Intrusion Detection and Performance Analysis Using Copula Functions

Abstract

Nowadays, interest in technology is growing as technology advances and makes our jobs easier. These rapid technological advancements bring with them a slew of unwanted negative attacks, such as cyber-attacks and unauthorized access. To prevent such negative attacks, intrusion detection systems are frequently used. In this research, we make some suggestions for novel and reliable classifiers for intrusion detection systems that are based on copulas. Using copula-based classifiers, we hope to detect intrusion in computer networks. Student's-t, Gumbel, Clayton, Gaussian, Independent and Frank classifiers, which are frequently used in the literature, have been preferred as copula-based classifiers. These classifiers were used to perform classification on the KDD'99 dataset. The 10-fold cross-validation method has been used in the classification phase. When the experimental results were examined, the proposed Gaussian copula-based classifier outperformed state-of-the-art basic methods on the KDD'99 dataset with a success rate of 99.41%. As a direct consequence of this, classifiers based on the copula have shown promising results in the field of intrusion detection. Classifiers that are based on the copula have been found to be a competitive alternative to the most recent and cutting-edge fundamental approaches.

Keywords

• Intrusion Detection
• Copula Functions
• KDD’99 Dataset
• Naive Bayes Classifier
• mRMR

Ethical Statement

The study is complied with research and publication ethics

References

1. M. Burukanlı, Ü. Budak, and M. Çıbuk, “Saldırı Tespit Sistemlerinde Makine Öğrenme Metotlarının Kullanımı,” in Uluslararası Bilim ve Mühendislik Sempozyumu, 2019, pp. 1052–1057.
2. B. W. Masduki, K. Ramli, F. A. Saputra, and D. Sugiarto, “Study on Implementation of Machine Learning Methods Combination for Improving Attacks Detection Accuracy on Intrusion Detection System (IDS),” in 2015 International Conference on Quality in Research (QiR), 2015, pp. 56–64.
3. M. Burukanlı, “Copula fonksiyonlarını kullanarak bilgisayar ağlarında saldırı tespiti,” M.S. thesis, Bitlis Eren Üniversitesi Lisansüstü Eğitim Enstitüsü, Bitlis, Turkey, 2020.
4. Ş. Sağıroğlu, E. N. Yolaçan, and U. Yavanoğlu, “Zeki Saldırı Tespit Sistemi Tasarımı ve Gerçekleştirilmesi,” Journal of Faculty of Engineering and Architecture of Gazi University, vol. 26, no. 2, pp. 325–340, 2011.
5. B. Huyot, Y. Mabiala, and J.-F. Marcotorchino, “Online Unsupervised Anomaly Detection in Large Information Systems Using Copula Theory,” in 2014 IEEE 3rd International Conference on Cloud Computing and Intelligence Systems, Nov. 2014, pp. 679–684, doi: 10.1109/CCIS.2014.7175820.
6. R. Salinas-Gutiérrez, A. Hernández-Aguirre, M. J. J. Rivera-Meraz, and E. R. Villa-Diharce, “Using Gaussian Copulas in Supervised Probabilistic Classification,” in Soft Computing for Intelligent Control and Mobile Robotics, C. Castillo, J. Kacprzyk, and W. Pedrycz, Eds., Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2010, pp. 355–372.
7. M. Scavnicky, “A study of Applying Copulas in Data Mining,” M.S. thesis, Charles University in Prague Faculty of Mathematics and Physics, Prague, Czech Republic, 2013.
8. H. A. Sonawane and T. M. Pattewar, “A Comparative Performance Evaluation of Intrusion Detection Based on Neural Network and PCA,” in 2015 International Conference on Communications and Signal Processing (ICCSP), 2015, pp. 841–845, doi: 10.1109/ICCSP.2015.7322612.

9. M. Govindarajan and R. M. Chandrasekaran, “Intrusion Detection using an Ensemble of Classification Methods,” in Lecture Notes in Engineering and Computer Science, 2012, vol. 1, pp. 459–464.
10. A. Dastanpour, S. Ibrahim, R. Mashinchi, and A. Selamat, “Comparison of Genetic Algorithm Optimization on Artificial Neural Network and Support Vector Machine in Intrusion Detection System,” in 2014 IEEE Conference on Open Systems (ICOS), Oct. 2014, pp. 72–77, doi: 10.1109/ICOS.2014.7042412.
11. W. Wang and R. Battiti, “Identifying Intrusions in Computer Networks with Principal Component Analysis,” in First International Conference on Availability, Reliability and Security (ARES’06), 2006, pp. 270–279, doi: 10.1109/ARES.2006.73.
12. S. Kumar and A. Yadav, “Increasing Performance Of Intrusion Detection System Using Neural Network,” in 2014 IEEE International Conference on Advanced Communication Control and Computing Technologies (ICACCCT), 2014, pp. 546–550.
13. J. Esmaily, R. Moradinezhad, and J. Ghasemi, “Intrusion Detection System Based on Multi-Layer Perceptron Neural Networks and Decision Tree,” in 2015 7th Conference on Information and Knowledge Technology (IKT), May 2015, pp. 1–5, doi: 10.1109/IKT.2015.7288736.
14. Y. B. Bhavsar and K. C. Waghmare, “Intrusion Detection System using Data Mining Technique: Support Vector Machine,” International Journal of Emerging Technologies and Advanced Engineering, vol. 3, no. 3, pp. 581–586, 2013.
15. G. Poojitha, K. N. Kumar, and P. J. Reddy, “Intrusion Detection using Artificial Neural Network,” in 2010 Second International Conference on Computing, Communication and Networking Technologies (ICCCNT), Jul. 2010, pp. 1–7, doi: 10.1109/ICCCNT.2010.5592568.
16. S. Sathe, “A Novel Bayesian Classifier using Copula Functions,” arXiv Preprint cs/0611150, 2006.
17. D. Qian et al., “Drowsiness Detection by Bayesian-Copula Discriminant Classifier Based on EEG Signals during Daytime Short Nap,” IEEE Transactions on Biomedical Engineering, vol. 64, no. 4, pp. 743–754, 2017, doi: 10.1109/TBME.2016.2574812.
18. L. Slechan and J. Górecki, “On the Accuracy of Copula-Based Bayesian Classifiers: An Experimental Comparison with Neural Networks,” in Computational Collective Intelligence, M. Nunez, N. T. Nguyen, D. Camacho, and B. Trawinski, Eds., Springer International, Madrid, 2015, pp. 485–493.
19. Y. Chen, “A Copula-Based Supervised Learning Classification for Continuous and Discrete Data,” Journal of Data Science, vol. 13, pp. 769–790, 2014.
20. N. Hammami, M. Bedda, and N. Farah, “Probabilistic Classification Based on Gaussian Copula for Speech Recognition: Application to Spoken Arabic Digits,” in Signal Processing - Algorithms, Architectures, Arrangements, and Applications Conference Proceedings (SPA), 2013, pp. 312–317.
21. Y. He, J. Deng, and H. Li, “Short-Term Power Load Forecasting with Deep Belief Network and Copula Models,” in 2017 9th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), Aug. 2017, vol. 1, pp. 191–194, doi: 10.1109/IHMSC.2017.50.
22. R. B. Nelsen, An Introduction to Copulas. Springer Science+Business Media, Inc., 2006.
23. J. Lu, W. Tian, and P. Zhang, “The Archimedean Copulas Measure of the Risk Characteristic for the Tail Dependent Asset Returns,” in 2008 International Conference on Management Science and Engineering 15th Annual Conference Proceedings, Sep. 2008, pp. 173–181, doi: 10.1109/ICMSE.2008.4668912.
24. P. Embrechts, F. Lindskog, and A. McNeil, “Modelling Dependence with Copulas and Applications to Risk Management,” in Handbook of Heavy Tailed Distributions in Finance, S. T. Rachev, Ed., Elsevier, Amsterdam, 2003, pp. 329–384.
25. T. Schmidt, “Coping with Copulas,” in Copulas: From Theory to Application in Finance, J. Rank, Ed., Risk Books Publishing, Berkeley, 2006, pp. 3–34.
26. E. Bouyé, V. Durrleman, A. Nikeghbali, G. Riboulet, and T. Roncalli, Copulas for Finance-A Reading Guide and Some Applications, SSRN Electronic Journal, 2000.
27. A. Surana and A. Pinto, “Analysis of Stochastic Automata Networks Using Copula Functions,” in 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Sep. 2010, pp. 1699–1706, doi: 10.1109/ALLERTON.2010.5707121.
28. B. Z. Karagül, “Hayat Dışı Sigortalarda Doğrusal Olmayan Bağımlılığın Kopulalar ile Dinamik Finansal Analizi,” M.S. thesis, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara, Turkey, 2013.
29. G. Yapakçı, “Kopulalar Teorisinin Finansta Uygulaması,” M.S. thesis, Ege Üniversitesi Fen Bilimleri Enstitüsü, İzmir, Turkey, 2007.
30. S. Aslan, S. Çelebioğlu, and F. Öztürk, “İki Boyutlu Arşimedyen Kopulalarda İstatistiksel Sonuç Çıkarımı ve Bir Uygulama,” Gazi Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, vol. 14, no. 2, pp. 1–18, 2012.
31. L. Andersen and J. Sidenius, “Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings,” Journal of Credit Risk, vol. 1, no. 1, pp. 29–70, 2005, doi: 10.21314/jcr.2005.003.
32. D. Çatal and R. S. Albayrak, “Riske Maruz Değer Hesabında Karışım Kopula Kullanımı: Dolar-Euro Portföyü,” Yaşar Üniversitesi E-Dergi, vol. 8, no. 31, pp. 5187–5202, 2013.
33. M. Mehdizadeh, R. Ghazi, and M. Ghayeni, “Power System Security Assessment with High Wind Penetration Using the Farms Models Based on Their Correlation,” IET Renewable Power Generation, vol. 12, no. 8, pp. 893–900, 2018, doi: 10.1049/iet-rpg.2017.0386.
34. P. Hájek and R. Mesiar, “On Copulas, Quasicopulas and Fuzzy Logic,” Soft Computing, vol. 12, no. 12, pp. 1239–1243, 2008, doi: 10.1007/s00500-008-0286-z.
35. J. Yan, “Enjoy the Joy of Copulas: With a Package copula,” Journal of Statistical Software, vol. 21, no. 4, pp. 1–21, 2007, doi: 10.18637/jss.v021.i04.
36. H. He and P. K. Varshney, “A Coalitional Game for Distributed Inference in Sensor Networks with Dependent Observations,” IEEE Transactions on Signal Processing, vol. 64, no. 7, pp. 1854–1866, 2016, doi: 10.1109/TSP.2015.2508781.
37. G. Van Der Wulp, “Using Copulas in Risk Management,” M.S. thesis, Tilburg University Department of Econometrics, Tilburg, Netherlands, 2003.
38. M. Sklar, “Fonctions de Répartition à n Dimensions et Leurs Marges,” Publications de l'Institut Statistique de l'Université de Paris, vol. 8, pp. 229–231, 1959.
39. A. Alhan, “Bağımsızlık Kapulasını İçeren Kapula Aileleri, Kapula Tahmin Yöntemleri ve İstanbul Menkul Kıymetler Borsasında Sektörler Arası Bağımlılık Yapısı,” Ph.D. dissertation, Gazi Üniversitesi Fen Bilimleri Enstitüsü, Ankara, Turkey, 2008.
40. A. M. Karataş, “Modeling of Daily Maximum and Minimum Temperature Changes in Bitlis Province Using Copula Method,” Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 7, no. 2, pp. 268–275, 2018.
41. J. Lu, W.-J. Tian, and P. Zhang, “The Extreme Value Copulas Analysis of the Risk Dependence for the Foreign Exchange Data,” in 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing (WiCom), Oct. 2008, pp. 1–6, doi: 10.1109/WiCom.2008.2405.
42. P. Mou, F. Tao, C. Jia, and W. Ma, “A Copula-Based Function Model in Fuzzy Reliability Analysis on the Planetary Steering Gear,” in 2013 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE), Jul. 2013, pp. 375–378, doi: 10.1109/QR2MSE.2013.6625605.
43. A. M. Karakaş, “Modelling Temperature Measurement Data by Using Copula Functions,” Bitlis Eren Üniversitesi Fen Bilimleri ve Teknoloji Dergisi, vol. 7, no. 1, pp. 27–32, 2017.
44. S. Jadhav and R. Daruwala, “3-D Modeling of Statistical Dependencies Using Copulas for Wireless Sensor Network,” in Proceedings of the 2016 IEEE International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), 2016, pp. 1886–1889, doi: 10.1109/WiSPNET.2016.7566469.
45. C. D. Tran, O. O. Rudovic, and V. Pavlovic, “Unsupervised Domain Adaptation with Copula Models,” in 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP), 2017, pp. 1–6.
46. C. Romano, “Calibrating and Simulating Copula Functions: An Application to the Italian Stock Market,” Risk Management Functional Capital, vol. 180, pp. 1–26, 2002.
47. Anonim, “Probability Distributions,” 2017. [Online]. Available: http://www.nematrian.com/Pages/ProbabilityDistributionsCombined.pdf. [Accessed: Apr. 13, 2020].
48. E. E. Sezgin, “Finansal Bağımlılık Analizi: Vine ve CD Vine Copula Yaklaşımları,” M.S. thesis, Bitlis Eren Üniversitesi ve Fırat Üniversitesi Fen Bilimleri Enstitüsü, Bitlis, Turkey, 2019.
49. S. Arslan, “Arşimedyen Kapulalar Üzerine Bir Çalışma,” Ph.D. dissertation, Ankara Üniversitesi Fen Bilimleri Enstitüsü, Ankara, Turkey, 2013.
50. S. Çelebioğlu, “Arşimedyen Kapulalar ve Bir Uygulama,” Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, vol. 22, no. 1, pp. 43–52, 2003.
51. S. S. Galiani, “Copula Functions and Their Application in Pricing and Risk Managing Multiname Credit Derivative Products,” M.S. thesis, Department of Mathematics, King’s College London, London, UK, 2003.
52. H. Manner, Estimation and Model Selection of Copulas with an Application to Exchange Rates. Maastricht: Maastricht Research School of Economics of Technology and Organizations (METEOR) Press, 2007.
53. Y. Dong, S. Zhang, G. Fan, L. Zhang, L. Yi, and M. Lin, “Application of Copula Function in the Reliability Analysis of the Electrical System and the Power Device of Certain-Type Armored Vehicle,” in CSAE 2012 - Proceedings of the 2012 IEEE International Conference on Computer Science and Automation Engineering, 2012, vol. 1, pp. 386–389, doi: 10.1109/CSAE.2012.6272621.
54. A. Setiawan, Soeheri, E. Panggabean, M. A. Elhias, F. Ikorasaki, and B. Riski, “Efficiency of Bayes Theorem in Detecting Early Symptoms of Avian Diseases,” in 2018 6th International Conference on Cyber and IT Service Management (CITSM), Aug. 2018, pp. 1–5, doi: 10.1109/CITSM.2018.8674273.
55. N. S. B. Sembiring, E. Ginting, M. Fauzi, Yudi, F. Tambunan, and E. V. Haryanto, “An Expert System to Diagnose Herpes Zoster Disease Using Bayes Theorem,” in 2019 7th International Conference on Cyber and IT Service Management (CITSM), Nov. 2019, pp. 1–3, doi: 10.1109/CITSM47753.2019.8965381.
56. A. H. Jahromi and M. Taheri, “A Non-Parametric Mixture of Gaussian Naive Bayes Classifiers Based on Local Independent Features,” in 2017 Artificial Intelligence and Signal Processing Conference (AISP), Oct. 2017, vol. 2018, pp. 209–212, doi: 10.1109/AISP.2017.8324083.
57. K. P. Murphy, “Naive Bayes Classifiers,” 2006. [Online]. Available: https://www.ic.unicamp.br/~rocha/teaching/2011s1/mc906/aulas/naive-bayes.pdf. [Accessed: Apr. 02, 2020].
58. K. Netti and Y. Radhika, “A Novel Method for Minimizing Loss of Accuracy in Naive Bayes Classifier,” in 2015 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), Dec. 2015, pp. 1–4, doi: 10.1109/ICCIC.2015.7435801.
59. F.-J. Yang, “An Implementation of Naive Bayes Classifier,” in 2018 International Conference on Computational Science and Computational Intelligence (CSCI), Dec. 2018, pp. 301–306, doi: 10.1109/CSCI46756.2018.00065.
60. Anonim, “Maximum A Posteriori Estimation,” 2020. [Online]. Available: https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation. [Accessed: May 04, 2020].
61. H. Bogunovic, J. M. Pozo, R. Cardenes, L. S. Roman, and A. F. Frangi, “Anatomical Labeling of the Circle of Willis Using Maximum A Posteriori Probability Estimation,” IEEE Transactions on Medical Imaging, vol. 32, no. 9, pp. 1587–1599, 2013.
62. F. Peng, D. Schuurmans, and S. Wang, “Augmenting Naive Bayes Classifiers with Statistical Language Models,” Information Retrieval Boston, vol. 7, no. 3–4, pp. 317–345, 2004.
63. M. J. Islam, Q. M. J. Wu, M. Ahmadi, and M. A. Sid Ahmed, “Investigating the Performance of Naive Bayes Classifiers and K-Nearest Neighbor Classifiers,” in 2007 International Conference on Convergence Information Technology (ICCIT), Nov. 2007, pp. 1541–1546, doi: 10.1109/ICCIT.2007.148.
64. J.-H. Lee, J.-H. Lee, S.-G. Sohn, J.-H. Ryu, and T.-M. Chung, “Effective Value of Decision Tree with KDD 99 Intrusion Detection Datasets for Intrusion Detection System,” in 2008 10th International Conference on Advanced Communication Technology (ICACT), Feb. 2008, vol. 2, pp. 1170–1175, doi: 10.1109/ICACT.2008.4493974.
65. Anonim, “Kddcup1999,” 1999. [Online]. Available: http://kdd.ics.uci.edu/databases/kddcup99/task.html. [Accessed: Apr. 09, 2020].
66. B. Nethu, “Classification of Intrusion Detection Dataset Using Machine Learning Approaches,” International Journal of Electronics and Computer Science Engineering, vol. 1, no. 3, pp. 1044–1051, 2012.
67. D. H. Deshmukh, T. Ghorpade, and P. Padiya, “Intrusion Detection System by Improved Preprocessing Methods and Naive Bayes Classifier Using NSL-KDD 99 Dataset,” in 2014 International Conference on Electronics and Communication Systems (ICECS), Feb. 2014, pp. 1–7, doi: 10.1109/ECS.2014.6892542.
68. T. Janarthanan and S. Zargari, “Feature Selection in UNSW-NB15 and KDDCUP’99 Datasets,” in 2017 IEEE 26th International Symposium on Industrial Electronics (ISIE), 2017, pp. 1881–1886.
69. G. Meena and R. R. Choudhary, “A Review Paper on IDS Classification Using KDD 99 and NSL KDD Dataset in WEKA,” in 2017 International Conference on Computer, Communications and Electronics (Comptelix), Jul. 2017, pp. 553–558, doi: 10.1109/COMPTELIX.2017.8004032.
70. Y. Vural, “Kurumsal Bilgi Güvenliğinde Güvenlik Testleri ve Öneriler,” Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, vol. 26, no. 1, pp. 89–103, 2011.
71. Anonim, “The UCI KDD Archive Information and Computer Science University of California, Irvine,” 1999. [Online]. Available: http://kdd.ics.uci.edu/databases/kddcup99/kddcup99.html. [Accessed: Jan. 26, 2021].
72. M. Burukanlı, M. Çıbuk, and Ü. Budak, “Saldırı Tespiti için Makine Öğrenme Yöntemlerinin Karşılaştırmalı Analizi,” BEÜ Fen Bilimleri Dergisi, vol. 10, no. 2, pp. 613–624, 2021.
73. H. Peng, F. Long, and C. Ding, “Feature Selection Based on Mutual Information: Criteria of Max-Dependency, Max-Relevance, and Min-Redundancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 8, pp. 1226–1238, 2005, doi: 10.1109/TPAMI.2005.159.
74. M. Çıbuk, U. Budak, Y. Guo, M. C. Ince, and A. Sengur, “Efficient Deep Features Selections and Classification for Flower Species Recognition,” Measurement, vol. 137, pp. 7–13, Apr. 2019, doi: 10.1016/j.measurement.2019.01.041.
75. S. Wang, Y.-H. Zhang, J. Lu, W. Cui, J. Hu, and Y.-D. Cai, “Analysis and Identification of Aptamer-Compound Interactions with a Maximum Relevance Minimum Redundancy and Nearest Neighbor Algorithm,” BioMed Research International, vol. 2016, pp. 1–12, 2016. [Online]. Available: http://downloads.hindawi.com/journals/bmri/2016/8351204.pdf. [Accessed: Apr. 29, 2020].