding Rank Regret Representatives

Selecting the best items in a dataset is common task data exploration. However, concept of “best” lies eyes beholder: Different users may consider different attributes more important and, hence, arrive at rankings. Nevertheless, one can remove “dominated” and create “representative” subset data, comprising “best items” it. A Pareto-optimal representative guaranteed to contain item each possible ranking, but it be large portion data. much smaller found if we relax requirement including for user instead just limit users’ “regret.” Existing work defines regret as loss score by limiting consideration full dataset, any chosen ranking function. often not meaningful number, understand its absolute value. Sometimes small ranges include fractions dataset. In contrast, do notion rank ordering. Therefore, items’ positions ranked list defining propose rank-regret minimal containing least top- k This problem polynomial time solvable two-dimensional space NP-hard on three or dimensions. We design suite algorithms fulfill purposes, such whether relaxation permitted , result size, both, distribution known, theoretical guarantees practical efficiency important, so on. Experiments real datasets demonstrate that efficiently find subsets with rank-regrets.