5 research outputs found
RRR: Rank-Regret Representative
Selecting the best items in a dataset is a common task in data exploration.
However, the concept of "best" lies in the eyes of the beholder: different
users may consider different attributes more important, and hence arrive at
different rankings. Nevertheless, one can remove "dominated" items and create a
"representative" subset of the data set, comprising the "best items" in it. A
Pareto-optimal representative is guaranteed to contain the best item of each
possible ranking, but it can be almost as big as the full data. Representative
can be found if we relax the requirement to include the best item for every
possible user, and instead just limit the users' "regret". Existing work
defines regret as the loss in score by limiting consideration to the
representative instead of the full data set, for any chosen ranking function.
However, the score is often not a meaningful number and users may not
understand its absolute value. Sometimes small ranges in score can include
large fractions of the data set. In contrast, users do understand the notion of
rank ordering. Therefore, alternatively, we consider the position of the items
in the ranked list for defining the regret and propose the {\em rank-regret
representative} as the minimal subset of the data containing at least one of
the top- of any possible ranking function. This problem is NP-complete. We
use the geometric interpretation of items to bound their ranks on ranges of
functions and to utilize combinatorial geometry notions for developing
effective and efficient approximation algorithms for the problem. Experiments
on real datasets demonstrate that we can efficiently find small subsets with
small rank-regrets
Optimization Over K-Set Polytopes and Efficient K-Set Enumeration
We present two versions of an algorithm based on the reverse search technique for enumerating all k-sets of a point set in R d . The key elements include the notion of a k-set polytope and the optimization of a linear function over a k-set polytope. 1 Introduction Let S be a set of n points in R d . A k-set of S is a set P of k points in S that can be separated from SnP by a hyperplane. The problem of enumerating the k-sets has many applications in computational geometry ([AW97a]), among others in computation of higher-order Voronoi diagrams ([Aur91, Mul93]), in orthogonal L 1 hyperplane fitting ([KM93]) and in halfspace range searching ([CP86, AM95]). The first output-sensitive algorithm for enumerating k-sets was given in [EW86] (for R 2 ), and other such algorithms appeared in [Mul91, AM95, AMdS94]. While the above algorithms concentrate on time-efficiency and require sophisticated data structures, we present here two output-sensitive algorithms which are highly memory-ef..
Collection of abstracts of the 24th European Workshop on Computational Geometry
International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop