Geometric approaches for Top-k Queries [Tutorial]

Top- k processing is a well-studied problem with numerous applications that is becoming increasingly relevant with the growing availability of recommendation systems and decision making software. The objective of this tutorial is twofold. First, we will delve into the geometric aspects of top- k processing. Second, we will cover complementary features to top- k queries, with strong practical relevance and important applications, that have a computational geometric nature. The tutorial will close with insights in the effect of dimensionality on the meaningfulness of top- k queries, and interesting similarities to nearest neighbor search. </jats:p

An Efficient Top-k Query Scheme Based on Multilayer Grouping

The top-k query is to find the k data that has the highest scores from a candidate dataset. Sorting is a common method to find out top-k results. However, most of existing methods are not efficient enough. To remove this issue, we propose an efficient top-k query scheme based on multilayer grouping. First, we find the reference item by computing the average score of the candidate dataset. Second, we group the candidate dataset into three datasets: winner set, middle set and loser set based on the reference item. Third, we further group the winner set to the second-layer three datasets according to k value. And so on, until the data number of winner set is close to k value. Meanwhile, if k value is larger than the data number of winner set, we directly return the winner set to the user as a part of top-k results almost without sorting. In this case, we also return the top results with the highest scores from the middle set almost without sorting. Based on above innovations, we almost minimize the sorting. Experimental results show that our scheme significantly outperforms the current classical method on the performance of memory consumption and top-k query

On Obtaining Stable Rankings

Decision making is challenging when there is more than one criterion to consider. In such cases, it is common to assign a goodness score to each item as a weighted sum of its attribute values and rank them accordingly. Clearly, the ranking obtained depends on the weights used for this summation. Ideally, one would want the ranked order not to change if the weights are changed slightly. We call this property {\em stability} of the ranking. A consumer of a ranked list may trust the ranking more if it has high stability. A producer of a ranked list prefers to choose weights that result in a stable ranking, both to earn the trust of potential consumers and because a stable ranking is intrinsically likely to be more meaningful. In this paper, we develop a framework that can be used to assess the stability of a provided ranking and to obtain a stable ranking within an "acceptable" range of weight values (called "the region of interest"). We address the case where the user cares about the rank order of the entire set of items, and also the case where the user cares only about the top-$k$ items. Using a geometric interpretation, we propose algorithms that produce stable rankings. In addition to theoretical analyses, we conduct extensive experiments on real datasets that validate our proposal

多次元データに対するランキング問合せ処理に関する研究

筑波大学 (University of Tsukuba)201