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    Foundations of Multidimensional and Metric Data Structures

    Technical book covering theory and practice of multidimensional and metric data structures for similarity search, forming a theoretical basis for index structures used in vector databases.

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    Foundations of Multidimensional and Metric Data Structures

    Technical book covering theory and practice of multidimensional and metric data structures for similarity search, forming a theoretical basis for index structures used in vector databases.

    https://www.researchgate.net/publication/275023439_Engineering_Efficient_and_Effective_Non-metric_Space_Library

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    Websitewww.researchgate.net
    PublishedDec 25, 2025

    Categories

    1 Item
    Concepts & Definitions

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    #Similarity Search#metric space#Data Structure

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    K-means Tree

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    M-tree

    M-tree is a dynamic index structure for organizing and searching large data sets in metric spaces, enabling efficient nearest neighbor queries and dynamic updates, which are important features for vector databases handling high-dimensional vectors.

    KD-Tree

    Tree-based data structure for organizing vectors through recursive axis-aligned partitioning, enabling logarithmic time complexity searches for balanced data but struggling with high-dimensional spaces.

    Dot Product Similarity

    Vector similarity metric combining both angle and magnitude information for comprehensive similarity measurement, equivalent to cosine similarity when vectors are normalized.

    Euclidean Distance

    Straight-line distance metric between vectors in multidimensional space, sensitive to both magnitude and direction, ideal when embedding magnitude carries important information.

    Locality-Sensitive Hashing

    Locality-Sensitive Hashing (LSH) is an algorithmic technique for approximate nearest neighbor search in high-dimensional vector spaces, commonly used in vector databases to speed up similarity search while reducing memory footprint.

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