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Index Structures for Fast Similarity Search for Binary Vectors

  • NEW MEANS OF CYBERNETICS, INFORMATICS, COMPUTER ENGINEERING, AND SYSTEMS ANALYSIS
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Abstract

This article reviews index structures for fast similarity search for objects represented by binary vectors (with components equal to 0 or 1). Structures for both exact and approximate search by Hamming distance and other similarity measures are considered. Mainly, index structures are presented that are based on hash tables and similarity-preserving hashing and also on tree structures, neighborhood graphs, and distributed neural autoassociative memory. Ideas of well-known algorithms and algorithms proposed in recent years are stated.

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References

  1. C. Manning, P. Raghavan, and Schütze, Introduction to Information Retrieval, Cambridge University Press, New York (2008).

    Book  MATH  Google Scholar 

  2. R. Datta, D. Joshi, J. Li, and J. Wang, “Image retrieval: Ideas, influences, and trends of the new age,” ACM Computing Surveys, Vol. 40, No. 2, 1–60 (2008).

    Article  Google Scholar 

  3. M. M. Fouad, “Content-based search for image retrieval. I,” J. Image, Graphics and Signal Processing, Vol. 5, No. 11, 46–52 (2013).

  4. D. A. Rachkovkij, “Distance-based index structures for fast similarity search,” Cybernetics and Systems Analysis, Vol. 53, No. 4, 636–658 (2017).

    Article  Google Scholar 

  5. J. Heinly, E. Dunn, and J.-M. Frahm, “Comparative evaluation of binary features,” in: Proc. ECCV’12, 759–773 (2012).

  6. F. A. Khalifa, N. A. Semary, H. M. El-Sayed, and M. M. Hadhoud, “Local detectors and descriptors for object class recognition,” International Journal of Intelligent Systems and Applications, Vol. 7, No. 10, 12–18 (2015).

    Article  Google Scholar 

  7. Y. Uchida, Local Feature Detectors, Descriptors, and Image Representations: A Survey. arXiv:1607.08368. 28 Jul 2016.

  8. M. Rastegari, V. Ordonez, J. Redmon, and A. Farhadi, “Xnor-net: Imagenet classification using binary convolutional neural networks,” in: Proc. ECCV’16 (2016), pp. 525–542.

  9. I. Hubara, M. Courbariaux, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks,” in: Proc. NIPS’16 (2016), pp. 4107–4115.

  10. W. Tang, G. Hua, and L. Wang, “How to train a compact binary neural network with high accuracy?” in: Proc. AAAI’17 (2017), pp. 2625–2631.

  11. S. Kumar, J. V. Desai, and S. Mukherjee, “Copy move forgery detection in contrast variant environment using binary DCT vectors. I,” J. Image, Graphics and Signal Processing, Vol. 7, No. 6, 38–44 (2015).

    Article  Google Scholar 

  12. M. Faruqui and C. Dyer, “Non-distributional word vector representations,” in: Proc. ACL-IJCNLP’15, Vol. 2 (2015), pp. 464–469.

  13. S. Ren, X. Cao, Y. Wei, and J. Sun, “Face alignment at 3000 fps via regressing local binary features,” in: Proc. CVPR’14 (2014), pp. 1685–1692.

  14. D. N. Pavlov, H. Mannila, and P. Smyth, “Beyond independence: Probabilistic models for query approximation on binary transaction data,” IEEE TKDE, Vol. 15, No. 6, 1409–1421 (2003).

    Google Scholar 

  15. J. Wang, H. T. Shen, J. Song, and J. Ji, Hashing for Similarity Search: A Survey. arXiv:1408.2927. 13 Aug 2014.

  16. D. A. Rachkovskij, E. M. Kussul, and T. N. Baidyk, “Building a world model with structure-sensitive sparse binary distributed representations,” BICA, Vol. 3, 64–86 (2013).

    Google Scholar 

  17. D. A. Rachkovskij, “Binary vectors for fast distance and similarity estimation,” Cybernetics and Systems Analysis, Vol. 53, No. 1, 138–156 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Wang, W. Liu, S. Kumar, and S.-F. Chang, “Learning to hash for indexing big data: A survey,” in: Proc. IEEE, Vol. 104, No. 1, 34–57 (2016).

  19. J. Wang, T. Zhang, J. Song, N. Sebe, and H. T. Shen, “A survey on learning to hash,” IEEE Trans. PAMI. DOI: https://doi.org/10.1109/TPAMI.2017.2699960

  20. D. A. Rachkovskij, “Real-valued vectors for fast distance and similarity estimation,” Cybernetics and Systems Analysis, Vol. 52, No. 6, 967–988 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  21. V. Gaede and O. Gunther, “Multidimensional access methods,” ACM Comput. Surv., Vol. 30, No. 2, 170–231 (1998).

    Article  Google Scholar 

  22. C. Böhm, S. Berchtold, and D. A. Keim, “Searching in high-dimensional spaces: Index structures for improving the performance of multimedia databases,” ACM Comp. Surv., Vol. 33, No. 3, 322–373 (2001).

    Article  Google Scholar 

  23. H. Samet, Foundations of Multidimensional and Metric Data Structures, Morgan Kaufmann, San Francisco (2006).

    MATH  Google Scholar 

  24. I. S. Haque, V. S. Pande, and W. P. Walters, “Anatomy of high-performance 2d similarity calculations,” Journal of Chemical Information and Modeling, Vol. 51, No. 9, 2345–2351 (2011).

    Article  Google Scholar 

  25. R. Donaldson, A. Gupta, Y. Plan, and T. Reimer, Random Mappings Designed for Commercial Search Engines. arXiv:1507.05929. 21 Jul 2015.

  26. G. Brodal and L. Gasieniec, “Approximate dictionary queries,” in: Proc. CPM’96 (1996), pp. 65–74.

  27. L. Carter and M. N. Wegman, “Universal classes of hash functions,” Journal of Computer and System Sciences, Vol. 18, No. 2, 143–154 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  28. M. L. Fredman, J. Komlos, and E. Szemeredi, “Storing a sparse table with O(1) worst case access time,” Journal of the ACM, Vol. 31, No 3, 538–544 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  29. I. Chegrane and D. Belazzougui, “Simple, compact and robust approximate string dictionary,” J. Discrete Algorithms, Vol. 28, 49–60 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Pagh, “Locality-sensitive hashing without false negatives,” in: Proc. SODA’16 (2016), pp. 1–9.

  31. A. Andoni and P. Indyk, “Nearest neighbors in high-dimensional spaces,” in: Handbook of Discrete and Computational Geometry, 3rd Edition, Ch. 43, 1133–1153 (2017).

  32. J. Zobel and A. Moffat, “Inverted files for text search engines,” ACM Comput. Surv., Vol. 38, No. 2, 6:1–6:56 (2006).

  33. D. A. Rachkovskij and S. V. Slipchenko, “Similarity-based retrieval with structure-sensitive sparse binary distributed representations,” Computational Intelligence, Vol. 28, No. 1, 106–129 (2012).

    Article  MathSciNet  Google Scholar 

  34. S. Ferdowsi, S. Voloshynovskiy, D. Kostadinov, and T. Holotyak, “Fast content identification in high-dimensional feature spaces using sparse ternary codes,” in: Proc. WIFS’16 (2016), pp. 1–6.

  35. 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.

  36. N. Tatti, T. Mielikainen, A. Goonies, and H. Mannila, “What is the dimension of your binary data?” in: Proc. ICDM’06 (2006), pp. 603–612.

  37. J. Alman and R. Williams, “Probabilistic polynomials and Hamming nearest neighbors,” in: Proc. FOCS’15 (2015), pp. 136–150.

  38. D. M. W. Powers, “Evaluation: From precision, recall and F-measure to ROC, informedness, markedness and correlation,” Journal of Machine Learning Tech., Vol. 2, No. 1, 37–63 (2011).

    MathSciNet  Google Scholar 

  39. M. Muja and D. G. Lowe, “Scalable nearest neighbor algorithms for high dimensional data,” IEEE TPAMI, Vol. 36, No. 11, 2227–2240 (2014).

    Article  Google Scholar 

  40. A. C. Yao and F. F. Yao, “Dictionary look-up with one error,” Journal of Algorithms, Vol. 25, No. 1, 194–202 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  41. G. S. Brodal and V. Srinivasan, “Improved bounds for dictionary look-up with one error,” Information Processing Letters, Vol. 75, Nos. 1–2, 57–59 (2000).

  42. R. Cole, L.-A. Gottlieb, and M. Lewenstein, “Dictionary matching and indexing with errors and do not cares,” in: Proc. STOC’04 (2004), pp. 91–100.

  43. H.-L. Chan, T.-W. Lam, W.-K. Sung, S.-L. Tam, and S.-S. Wong, “A linear size index for approximate pattern matching,” Journal of Discrete Algorithms, Vol. 9, No. 4, 358–364 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  44. H. Chan, T. W. Lam, W. Sung, S. Tam, and S. Wong, “Compressed indexes for approximate string matching,” Algorithmica, Vol. 58, No. 2, 263–281 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  45. D. Greene, M. Parnas, and F. Yao, “Multi-index hashing for information retrieval,” in Proc. FOCS’94 (1994), pp. 722–731.

  46. S. Wu and U. Manber, “Fast text searching allowing errors,”. Communications of the ACM, Vol. 35, No. 10, 83–91 (1992).

    Article  Google Scholar 

  47. G. S. Manku, A. Jain, and A. D. Sarma, “Detecting near-duplicates for web crawling,” in: Proc. WWW’07 (2007), pp. 141–150.

  48. A. X. Liu, S. Ke, and E. Torng, “Large scale Hamming distance query processing,” in: Proc. ICDE’11 (2011), pp. 553–564.

  49. S. Gog and R. Venturini, “Fast and compact Hamming distance index,” in: Proc. SIGIR’16 (2016), pp. 285–294.

  50. X. Zhang, J. Qin, W. Wang, Y. Sun, and J. Lu, “Hmsearch: An efficient Hamming distance query processing algorithm,” in: Proc. SSDBM’13 (2013), pp. 19:1–19:12.

  51. M. Norouzi, A. Punjani, and D. J. Fleet, “Fast exact search in Hamming space with multi-index hashing,” IEEE Trans. PAMI, Vol. 36, No. 6, 1107–1119 (2014).

    Article  Google Scholar 

  52. J. Wan, S. Tang, Y. Zhang, L. Huang, and J. Li, “Data driven multi-index hashing,” in: Proc. ICIP’13 (2013), pp. 2670–2673.

  53. Y. Ma, H. Zou, H. Xie, and Q. Su, “Fast search with data-oriented multi-index hashing for multimedia data,” KSII TIIS, Vol. 9, No. 7, 2599–2613 (2015).

    Google Scholar 

  54. M. Wang, X. Feng, and J. Cui, “Multi-index hashing with repeat-bits in Hamming space” in: Proc. FSKD’15 (2015), pp. 1307–1313.

  55. J. Song, H. T. Shen, J. Wang, Z. Huang, N. Sebe, and J. Wang, “A distance-computation-free search scheme for binary code databases,” IEEE Trans. Multimedia, Vol. 18, No. 3, 484–495 (2016).

    Article  Google Scholar 

  56. E.-J. Ong and M. Bober, “Improved Hamming distance search using variable length hashing,” in: Proc. CVPR’16 (2016), pp. 2000–2008.

  57. S. Eghbali and L. Tahvildari, Cosine Similarity Search with Multi-Index Hashing. arXiv:1610.00574. 14 Sep 2016.

  58. A. Andoni and P. Indyk, “Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions,” Communications of the ACM, Vol. 51, No. 1, 117–122 (2008).

    Article  Google Scholar 

  59. S. Har-Peled, P. Indyk, and R. Motwani, “Approximate nearest neighbor: Towards removing the curse of dimensionality,” Theory Comput., Vol. 8, 321–350 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  60. A. Shrivastava and P. Li, “Asymmetric LSH (ALSH) for sublinear time maximum inner product search (MIPS),” in: Proc. NIPS’14 (2014), pp. 2321–2329.

  61. M. Charikar, “Similarity estimation techniques from rounding algorithms,” in: Proc. STOC’02 (2002), pp. 380–388.

  62. A. Shrivastava and P. Li, “Asymmetric minwise hashing for indexing binary inner products and set containment,” in: Proc. WWW’15 (2015), pp. 981–991.

  63. A. Andoni, M. Datar, N. Immorlica, P. Indyk, and V. S. Mirrokni, “Locality-sensitive hashing using stable distributions,” in: Nearest Neighbor Methods for Learning and Vision: Theory and Practice, MIT Press, Cambridge (2006), pp. 61–72.

  64. R. O’Donnell, Y. Wu, and Y. Zhou, “Optimal lower bounds for locality sensitive hashing (except when q is tiny),” ACM TOCS, Vol. 6, No. 1, 5.1–5.13 (2014).

  65. A. Z. Broder, “On the resemblance and containment of documents,” in: Proc. SEQUENCES’97 (1997), pp. 21–29.

  66. A. Z. Broder, S. C. Glassman, M. S. Manasse, and G. Zweig, “Syntactic clustering of the web,” Computer Networks and ISDN Systems, Vol. 29, No. 8–13, 1157–1166 (1997).

  67. A. Z. Broder, M. Charikar, A. M. Frieze, and M. Mitzenmacher, “Min-wise independent permutations,” J. Comput. System Sci., Vol. 60, 327–336 (1998).

    MathSciNet  MATH  Google Scholar 

  68. J. Tang and Y. Tian, “A systematic review on minwise hashing algorithms,” Annals of Data Science, Vol. 3, No. 4, 445–468 (2016).

    Article  Google Scholar 

  69. S. Dahlgaard, M. B. T. Knudsen, and M. Thorup, Fast Similarity Sketching. arXiv:1704.04370. 14 Apr 2017.

  70. P. Li, and A.C. König, “Theory and applications of b-bit minwise hashing,” Communications of the ACM, Vol. 54, No. 8, 101–109 (2011).

    Article  Google Scholar 

  71. A. Shrivastava, Optimal Densification for Fast and Accurate Minwise Hashing. arXiv:1703.04664. 14 Mar 2017.

  72. A. Shrivastava and P. Li, “In defense of minhash over simhash,” in: Proc. AISTATS’14 (2014), pp. 886–894.

  73. T. D. Ahle, R. Pagh, I. Razenshteyn, and F. Silvestri, “On the complexity of inner product similarity join,” in: Proc. PODS’16 (2016), pp. 151–164.

  74. D. Bera and R. Pratap, “Frequent-itemset mining using locality-sensitive hashing,” in: Proc. COCOON’16 (2016), pp. 143–155.

  75. T. Trzcinski, V. Lepetit and, P. Fua, “Thick boundaries in binary space and their influence on nearest-neighbor search,” Pattern Recognition Letters, Vol. 33, No. 16, 2173–2180 (2012).

    Article  Google Scholar 

  76. M. M. Esmaeili, R. K. Ward, and M. Fatourechi, “A fast approximate nearest neighbor search algorithm in the Hamming space,” IEEE Trans. PAMI, Vol. 34, No. 12, 2481–2488 (2012).

    Article  Google Scholar 

  77. S. Har-Peled and S. Mahabadi, “Proximity in the age of distraction: Robust approximate nearest neighbor search,” in: Proc. SODA’17 (2017), pp. 1–15.

  78. T. D. Ahle, M. Aumuller, and R. Pagh, “Parameter-free locality sensitive hashing for spherical range reporting,” in: Proc. SODA’17 (2017), pp. 239–256.

  79. N. Pham, “Hybrid LSH: Faster near neighbors reporting in high-dimensional space,” in: Proc. EDBT’17 (2017), pp. 454–457.

  80. P. Flajolet, E. Fusy, O. Gandouet, and F. Meunier, “Hyperloglog: The analysis of a near-optimal cardinality estimation algorithm,” in: Proc. AofA’07 (2007), pp. 127–146.

  81. N. Pham and R. Pagh, “Scalability and total recall with fast CoveringLSH,” in: Proc. CIKM’16 (2016), pp. 1109–1118.

  82. A. Becker, L. Ducas, N. Gama, and T. Laarhoven, “New directions in nearest neighbor searching with applications to lattice sieving,” in: Proc. SODA’16 (2016), pp. 10–24.

  83. A. Andoni, T. Laarhoven, I. Razenshteyn, and E. Waingarten, “Optimal hashing-based time-space trade-offs for approximate near neighbors,” in: Proc. SODA’17 (2017), pp. 47–66.

  84. T. Christiani and R. Pagh, “Set similarity search beyond MinHash,” in: Proc. STOC’17 (2017), pp. 1094–1107.

  85. T. D. Ahle, Optimal Las Vegas Locality Sensitive Data Structures. arXiv:1704.02054. April 6, 2017

  86. A. Andoni and I. Razenshteyn, “Optimal data-dependent hashing for approximate near neighbors,” in: Proc. STOC’15, pp. 793–801 (2015).

  87. A. Andoni, I. Razenshteyn, and N. Shekel Nosatzki, “Lsh forest: Practical algorithms made theoretical,” in: Proc. SODA’17 (2017), pp. 67–78.

  88. M. Bawa, T. Condie, and P. Ganesan, “Lsh forest: Self-tuning indexes for similarity search,” in: Proc. WWW’05 (2005), pp. 651–660.

  89. G. Qian, Q. Zhu, Q. Xue, and S. Pramanik, “Dynamic indexing for multidimensional non-ordered discrete data spaces using a data-partitioning approach,” ACM TODS, Vol. 31, No. 2, 439–484 (2006).

    Article  Google Scholar 

  90. G. Qian, Q. Zhu, Q. Xue, and S. Pramanik, “A space-partitioning-based indexing method for multidimensional non-ordered discrete data spaces,” ACM TOIS, Vol. 23, 79–110 (2006).

    Article  Google Scholar 

  91. C. C. Yan, H. Xie, B. Zhang, Y. Ma, Q. Dai, and Y. Liu, “Fast approximate matching of binary codes with distinctive bits,” Front. Comput. Sci., Vol. 9, No. 5, 741–750 (2015).

    Article  Google Scholar 

  92. D. Galvez-Lopez and J. D. Tardos, “Bags of binary words for fast place recognition in image sequences,” IEEE Trans. Robotics, Vol. 28, No. 5, 1188–1197 (2012).

    Article  Google Scholar 

  93. Q. Luo, S. Zhang, T. Huang, W. Gao, and Q. Tian, “Scalable mobile search with binary phrase,” in: Proc. ICIMCS’13 (2013), pp. 66–70.

  94. J. Niedermayer and P. Kroger, “Retrieval of binary features in image databases: A study,” in: Proc. SISAP’14 (2014), pp. 151–163.

  95. V. Kryzhanovsky, M. Malsagov, J. A. C. Tomas, and I. Zhelavskaya, “On error probability of search in high-dimensional binary space with scalar neural network tree,” in Proc. NCTA’14 (2014).

  96. M. Tang, Y. Yu, W. G. Aref, Q. M. Malluhi, and M. Ouzzani, “Efficient processing of Hamming-distance-based similarity-search queries over mapreduce,” in: Proc. EDBT’15 (2015), pp. 361–372.

  97. Y. Tao, K. Yi, C. Sheng, and P. Kalnis, “Efficient and accurate nearest neighbor and closest pair search in high-dimensional space,” ACM Trans. Database Syst., Vol. 35, No. 3, 20:1–20:46 (2010).

  98. Z. Jiang, L. Xie, X. Deng, W. Xu, and J. Wang, “Fast nearest neighbor search in the Hamming space,” in: Proc. MMM ’16 (2016), pp. 325–336.

  99. 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.

  100. 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).

  101. L. G. Valiant, “Functionality in neural nets,” in: Proc. AAAI’88, Vol. 2 (1988), pp. 629–634.

  102. J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” in: Proc. of the Nat. Acad. Sci. USA, Vol. 79, No. 8, 2554–2558 (1982).

  103. M. Tsodyks and M. Feigelman, “The enhanced storage capacity in neural networks with low activity level,” Europhysics Letters, Vol. 6, No. 2, 101–105 (1988).

    Article  Google Scholar 

  104. A. A. Frolov, D. Husek, and I. P. Muraviev, “Information capacity and recall quality in sparsely encoded Hopfield-like neural network: Analytical approaches and computer simulation,” Neural Networks, Vol. 10, No. 5, 845–855 (1997).

    Article  Google Scholar 

  105. A. A. Frolov, D. Husek, and I. P. Muraviev, “Informational efficiency of sparsely encoded Hopfield-like associative memory,” Optical Memory & Neural Networks, Vol. 12, No. 3, 177–197 (2003).

    Google Scholar 

  106. S. Amari, “Characteristics of sparsely encoded associative memory,” Neural Networks, Vol. 2, No. 6, 451–457 (1989).

    Article  Google Scholar 

  107. J. Heusel, M. Lowe, and F. Vermet, “On the capacity of an associative memory model based on neural cliques,” Statist. Probab. Lett., Vol. 106, 256–261 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  108. V. Gripon, J. Heusel, M. Lowe, F. Vermet, “A comparative study of sparse associative memories,” Journal of Statistical Physics, Vol. 164, 105–129 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  109. 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).

    Article  MATH  Google Scholar 

  110. G. Palm, “On associative memory,” Biological Cybernetics, Vol. 36, 19–31 (1980).

    Article  MATH  Google Scholar 

  111. M. V. Tsodyks, “Associative memory in neural networks with binary synapses,” Mod. Phys. Lett., Vol. B4, 713–716 (1990).

    Article  MathSciNet  Google Scholar 

  112. A. Frolov, A. Kartashov, A. Goltsev, and R. Folk, “Quality and efficiency of retrieval for Willshaw-like autoassociative networks. I. Correction,” Network, Vol. 6, 513–534 (1995).

    Article  MATH  Google Scholar 

  113. F. Schwenker, F. T. Sommer, and G. Palm, “Iterative retrieval of sparsely coded associative memory patterns,” Neural Networks, Vol. 9, 445-455 (1996).

    Article  Google Scholar 

  114. 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 

  115. I. Kanter, “Potts-glass models of neural networks,” Physical Rev. A, Vol. 37 (7), 2739–2742 (1988).

    Article  MathSciNet  Google Scholar 

  116. M. Lowe and F. Vermet, “The capacity of q-state Potts neural networks with parallel retrieval dynamics,” Statistics and Probability Letters, Vol. 77, No. 4, 1505–1514 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  117. N. Onizawa, H. Jarollahi, T. Hanyu, and W. J. Gross, “Hardware execution of associative memories based on multiple-valued sparse clustered networks,” IEEE Journal on Emerging and Selected Topics in Circuits and Systems, Vol. 6, No. 1, 13–24 (2016).

    Article  Google Scholar 

  118. A. Kartashov, A. Frolov, A. Goltsev, and R. Folk, “Quality and efficiency of retrieval for Willshaw-like autoassociative networks. III. Willshaw–Potts model,” Network, Vol. 8, No. 1, 71–86 (1997).

    Article  MATH  Google Scholar 

  119. V. Gripon and C. Berrou, “Sparse neural networks with large learning diversity,” IEEE Trans. on Neural Networks, Vol. 22, No. 7, 1087–1096 (2011).

    Article  Google Scholar 

  120. M. Tsodyks, “Associative memory in asymmetric diluted network with low level of activity,” Europhysics Letters, Vol. 7, No. 3, 203–208 (1988).

    Article  Google Scholar 

  121. J. Buckingham and D. Willshaw, “On setting unit thresholds in an incompletely connected associative net,” Network, Vol. 4, 441–459 (1993).

    Article  Google Scholar 

  122. C. Yu, V. Gripon, X. Jiang, and H. Jegou, “Neural associative memories as accelerators for binary vector search,” in: Proc. COGNITIVE’15 (2015), pp. 85–89.

  123. A. A. Frolov, D. Husek, I. P. Muraviev, and P. Polyakov, “Boolean factor analysis by attractor neural network,” IEEE Trans. Neural Networks, Vol. 18, No. 3, 698–707 (2007).

    Article  Google Scholar 

  124. P. Peretto and J. J. Niez, “Long term memory storage capacity of multiconnected neural networks” Biol. Cybern., Vol. 54, No. 1, 53–63 (1986).

    Article  MATH  Google Scholar 

  125. P. Baldi and S. S. Venkatesh, “Number of stable points for spin-glasses and neural networks of higher orders,” Physical Review Letters, Vol. 58, No. 9, 913–916 (1987).

    Article  MathSciNet  Google Scholar 

  126. D. Krotov and J. J. Hopfield, “Dense associative memory for pattern recognition,” in: Proc. NIPS’16 (2016), pp. 1172–1180.

  127. D. Krotov and J. Hopfield, Dense Associative Memory is Robust to Adversarial Inputs. arXiv:1701.00939. 4 Jan 2017.

  128. M. Demircigil, J. Heusel, M. Lowe, S. Upgang, and F. Vermet, “On a model of associative memory with huge storage capacity,” Journal Stat. Phys., Vol. 168, No. 2, 288–299 (2017).

    Article  MathSciNet  Google Scholar 

  129. A. Karbasi, A. H. Salavati, and A. Shokrollahi, “Iterative learning and denoising in convolutional neural associative memories,” in: Proc. ICML’13 (2013), pp. 445–453.

  130. A. H. Salavati, K. R. Kumar, and A. Shokrollahi, “Nonbinary associative memory with exponential pattern retrieval capacity and iterative learning,” IEEE Trans. Neural Networks and Learning Systems, Vol. 25, No. 3, 557–570 (2014).

    Article  Google Scholar 

  131. A. Mazumdar and A. S. Rawat, “Associative memory via a sparse recovery model,” in: Proc. NIPS’15 (2015), pp. 2683–2691.

  132. A. Mazumdar and A. S. Rawat, “Associative memory using dictionary learning and expander decoding,” in: Proc. AAAI’17 (2017), pp. 267–273.

  133. M. A. Mansor, M. S. M. Kasihmuddin, and S. Sathasivam, “VLSI circuit configuration using satisfiability logic in Hopfield network,” International Journal of Intelligent Systems and Applications (IJISA), Vol. 8, No. 9, 22–29 (2016).

    Article  Google Scholar 

  134. M. A. Mansor, M. S. M. Kasihmuddin, and S. Sathasivam, “Enhanced Hopfield network for pattern satisfiability optimization,” International Journal of Intelligent Systems and Applications (IJISA), Vol. 8, No. 11, 27–33 (2016).

    Article  Google Scholar 

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Correspondence to D. A. Rachkovskij.

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2017, pp. 167–192.

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Rachkovskij, D.A. Index Structures for Fast Similarity Search for Binary Vectors. Cybern Syst Anal 53, 799–820 (2017). https://doi.org/10.1007/s10559-017-9983-x

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