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A hybrid quantum feature selection algorithm using a quantum inspired graph theoretic approach

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Quantum machine learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. It generally exposes the synthesis of important machine learning algorithms in a quantum framework. Dimensionality reduction of a dataset with a suitable feature selection strategy is one of the most important tasks in knowledge discovery and data mining. The efficient feature selection strategy helps to improve the overall accuracy of a large dataset in terms of machine learning operations. In this paper, a quantum feature selection algorithm using a graph-theoretic approach has been proposed. The proposed algorithm has used the concept of correlation coefficient based graph-theoretic classical approach initially and then applied the quantum Oracle with CNOT operation to verify whether the dataset is suitable for dimensionality reduction or not. If it is suitable, then our algorithm can efficiently estimate their high correlation values by using quantum parallel amplitude estimation and amplitude amplification techniques. This paper also shows that our proposed algorithm substantially outperforms than some popular classical feature selection algorithms for supervised classification in terms of query complexity of \(O(\frac {k\sqrt {N_{c}^{(k)}N_{f}^{(k)}}}{\epsilon })\), where N is the size of the feature vectors whose values are ⩾ THmin(minimum threshold), k is the number of iterations and where 𝜖 is the error for estimating those feature vectors. Compared with the classical counterpart, i.e. the performance of our quantum algorithm quadratically improves than others.

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  1. 1.

    Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S (2016) Quantum machine learning. arXiv:1611.09347

  2. 2.

    Schuld M, Sinayskiy I, Petruccione F (2015) An introduction to quantum machine learning. Contemp Phys 56(2):172–185

  3. 3.

    Lloyd S, Mohseni M, Rebentrost P (2013) Quantum algorithms for supervised and unsupervised machine learning. arXiv:1307.0411

  4. 4.

    Cai XD, Wu D, Su ZE, Chen MC, Wang XL, Li L, Pan JW (2015) Entanglement-based machine learning on a quantum computer. Phys Rev Lett 114(11):110504

  5. 5.

    Lichman M, Bache K (2013) Uci machine learning repository. university of california, irvine, school of information and computer sciences. In [Online]. Available: http://archive.ics.uci.edu/ml

  6. 6.

    Zhang G, Hu L, Jin W (2004) Resemblance coefficient and a quantum genetic algorithm for feature selection. In: International Conference on Discovery Science . Springer, Berlin, pp 155–168

  7. 7.

    Barani F, Mirhosseini M, Nezamabadi-pour H (2017) Application of binary quantum-inspired gravitational search algorithm in feature subset selection. Appl Intell 47(2):304–318

  8. 8.

    Dey L, Chakraborty S, Biswas A, Bose B, Tiwari S (2016) Sentiment Analysis of Review Datasets Using Naï,ve Bayes’ and K-NN Classifier. Int J Inf Eng Electron Bus (IJIEEB) 8(4):54–62

  9. 9.

    Das AK, Goswami S, Chakrabarti A, Chakraborty B (2017) A new hybrid feature selection approach using feature association map for supervised and unsupervised classification. Expert Syst Appl 88:81–94

  10. 10.

    McMahon D (2007) Quantum computing explained. Wiley, New York

  11. 11.

    Kohavi R, John GH (1997) Wrappers for feature subset selection. Artif Intell 97(1-2):273–324

  12. 12.

    Song Q, Jiang H, Liu J (2017) Feature selection based on FDA and F-score for multi-class classification. Expert Syst Appl 81:22–27

  13. 13.

    He Z, Li L, Huang Z, Situ H (2018) Quantum-enhanced feature selection with forward selection and backward elimination. Quantum Inf Process 17(7):154

  14. 14.

    Goswami S, Das AK, Chakrabarti A, Chakraborty B (2017) A feature cluster taxonomy based feature selection technique. Expert Syst Appl 79:76–89

  15. 15.

    Bennett CH, Shor PW (1998) Quantum information theory. IEEE Trans Inf Theory 44(6):2724–2742

  16. 16.

    Soliman OS, Rassem A (2012, December) Correlation based feature selection using quantum bio inspired estimation of distribution algorithm. In: International Workshop on Multi-disciplinary Trends in Artificial Intelligence. Springer, Berlin, pp 318–329

  17. 17.

    Al-Rajab M, Lu J, Xu Q (2017) Examining applying high performance genetic data feature selection and classification algorithms for colon cancer diagnosis. Comput Methods Prog Biomed 146:11–24

  18. 18.

    Yang C-H, Chuang L-Y, Yang C-H (2010) IG-GA: a hybrid filter/wrapper method for feature selection of microarray data. J Med Biol Eng 30(1):23–28

  19. 19.

    Taylor R (1990) Interpretation of the correlation coefficient: a basic review. J Diagnost Med Sonograph 6:35–39

  20. 20.

    Gupta S, Zia RKP (2001) Quantum neural networks. J Comput Syst Sci 63(3):355–383

  21. 21.

    Nielsen MA, Chuang IL (2010) Quantum Computation and Quantum Information. Cambridge University Press, New York. ISBN 978-1-107-00217-3 hardback

  22. 22.

    Nezamabadi-pour H (2015) A quantum-inspired gravitational search algorithm for binary encoded optimization problems. Eng Appl Artif Intell 40:62–75

  23. 23.

    Ibrahim AA, Mohamed A, Shareef H (2014) Optimal power quality monitor placement in power systems using an adaptive quantum-inspired binary gravitational search algorithm. Int J Electr Power Energy Syst 57:404–413

  24. 24.

    Singh KV, Raza Z (2017) A quantum-inspired binary gravitational search algorithm–based job-scheduling model for mobile computational grid. Concurr Comput Practice Exper 29 :12

  25. 25.

    Han KH, Kim JH (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evolut Comput 6(6):580–593

  26. 26.

    Han KH, Kim KJ (2004) Quantum-inspired evolutionary algorithms with a new termination criterion, h-epsilon gate,and two-phase scheme. IEEE Trans Evolut Comput 8(2):156–169

  27. 27.

    Brassard G, Høyer P, Mosca M, Tapp A (2002) Quantum Amplitude Amplification and Estimation, Contemporary Mathematics Series Millenium, vol 305. AMS, New York

  28. 28.

    Zouache D, Abdelaziz FB (2018) A cooperative swarm intelligence algorithm based on quantum-inspired and rough sets for feature selection. Comput Ind Eng 115:26–36

  29. 29.

    Khosravi MH, Bagherzadeh P (2019) A new method for feature selection based on intelligent water drops. Appl Intell 49(3):1172–1184

  30. 30.

    Abualigah LM, Khader AT, Hanandeh ES (2018) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466

  31. 31.

    Goswami S, Chakraborty S, Guha P, Tarafdar A, Kedia A (2019) Filter-Based Feature Selection Methods Using Hill Climbing Approach. In: Natural Computing for Unsupervised Learning. Springer, Cham, pp 213–234

  32. 32.

    Dörn S (2007) Quantum algorithms for graph traversals and related problems. In: Proceedings of CIE, vol 7, pp 123–131

  33. 33.

    Dürr C, Heiligman M, HOyer P, Mhalla M (2006) Quantum query complexity of some graph problems. SIAM J Comput 35(6):1310–1328

  34. 34.

    D’Hondt E (2009) Quantum approaches to graph colouring. Theor Comput Sci 410(4-5):302–309

  35. 35.

    Ambainis A, ˇspalek R (2006) Quantum Algorithms for Matching and Network Flows Proceedings of STACS’06

  36. 36.

    Brassard G, Høyer P, Tapp A (1998) Quantum counting. In: International Colloquium on Automata, Languages, and Programming. Springer, Berlin, pp 820–831

  37. 37.

    Mafarja M, Mirjalili S (2018) Whale optimization approaches for wrapper feature selection. Appl Soft Comput 62:441–453

  38. 38.

    Dasgupta A, Banerjee A, Dastider AG, Barman A, Chakraborty S (2019) A Study and Analysis of a Feature Subset Selection Technique using Penguin Search Optimization Algorithm (FS-peSOA), In: Book: Data Science: theory, Analysis, and ApplicationsPublisher: CRC Press, Taylor and Francis (accepted), arXiv:1611.09347

  39. 39.

    Tubishat M, Abushariah MA, Idris N, Aljarah I (2019) Improved whale optimization algorithm for feature selection in Arabic sentiment analysis. Appl Intell 49(5):1688–1707

  40. 40.

    Hancer E, Xue B, Zhang M, Karaboga D, Akay B (2018) Pareto front feature selection based on artificial bee colony optimization. Inf Sci 422:462–479

  41. 41.

    Zhou H, Zhang Y, Zhang Y, Liu H (2019) Feature selection based on conditional mutual information: minimum conditional relevance and minimum conditional redundancy. Appl Intell 49(3):883–896

  42. 42.

    Wu Q, Ma Z, Fan J, Xu G, Shen Y (2019) A Feature Selection Method Based on Hybrid Improved Binary Quantum Particle Swarm Optimization. IEEE Access

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Correspondence to Sanjay Chakraborty.

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Chakraborty, S., Shaikh, S.H., Chakrabarti, A. et al. A hybrid quantum feature selection algorithm using a quantum inspired graph theoretic approach. Appl Intell (2020). https://doi.org/10.1007/s10489-019-01604-3

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  • Quantum machine learning
  • Quantum graph theoretic approach
  • Quantum information processing
  • Quantum feature selection
  • Quantum amplitude estimation