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Enabling high-dimensional range queries using kNN indexing techniques: approaches and empirical results

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Abstract

Many modern search applications are high-dimensional and depend on efficient orthogonal range queries. These applications span web-based and scientific needs as well as uses for data mining. Although k-nearest neighbor queries are becoming increasingly common due to mobile and geospatial applications, orthogonal range queries in high-dimensional data remain extremely important and relevant. For efficient querying, data is typically stored in an index optimized for either kNN or range queries. This can be problematic when data is optimized for kNN retrieval and a user needs a range query or vice versa. Here, we address the issue of using a kNN-based index for range queries, as well as outline the general computational geometry problem of adapting these systems to range queries. We refer to these methods as space-based decompositions and provide a straightforward heuristic for this problem. Using iDistance as our applied kNN indexing technique, we also develop an optimal (data-based) algorithm designed specifically for its indexing scheme. We compare this method to the suggested naïve approach using real world datasets. The data-based algorithm consistently performs better.

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Notes

  1. http://archive.ics.uci.edu/ml/datasets/Corel+Image+Features.

  2. http://archive.ics.uci.edu/ml/datasets/YearPredictionMSD.

  3. http://corpus-texmex.irisa.fr/.

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Authors and Affiliations

  1. University of Texas - Rio Grande Valley, Edinburg, TX, 78539, USA

    Tim Wylie

  2. Montana State University, Bozeman, MT, 59717, USA

    Michael A. Schuh

  3. Georgia State University, Atlanta, GA, 30302, USA

    Rafal A. Angryk

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  1. Tim Wylie
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  2. Michael A. Schuh
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  3. Rafal A. Angryk
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Correspondence to Tim Wylie.

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Wylie, T., Schuh, M.A. & Angryk, R.A. Enabling high-dimensional range queries using kNN indexing techniques: approaches and empirical results. J Comb Optim 32, 1107–1132 (2016). https://doi.org/10.1007/s10878-015-9927-1

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