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XM-tree: data driven computational model by using metric extended nodes with non-overlapping in high-dimensional metric spaces

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Abstract

Finding similar objects based on a query and a distance, remains a fundamental problem for many applications. The general problem of many similarity measures is to focus the search on as few elements as possible to find the answer. The index structures divides the target dataset into subsets. With large amounts of data, the volumes of the subspaces grow exponentially, that will affect the search algorithms. This problem is caused by inherent deficiencies of space partitioning, and also, the overlap factor between regions. This methods have proven to be unreliable, it becomes hard to store, manage, and analyze these quantities. The research tends to degenerate into a complete analysis of the data set. In this paper, we propose a new indexing technique called XM-tree, that partitions the space using spheres. The idea is to combine two structures, arborescent and sequential, in order to limit the volume of the outer regions of the spheres, by creating extended regions and inserting them into linked lists named extended regions, and also by excluding of the empty sets—separable partitions—that do not contain objects. The goal is to eliminate some objects without the need to compute their relative distances to a query object. Therefore, we proposed a parallel version of the structure on a set of real machine. We also discuss the efficiency of the construction and querying phases, and the quality of our index by comparing it with recent techniques.

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Notes

  1. The first dataset is available from the COPhIR collection at http://cophir.isti.cnr.it, whereas the second one can be found at http://kdd.ics.uci.edu.

  2. GBDI Arboretum is a library C++ that implements different metric access methods (MAM) (cf. http://www.gbdi.icmc.usp.br/old/arboretum).

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Authors and Affiliations

  1. Labstic Laboratory, University of GUELMA, Guelma, Algeria

    Zineddine Kouahla

  2. Department of Computer Sciences, COMSATS Institute of Information Technology, Islamabad, Pakistan

    Adeel Anjum

  3. Department of Software Engineering, Foundation University, Rawalpindi Campus, Islamabad, Pakistan

    Sheeraz Akram

  4. Prince Sultan University, Riyadh, Saudi Arabia

    Tanzila Saba

  5. Duke Research Group, LINA Laboratory UMR 6241, University of Nantes, Nantes, France

    José Martinez

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  1. Zineddine Kouahla
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  2. Adeel Anjum
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  3. Sheeraz Akram
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  4. Tanzila Saba
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  5. José Martinez
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Correspondence to Adeel Anjum.

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Kouahla, Z., Anjum, A., Akram, S. et al. XM-tree: data driven computational model by using metric extended nodes with non-overlapping in high-dimensional metric spaces. Comput Math Organ Theory 25, 196–223 (2019). https://doi.org/10.1007/s10588-018-9272-x

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