Efficient RkNN retrieval with arbitrary non-metric similarity measures

Abstract

A RkNN query returns all objects whose nearest k neighbors contain the query object. In this paper, we consider RkNN query processing in the case where the distances between attribute values are not necessarily metric. Dissimilarities between objects could then be a monotonic aggregate of dissimilarities between their values, such aggregation functions being specified at query time. We outline real world cases that motivate RkNN processing in such scenarios. We consider the AL-Tree index and its applicability in RkNN query processing. We develop an approach that exploits the group level reasoning enabled by the AL-Tree in RkNN processing. We evaluate our approach against a Naive approach that performs sequential scans on contiguous data and an improved block-based approach that we provide. We use real-world datasets and synthetic data with varying characteristics for our experiments. This extensive empirical evaluation shows that our approach is better than existing methods in terms of computational and disk access costs, leading to significantly better response times.

Optimizing Hashing Functions for Similarity Indexing in Arbitrary Metric and Nonmetric Spaces

“…That method can be combined with any distance-based indexing scheme and is orthogonal to such schemes, including the method proposed in this paper. A tree-based reverse kNN was proposed [10] for indexing non-metric spaces; however, this problem is orthogonal to ours, while the asymmetric relationship between kNN and reverse kNN makes it hard to adapt techniques for kNN to reverse kNN.…”

Efficient reverse skyline retrieval with arbitrary non-metric similarity measures

“…[24] points out specific cases in which each of the metric properties (viz., reflexivity, symmetry and triangle inequality) may not be intuitively satisfied. Similarity search on arbitrary non-metric similarity measures has attracted recent attention [10,21,20].…”