Cybernetics and Systems Analysis

, Volume 54, Issue 2, pp 320–335 | Cite as

Index Structures for Fast Similarity Search for Real Vectors. II*

  • D. A. Rachkovskij


This survey article considers index structures for fast similarity search for objects represented by real-valued vectors. Structures for both exact and faster but approximate similarity search are considered. Index structures based on partitioning into regions (including hierarchical ones) and on proximity graphs are mainly presented. The acceleration of similarity search using the transformation of initial data is also discussed. The ideas of concrete algorithms including recently proposed ones are outlined. The approaches to the acceleration of similarity search in index structures of the considered types and also on the basis of similarity-preserving hashing are discussed and compared.


similarity search nearest neighbor near neighbor index structure branch and bound method tree and forest clustering proximity graph locality-sensitive hashing 


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  1. 1.
    D. A. Rachkovskij, “Index structures for fast similarity search for real-valued vectors. I,” Cybernetics and Systems Analysis, Vol. 54, No. 1, 152–164 (2018).CrossRefGoogle Scholar
  2. 2.
    V. Gaede and O. Gunther, “Multidimensional access methods,” ACM Comput. Surv., Vol. 30, No. 2, 170–231 (1998).CrossRefGoogle Scholar
  3. 3.
    C. Bohm, S. Berchtold, and D. A. Keim, “Searching in high-dimensional spaces: Index structures for improving performance of multimedia databases,” ACM Comput. Surv., Vol. 33, No. 3, 322–373 (2001).CrossRefGoogle Scholar
  4. 4.
    H. Samet, Foundations of Multidimensional and Metric Data Structures, Morgan Kaufmann, San Francisco (2006).zbMATHGoogle Scholar
  5. 5.
    D. A. Rachkovskij, “Real-valued embeddings and sketches for fast distance and similarity estimation,” Cybernetics and Systems Analysis, Vol. 52, No. 6, 967–988 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    D. A. Rachkovskij, “Binary vectors for fast distance and similarity estimation,” Cybernetics and Systems Analysis, Vol. 53, No. 1, 138–156 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    D. A. Rachkovskij, “Distance-based index structures for fast similarity search,” Cybernetics and Systems Analysis, Vol. 53, No. 4, 636–658 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    D. A. Rachkovskij, “Index structures for fast similarity search for binary vectors,” Cybernetics and Systems Analysis, Vol. 53, No. 5, 799–820 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    A. Andoni and P. Indyk, “Nearest neighbors in high-dimensional spaces,” in: Handbook of Discrete and Computational Geometry, Ch. 43, 3rd Ed., CRC Press, Boca Raton, USA (2017), pp. 1135–1155.Google Scholar
  10. 10.
    M. Patella and P. Ciaccia, “Approximate similarity search: A multi-faceted problem,” J. Discrete Algorithms, Vol. 7, No. 1, 36–48 (2009).Google Scholar
  11. 11.
    M. Muja and D. G. Lowe, “Scalable nearest neighbor algorithms for high dimensional data,” IEEE TPAMI, Vol. 36, No. 11, 2227–2240 (2014).CrossRefGoogle Scholar
  12. 12.
    S. Arya, D. Mount, N. Netanyahu, R. Silverman, and A. Wu, “An optimal algorithm for approximate nearest neighbor searching fixed dimensions,” Journal of the ACM, Vol. 45, No. 6, 891–923 (1998).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    J. K. Friedman, J. L. Bentley, and R. A. Finkel, “An algorithm for finding best matches in logarithmic expected time,” ACM Tran. on Mathematical Software, Vol. 3, No. 3, 209–226 (1977).CrossRefzbMATHGoogle Scholar
  14. 14.
    R. Weber, H. Schek, and S. Blott, “A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces,” in: Proc. VLDB’98 (1998), pp. 194–205.Google Scholar
  15. 15.
    S. Arya and D. M. Mount, “Approximate nearest neighbor queries in fixed dimensions,” in: Proc. SODA’93 (1993), pp. 271–280.Google Scholar
  16. 16.
    T. Liu, A. W. Moore, A. Gray, and K. Yang, “An investigation of practical approximate nearest neighbor algorithms,” in: Proc. NIPS’04 (2004), pp. 825–832.Google Scholar
  17. 17.
    D. T. Lee and C. K. Wong, “Worst-case analysis for region and partial region searches in multidimensional binary trees and balanced quad trees,” Acta Informatica, Vol. 9, No. 1, 23–29 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    A. Guttman, “R-trees: A dynamic index structure for spatial searching,” in: Proc. ACM SIGMOD ICMD’84 (1984), pp. 47–57.Google Scholar
  19. 19.
    B. U. Pagel, F. Korn, and C. Faloutsos, “Deflating the dimensionality curse using multiple fractal dimensions,” in: Proc. ICDE’00 (2000), pp. 589–598.Google Scholar
  20. 20.
    D. A. White and R. Jain, “Similarity indexing with the SS-tree,” in: Proc. ICDE’96 (1996), pp. 516–523.Google Scholar
  21. 21.
    S. M. Omohundro, Five Balltree Construction Algorithms, ICSI TR-89-063 (1989).Google Scholar
  22. 22.
    N. Katayama and S. Satoh, “The SR-tree: An index structure for high-dimensional nearest neighbor queries,” in: Proc. ACM SIGMOD ICMD’97 (1997), pp. 369–380.Google Scholar
  23. 23.
    L. Arge, M. de Berg, H. J. Haverkort, and K. Yi, “The priority R-tree: A practically efficient and worst-case optimal R-tree,” ACM Trans. on Algorithms, Vol. 4, No. 1, 9:1–9:30 (2008).Google Scholar
  24. 24.
    S. Dasgupta and K. Sinha, “Randomized partition trees for nearest neighbor search,” Algorithmica, Vol. 72, No. 1, 237–263 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    P. Yianilos, “Locally lifting the curse of dimensionality for nearest neighbor search,” in: Proc. SODA’00 (2000), pp. 361–370.Google Scholar
  26. 26.
    C. Silpa-Anan and R. Hartley, “Optimised kd-trees for fast image descriptor matching,” in: Proc. CVPR’08 (2008), pp. 1–8.Google Scholar
  27. 27.
    S. Dasgupta and Y. Freund, “Random projection trees and low dimensional manifolds,” in: Proc. STOC’08 (2008), pp. 537–546.Google Scholar
  28. 28.
    Z. Allen-Zhu, R. Gelashvili, S. Micali, and N. Shavit, “Sparse sign-consistent Johnson-Lindenstrauss matrices: Compression with neuroscience-based constraints,” PNAS, Vol. 111, 16872–16876 (2014).CrossRefGoogle Scholar
  29. 29.
    D. A. Rachkovskij, “Formation of similarity-reflecting binary vectors with random binary projections,” Cybernetics and Systems Analysis, Vol. 51, No. 2, 313–323 (2015).CrossRefzbMATHGoogle Scholar
  30. 30.
    M. Jagadeesan, Simple Analysis of Sparse, Sign-Consistent JL. arXiv:1708.02966. 9 Aug 2017.Google Scholar
  31. 31.
    S. Dasgupta, C. F. Stevens, and S. Navlakha, “A neural algorithm for a fundamental computing problem,” Science, Vol. 358, No. 6364, 793–796 (2017).MathSciNetCrossRefGoogle Scholar
  32. 32.
    K. Sinha, “Fast L1-norm nearest neighbor search using a simple variant of randomized partition tree,” Procedia Computer Science, Vol. 53, 64–73 (2015).CrossRefGoogle Scholar
  33. 33.
    J. Wang, N. Wang, Y. Jia, J. Li, G. Zeng, H. Zha, and X.-S. Hua, “Trinary-projection trees for approximate nearest neighbor search,” IEEE Trans. PAMI, Vol. 36, No. 2, 388–403 (2014).CrossRefGoogle Scholar
  34. 34.
    S. Vempala, “Randomly-oriented k-d trees adapt to intrinsic dimension,” in: Proc. FSTTCS’12 (2012), pp. 48–57.Google Scholar
  35. 35.
    J. B. MacQueen, “Some methods for classification and analysis of multivariate observations,” in: Proc. MSP’67, (1967), pp. 281–297.Google Scholar
  36. 36.
    R. M. Gray and D. L. Neuhoff, “Quantization,” IEEE Trans. IT, Vol. 44, 2325–2384 (1998).CrossRefzbMATHGoogle Scholar
  37. 37.
    R. Xu and D. Wunsch, “Survey of clustering algorithms,” IEEE TNN, Vol. 16, 645–678 (2005).Google Scholar
  38. 38.
    A. C. Fabregas, B. D. Gerardo, and B. T. Tanguilig III, “Enhanced initial centroids for kmeans algorithm,” Int. J. of Information Technology and Computer Science, Vol. 9, No. 1, 26–33 (2017).CrossRefGoogle Scholar
  39. 39.
    H. Kaur and P. Verma, “Comparative Weka analysis of clustering algorithm’s,” International Journal of Information Technology and Computer Science, Vol. 9, No. 8, 56–67 (2017).CrossRefGoogle Scholar
  40. 40.
    K. Fukunaga and P. M. Narendra, “A branch and bound algorithm for computing k-nearest neighbors,” IEEE Trans. Comput., Vol. C-24, No. 7, 750–753 (1975).CrossRefzbMATHGoogle Scholar
  41. 41.
    D. Nister and H. Stewenius, “Scalable recognition with a vocabulary tree,” in: Proc. CVPR’06 (2006), pp. 2161–2168.Google Scholar
  42. 42.
    T.-A. Pham, “Pair-wisely optimized clustering tree for feature indexing,” Computer Vision and Image Understanding, Vol. 154, 35–47 (2017).CrossRefGoogle Scholar
  43. 43.
    D. Zhang, G. Yang, Y. Hu, Z. Jin, D. Cai, and X. He, “A unified approximate nearest neighbor search scheme by combining data structure and hashing,” in: Proc. IJCAI’13 (2013), pp. 681–687.Google Scholar
  44. 44.
    R. F. Sproull, “Refinements to nearest-neighbor searching in k-dimensional trees,” Algorithmica, Vol. 6, No. 1, 579–589 (1991).MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    J. McNames, “A fast nearest-neighbor algorithm based on a principal axis search tree,” IEEE Trans. PAMI, Vol. 23, No. 9, 964–976 (2001).CrossRefGoogle Scholar
  46. 46.
    N. Verma, S. Kpotufe, and S. Dasgupta, “Which spatial partition trees are adaptive to intrinsic dimension?” in: Proc. UAI’09 (2009), pp. 565–574.Google Scholar
  47. 47.
    P. Ram and A. G. Gray, “Which space partitioning tree to use for search?” in: Proc. NIPS’13 (2013), pp. 656–654.Google Scholar
  48. 48.
    P. Ram, D. Lee, and A. G. Gray, “Nearest-neighbor search on a time budget via max-margin trees,” in: Proc. ICDM’12 (2012), pp. 1011–1022.Google Scholar
  49. 49.
    B. McFee and G. Lanckriet, “Large-scale music similarity search with spatial trees,” in: Proc. ISMIR’11 (2011), pp. 55–60.Google Scholar
  50. 50.
    S. Har-Peled, P. Indyk, and R. Motwani, “Approximate nearest neighbor: Towards removing the curse of dimensionality,” Theory Comput., Vol. 8, 321–350 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    P. W. Jones, A. Osipov, and V. Rokhlin, “A randomized approximate nearest neighbors algorithm,” Applied and Computational Harmonic Analysis, Vol. 34, No. 3, 415–444 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Y. Avrithis, I. Z. Emiris, and G. Samaras, “High-dimensional visual similarity search: k-d generalized randomized forests,” in: Proc. CGI’16 (2016), pp. 25–28.Google Scholar
  53. 53.
    V. Hyvönen, T. Pitkänen, S. Tasoulis, E. Jääsaari, R. Tuomainen, L. Wang, J. Corander, and T. Roos, “Fast nearest neighbor search through sparse random projections and voting,” in: Proc. BigData’16 (2016), pp. 881–888.Google Scholar
  54. 54.
    S. Ramaswamy and K. Rose, “Adaptive cluster distance bounding for high-dimensional indexing,” IEEE Trans. on KDE, Vol. 23, No. 6, 815–830 (2011).Google Scholar
  55. 55.
    X. Wang, “A fast exact k-nearest neighbors algorithm for high dimensional search using k-means clustering and triangle inequality,” in: Proc. ICNN’11 (2011), pp. 1293–1299.Google Scholar
  56. 56.
    H. Hong, G. Juan, and W. Ben, “An improved KNN algorithm based on adaptive cluster distance bounding for high dimensional indexing,” in: Proc. GCIS’12 (2012), pp. 213–217.Google Scholar
  57. 57.
    X. Feng, J. Cui, Y. Liu, and H. Li, “Effective optimizations of clusterbased nearest neighbor search in highdimensional space,” Multimedia Systems, Vol. 23, No. 1, 139–153 (2017).CrossRefGoogle Scholar
  58. 58.
    L. Liu, F. Fenghong Xiang, J. Mao, and M. Zhang, “High-dimensional indexing algorithm based on the hyperplane tree-structure,” in: Proc. IEEE ICIA’15 (2015), pp. 2730–2733.Google Scholar
  59. 59.
    H. Jegou, M. Douze, and C. Schmid, “Product quantization for nearest neighbor search,” IEEE Trans. PAMI, Vol. 33, No. 1, 117–128 (2011).Google Scholar
  60. 60.
    R. Tavenard, H. Jegou, and L. Amsaleg, “Balancing clusters to reduce response time variability in large scale image search,” in: Proc. CBMI’11 (2011), pp. 19–24.Google Scholar
  61. 61.
    A. Babenko and V. Lempitsky, “The inverted multi-index,” IEEE Trans. PAMI, Vol. 37, No. 6, 1247–1260 (2015).Google Scholar
  62. 62.
    M. Iwamura, T. Sato, and K. Kise, “What is the most efficient way to select nearest neighbor candidates for fast approximate nearest neighbor search?” in: Proc. ICCV’13 (2013), pp. 3535–3542.Google Scholar
  63. 63.
    J. P. Heo, Z. Lin, X. Shen, J. Brandt, and S. E. Yoon, “Shortlist selection with residual-aware distance estimator for k-nearest neighbor search,” in: Proc. CVPR’16 (2016), pp. 2009–2017.Google Scholar
  64. 64.
    L. Pauleve, H. Jegou, and L. Amsaleg, “Locality sensitive hashing: A comparison of hash function types and querying mechanisms,” Pattern Recognition Letters, Vol. 31, No. 11, 1348–1358 (2010).CrossRefGoogle Scholar
  65. 65.
    Y. Xia, K. He, F. Wen, and J. Sun, “Joint inverted indexing,” in: Proc. ICCV’13 (2013), pp. 3416–3423.Google Scholar
  66. 66.
    J. Philbin, O. Chum, M. Isard, J. Sivic, and A. Zisserman, “Object retrieval with large vocabularies and fast spatial matching,” in: Proc. CVPR’07 (2007), pp. 1–8.Google Scholar
  67. 67.
    Z. Hu, Y. V. Bodyanskiy, O. K. Tyshchenko, and V. O. Samitova, “Fuzzy clustering data given on the ordinal scale based on membership and likelihood functions sharing,” International Journal of Intelligent Systems and Applications, Vol. 9, No. 2, 1–9 (2017).CrossRefGoogle Scholar
  68. 68.
    Z. Hu, Y. V. Bodyanskiy, O. K. Tyshchenko, and V. O. Samitova, “Possibilistic fuzzy clustering for categorical data arrays based on frequency prototypes and dissimilarity measures,” International Journal of Intelligent Systems and Applications, Vol. 9, No. 5, 55–61 (2017).CrossRefGoogle Scholar
  69. 69.
    Z. Hu, Y. V. Bodyanskiy, O. K. Tyshchenko, and V. M. Tkachov, “Fuzzy clustering data arrays with omitted observations,” Int. J. Intelligent Systems and Applications, Vol. 9, No. 6, 24–32 (2017).CrossRefGoogle Scholar
  70. 70.
    A. Jain, P. Mehar, and B. Buksh, “Advancement in clustering with the concept of correlation clustering — a survey,” Int. J. Engineering Development and Research, Vol. 4, No. 2, 1002–1005 (2016).Google Scholar
  71. 71.
    A. Jain and S. Tyagi, “Priority based new approach for correlation clustering,” International Journal of Information Technology and Computer Science, Vol. 9, No. 3, 71–79 (2017).CrossRefGoogle Scholar
  72. 72.
    J. Wang, H. T. Shen, J. Song, and J. Ji, Hashing for Similarity Search: A Survey. arXiv:1408.2927. 13 Aug 2014.Google Scholar
  73. 73.
    J. Wang, W. Liu, S. Kumar, and S.-F. Chang, “Learning to hash for indexing big data: A survey,” Proc. of the IEEE, Vol. 104, No. 1, 34–57 (2016).Google Scholar
  74. 74.
    J. Wang, T. Zhang, J. Song, N. Sebe, and H. T. Shen, A Survey on Learning to Hash. IEEE Trans. PAMI. DOI:
  75. 75.
    L. Gao, J. Song, X. Liu, J. Shao, J. Liu, and J. Shao, “Learning in high-dimensional multimedia data: The state of the art,” Multimedia Systems, 1–11 (2015).Google Scholar
  76. 76.
    D. Comer, “The ubiquitous B-tree,” ACM Comput. Surv., Vol. 11, 121–138 (1979).CrossRefzbMATHGoogle Scholar
  77. 77.
    S. Berchtold, C. Bohm, and H.-P. Kriegel, “The pyramid technique: Towards breaking the curse of dimensionality,” in: Proc. SIGMOD’98 (1998), pp. 142–153.Google Scholar
  78. 78.
    H. V. Jagadish, B. C. Ooi, K. L. Tan, C. Yu, and R. Zhang, “iDistance: An adaptive B+-tree based indexing method for nearest neighbor search,” ACM TODS, Vol. 30, No. 2, 364–397 (2005).CrossRefGoogle Scholar
  79. 79.
    J. K. Lawder and P. J. H. King, “Querying multi-dimensional data indexed using the Hilbert space-filling curve,” ACM SIGMOD Record, Vol. 30, No. 1, 19–24 (2001).CrossRefGoogle Scholar
  80. 80.
    S. Liao, M. Lopez, and S. Leutenegger, “High dimensional similarity search with space filling curves,” in: Proc. ICDE’01 (2001), pp. 615–622.Google Scholar
  81. 81.
    G. Mainar-Ruiz and J. Perez-Cortes, “Approximate nearest neighbor search using a single space-filling curve and multiple representations of the data points,” in: Proc. ICPR’06, Vol. 2 (2006), pp. 502–505.Google Scholar
  82. 82.
    Y. Sun, W. Wang, J. Qin, Y. Zhang, and X. Lin, “SRS: Solving c-approximate nearest neighbor queries in high dimensional Euclidean space with a tiny index,” Proc. VLDB Endowment, Vol. 8, No. 1, 1–12 (2014).CrossRefGoogle Scholar
  83. 83.
    E. Anagnostopoulos, I. Z. Emiris, and I. Psarros, Randomized Embeddings with Slack, and High-Dimensional Approximate Nearest Neighbor. arXiv:1412.1683. 3 Dec 2016.Google Scholar
  84. 84.
    G. Avarikioti, I. Z. Emiris, I. Psarros, and G. Samaras, Practical Linear-Space Approximate Near Neighbors in High Dimension. arXiv:1612.07405. 22 Dec 2016.Google Scholar
  85. 85.
    R. Donaldson, A. Gupta, Y. Plan, and T. Reimer, Random Mappings Designed for Commercial Search Engines. arXiv:1507.05929. 21 Jul 2015.Google Scholar
  86. 86.
    D. A. Rachkovskij, I. S. Misuno, and S. V. Slipchenko, “Randomized projective methods for construction of binary sparse vector representations,” Cybernetics and Systems Analysis, Vol. 48, No. 1, 146–156 (2012).CrossRefzbMATHGoogle Scholar
  87. 87.
    S. Ferdowsi, S. Voloshynovskiy, D. Kostadinov, and T. Holotyak, “Fast content identification in highdimensional feature spaces using sparse ternary codes,” in: Proc. WIFS’16 (2016), pp. 1–6.Google Scholar
  88. 88.
    I. S. Misuno, D. A. Rachkovskij, S. V. Slipchenko, and A. M. Sokolov, “Searching for text information with the help of vector representations,” Problems in Programming, No. 4, 50–59 (2005).Google Scholar
  89. 89.
    V. I. Gritsenko, D. A. Rachkovskij, A. A. Frolov, R. Gayler, D. Kleyko, and E. Osipov, “Neural distributed autoassociative memories: A survey,” Cybernetics and Computer Engineering, No. 2 (188), 5–35 (2017).Google Scholar
  90. 90.
    P. Indyk, J. Matousek, and A. Sidiropoulos, “Low-distortion embeddings of finite metric spaces,” in: Handbook of Discrete and Computational Geometry, Ch. 8, 3rd Ed., CRC Press, Boca Raton, USA (2017), pp. 211–231.Google Scholar
  91. 91.
    S. Fortune, “Voronoi diagrams and Delaunay triangulations,” in: Handbook of Discrete and Computational Geometry, Ch. 27, 3rd Ed., CRC Press, Boca Raton, USA (2017), pp. 705–721.Google Scholar
  92. 92.
    T. Sebastian and B. Kimia, “Metric-based shape retrieval in large databases,” in: Proc. ICPR’02, Vol. 3 (2002), pp. 291–296.Google Scholar
  93. 93.
    J. Chen, H. Fang, and Y. Saad, “Fast approximate knn graph construction for high dimensional data via recursive Lanczos bisection,” Journal MLR, Vol. 10, 1989–2012 (2009).Google Scholar
  94. 94.
    J. Wang, J. Wang, G. Zeng, Z. Tu, R. Gan, and S. Li, “Scalable k-NN graph construction for visual descriptors,” in: Proc. CVPR’12 (2012), pp. 1106–1113.Google Scholar
  95. 95.
    Y.-M. Zhang, K. Huang, G. Geng, and C.-L. Liu, “Fast knn graph construction with locality sensitive hashing,” in: Proc. ECMLPKDD’13 (2013), pp. 660–674.Google Scholar
  96. 96.
    J. Tang, J. Liu, M. Zhang, and Q. Mei, “Visualizing large-scale and high-dimensional data,” in: Proc. WWW’16 (2016), pp. 287–297.Google Scholar
  97. 97.
    C. Fu and D. Cai, Efanna: An Extremely Fast Approximate Nearest Neighbor Search Algorithm Based on kNN Graph. arXiv:1609.07228. 3 Dec 2016.Google Scholar
  98. 98.
    W. Dong, M. Charikar, and K. Li, “Efficient K-nearest neighbor graph construction for generic similarity measures,” in: Proc. WWW’11 (2011), pp. 577–586.Google Scholar
  99. 99.
    W.-L. Zhao, J. Yang, and C.-H. Deng, Scalable Nearest Neighbor Search Based on kNN Graph. arXiv:1701.08475. 3 Feb 2017.Google Scholar
  100. 100.
    W. Li, Y. Zhang, Y. Sun, W. Wang, W. Zhang, and X. Lin, Approximate Nearest Neighbor Search on High Dimensional Data — Experiments, Analyses, and Improvement. arXiv:1610.02455. 8 Oct 2016.Google Scholar
  101. 101.
    J. Johnson, M. Douze, and H. Jegou, Billion-Scale Similarity Search with GPUs. arXiv:1702.08734. 28 Feb 2017.Google Scholar
  102. 102.
    D. C. Anastasiu and G. Karypis, “L2knng: Fast exact k-nearest neighbor graph construction with l2-norm pruning,” in: Proc. CIKM’15 (2015), pp. 791–800.Google Scholar
  103. 103.
    A. Boutet, A. M. Kermarrec, N. Mittal, and F. Taiani, “Being prepared in a sparse world: The case of kNN graph construction,” in: Proc. ICDE’16 (2016), pp. 241–252.Google Scholar
  104. 104.
    Y. Wang, A. Shrivastava, and J. Ryu, FLASH: Randomized Algorithms Accelerated over CPU-GPU for Ultra-High Dimensional Similarity Search. arXiv:1709.01190. 4 Sep 2017.Google Scholar
  105. 105.
    J. Wang and S. Li, “Query-driven iterated neighborhood graph search for large scale indexing,” in: Proc. MM’12 (2012), pp. 179–188.Google Scholar
  106. 106.
    Z. Jin, D. Zhang, Y. Hu, S. Lin, D. Cai, and X. He, “Fast and accurate hashing via iterative nearest neighbors expansion,” IEEE Trans. on Cybernetics, Vol. 44, No. 11, 2167–2177 (2014).CrossRefGoogle Scholar
  107. 107.
    J. Wang, J. Wang, G. Zeng, R. Gan, S. Li, and B. Guo, “Fast neighborhood graph search using cartesian concatenation,” in: Multimedia Data Mining and Analytics, Springer, Cham (2015), pp. 397–417.Google Scholar
  108. 108.
    B. Neyshabur and N. Srebro, “On symmetric and asymmetric LSHs for inner product search,” in: Proc. ICML’15 (2015), pp. 1926–1934.Google Scholar
  109. 109.
    A. Ponomarenko, N. Avrelin, B. Naidan, and L. Boytsov, “Comparative analysis of data structures for approximate nearest neighbor search,” in: Proc. Data Analytics’14 (2014), pp. 125–130.Google Scholar
  110. 110.
    B. Naidan, L. Boytsov, and E. Nyberg, “Permutation search methods are efficient, yet faster search is possible,” Proc. VLDB Endowment, Vol. 8, No. 12, 1618–1629 (2015).Google Scholar
  111. 111.
    Yu. A. Malkov and D. A. Yashunin, Efficient and Robust Approximate Nearest Neighbor Search Using Hierarchical Navigable Small World Graphs. arXiv:1603.09320. 21 May 2016.Google Scholar
  112. 112.
    M. Aumuller, E. Bernhardsson, and A. Faithfull, “ANN-Benchmarks: A benchmarking tool for approximate nearest neighbor algorithms,” in: Proc. SISAP’17 (2017), pp. 34–49.Google Scholar
  113. 113.
    A. A. Frolov, D. A. Rachkovskij, and D. Husek, “On information characteristics of Willshaw-like auto-associative memory,” Neural Network World, Vol. 12, No. 2, 141–157 (2002).Google Scholar
  114. 114.
    A. A. Frolov, D. Husek, and D. A. Rachkovskij, “Time of searching for similar binary vectors in associative memory,” Cybernetics and Systems Analysis, Vol. 42, No. 5, 615–623 (2006).CrossRefzbMATHGoogle Scholar
  115. 115.
    A. H. Salavati, K. R. Kumar, and A. Shokrollahi, “Nonbinary associative memory with exponential pattern retrieval capacity and iterative learning,” IEEE TNNLS, Vol. 25, No. 3, 557–570 (2014).Google Scholar
  116. 116.
    A. Mazumdar and A. S. Rawat, “Associative memory using dictionary learning and expander decoding,” in: Proc. AAAI’17 (2017), pp. 267–273.Google Scholar
  117. 117.
    D. Ferro, V. Gripon, and X. Jiang, “Nearest neighbour search using binary neural networks,” in: Proc. IJCNN’16 (2016), pp. 5106–5112.Google Scholar
  118. 118.
    A. Iscen, T. Furon, V. Gripon, M. Rabbat, and H. Jegou, “Memory Vectors for Similarity Search in High-Dimensional Spaces,” IEEE Trans. on Big Data (2017). DOI:

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Authors and Affiliations

  1. 1.International Scientific-Educational Center of Information Technologies and SystemsNAS of Ukraine and MES of UkraineKyivUkraine

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