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

HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.Comment: PVLDB 11(8):906-919, 201

Data sensitive approximate query approaches in metric spaces

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 56-59.Similarity searching is the task of retrieval of relevant information from datasets. We are particularly interested in datasets that contain complex and unstructured data such as images, videos, audio recordings, protein and DNA sequences. The relevant information is typically defined using one of two common query types: a range query involves retrieval of all the objects within a specified distance to the query object; whereas a k-nearest neighbor query deals with obtaining k closest database objects to the query object. A variety of index structures based on the notion of metric spaces have been offered to process these two query types. The query performances of the proposed index structures have not been satisfactory particularly for high dimensional datasets. As a solution, various approximate similarity search methods offering the users a quality/time trade-off have been proposed. The rationale is that the users might be willing to tolerate query precision to retrieve query results relatively faster. The proposed approximate searching schemes usually have strong connections to the underlying data structures, making the comparison of the quality of the essence of their ideas difficult. In this thesis we investigate various approximation approaches to decrease the response time of similarity queries. These approaches use a variety of statistics about the dataset in order to obtain dynamic (at the time of querying) and specific guidance on the approximation for each query object individually. The experiments are performed on top of a simple underlying pivot-based index structure to minimize the effects of the index to our approximation schemes. The results show that it is possible to improve the performance/precision of the approximation based on data and query object sensitive guidance.Dilek, MerveM.S