Ptolemaic Indexing

This paper discusses a new family of bounds for use in similarity search, related to those used in metric indexing, but based on Ptolemy's inequality, rather than the metric axioms. Ptolemy's inequality holds for the well-known Euclidean distance, but is also shown here to hold for quadratic form metrics in general, with Mahalanobis distance as an important special case. The inequality is examined empirically on both synthetic and real-world data sets and is also found to hold approximately, with a very low degree of error, for important distances such as the angular pseudometric and several Lp norms. Indexing experiments demonstrate a highly increased filtering power compared to existing, triangular methods. It is also shown that combining the Ptolemaic and triangular filtering can lead to better results than using either approach on its own

A hybrid data structure for searching in metric spaces

The concept of “approximate” searching has applications in a vast number of fields. Some examples are non-traditional databases (e. g. storing images, fingerprints or audio clips, where the concept of exact search is of no use and we search instead for similar objects), text searching, information retrieval, machine learning and classification, image quantization and compression, computational biology, and function prediction.Eje: Base de datosRed de Universidades con Carreras en Informática (RedUNCI

Fully dynamic and memory-adaptative spatial approximation trees

Hybrid dynamic spatial approximation trees are recently proposed data structures for searching in metric spaces, based on combining the concepts of spatial approximation and pivot based algorithms. These data structures are hybrid schemes, with the full features of dynamic spatial approximation trees and able of using the available memory to improve the query time. It has been shown that they compare favorably against alternative data structures in spaces of medium difficulty. In this paper we complete and improve hybrid dynamic spatial approximation trees, by presenting a new search alternative, an algorithm to remove objects from the tree, and an improved way of managing the available memory. The result is a fully dynamic and optimized data structure for similarity searching in metric spaces.Eje: Teoría (TEOR)Red de Universidades con Carreras en Informática (RedUNCI

Modelling Efficient Novelty-based Search Result Diversification in Metric Spaces

Novelty-based diversification provides a way to tackle ambiguous queries by re-ranking a set of retrieved documents. Current approaches are typically greedy, requiring O(n2) document–document comparisons in order to diversify a ranking of n documents. In this article, we introduce a new approach for novelty-based search result diversification to reduce the overhead incurred by document–document comparisons. To this end, we model novelty promotion as a similarity search in a metric space, exploiting the properties of this space to efficiently identify novel documents. We investigate three different approaches: pivoting-based, clustering-based, and permutation-based. In the first two, a novel document is one that lies outside the range of a pivot or outside a cluster. In the latter, a novel document is one that has a different signature (i.e., the documentʼs relative distance to a distinguished set of fixed objects called permutants) compared to previously selected documents. Thorough experiments using two TREC test collections for diversity evaluation, as well as a large sample of the query stream of a commercial search engine show that our approaches perform at least as effectively as well-known novelty-based diversification approaches in the literature, while dramatically improving their efficiency.Fil: Gil Costa, Graciela Verónica. Yahoo; México. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis; ArgentinaFil: Santos, Rodrygo L. T.. University Of Glasgow; Reino UnidoFil: Macdonald, Craig. University Of Glasgow; Reino UnidoFil: Ounis, Iadh. University Of Glasgow; Reino Unid

Indexing Metric Spaces for Exact Similarity Search

With the continued digitalization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when attempting to enable value creation from big data: volume, velocity and variety. Many studies address volume or velocity, while much fewer studies concern the variety. Metric space is ideal for addressing variety because it can accommodate any type of data as long as its associated distance notion satisfies the triangle inequality. To accelerate search in metric space, a collection of indexing techniques for metric data have been proposed. However, existing surveys each offers only a narrow coverage, and no comprehensive empirical study of those techniques exists. We offer a survey of all the existing metric indexes that can support exact similarity search, by i) summarizing all the existing partitioning, pruning and validation techniques used for metric indexes, ii) providing the time and storage complexity analysis on the index construction, and iii) report on a comprehensive empirical comparison of their similarity query processing performance. Here, empirical comparisons are used to evaluate the index performance during search as it is hard to see the complexity analysis differences on the similarity query processing and the query performance depends on the pruning and validation abilities related to the data distribution. This article aims at revealing different strengths and weaknesses of different indexing techniques in order to offer guidance on selecting an appropriate indexing technique for a given setting, and directing the future research for metric indexes