Abstract
The Linear Discriminant Analysis (LDA) is a powerful linear feature reduction technique. It often produces satisfactory results under two conditions. The first one requires that the global data structure and the local data structure must be coherent. The second concerns data classes distribution nature. It should be a Gaussian distribution. Nevertheless, in pattern recognition problems, especially network anomalies detection, these conditions are not always fulfilled. In this paper, we propose an improved LDA algorithm, the median nearest neighbors LDA (median NN-LDA), which performs well without satisfying the above two conditions. Our approach can effectively get the local structure of data by working with samples that are near to the median of every data class. The further samples will be essential for preserving the global structure of every class. Extensive experiments on two well known datasets namely KDDcup99 and NSL-KDD show that the proposed approach can achieve a promising attack identification accuracy.
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References
Fukunaga, R.: Statistical Pattern Recognition. Academic Press, New York (1990)
Thapngam, T., Yu, S., Zhou, W.: DDoS discrimination by linear discriminant analysis (LDA). In: 2012 International Conference on Computing, Networking and Communications (ICNC), pp. 532–536. IEEE (2012)
An, W., Liang, M.: A new intrusion detection method based on SVM with minimum within-class scatter. Secur. Commun. Netw. 6(9), 1064–1074 (2013)
Subba, B., Biswas, S., Karmakar, S.: Intrusion detection systems using linear discriminant analysis and logistic regression. In: 2015 Annual IEEE India Conference (INDICON), pp. 1–6. IEEE (2015)
Yu, H., Yang, J.: A direct LDA algorithm for high-dimensional data with application to face recognition. Pattern Recogn. 34(10), 2067–2070 (2001)
Chen, L.F., Liao, H.Y.M., Ko, M.T., Lin, J.C., Yu, G.J.: A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recogn. 33(10), 1713–1726 (2000)
Jolliffe, I.: Principal Component Analysis. Wiley Online Library (2002)
Zhang, T., Fang, B., Tang, Y.Y., Shang, Z., Xu, B.: Generalized discriminant analysis: a matrix exponential approach. IEEE Trans. Syst. Man Cybern. Part B Cybern. 40(1), 186–197 (2010)
Ye, J., Janardan, R., Park, C.H., Park, H.: An optimization criterion for generalized discriminant analysis on under sampled problems. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 982–994 (2004)
Wang, X., Tang, X.: Random sampling for subspace face recognition. Int. J. Comput. Vis. 70(1), 91–104 (2006)
Liu, J., Chen, S., Tan, X.: A study on three linear discriminant analysis based methods in small sample size problem. Pattern Recogn. 41(1), 102–116 (2008)
Dai, D.Q., Yuen, P.C.: Regularized discriminant analysis and its application to face recognition. Pattern Recogn. 36(3), 845–847 (2003)
Cevikalp, H., Neamtu, M., Wilkes, M., Barkana, A.: Discriminative common vectors for face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 27(1), 4–13 (2005)
Li, H., Jiang, T., Zhang, K.: Efficient and robust feature extraction by maximum margin criterion. IEEE Trans. Neural Netw. 17(1), 157–165 (2006)
Ye, J., Li, Q., Xiong, H., Park, H., Janardan, R., Kumar, V.: IDR/QR: an incremental dimension reduction algorithm via QR decomposition. IEEE Trans. Knowl. Data Eng. 17(9), 1208–1222 (2005)
Pang, S., Ozawa, S., Kasabov, N.: Incremental linear discriminant analysis for classification of data streams. IEEE Trans. Syst. Man Cybern. Part B Cybern. 35(5), 905–914 (2005)
Kim, T.K., Wong, S.F., Stenger, B., Kittler, J., Cipolla, R.: Incremental linear discriminant analysis using sufficient spanning set approximations. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2007, pp. 1–8. IEEE (2007)
Li, X., Hu, W., Wang, H., Zhang, Z.: Linear discriminant analysis using rotational invariant L1 norm. Neurocomputing 73(13), 2571–2579 (2010)
Wang, H., Lu, X., Hu, Z., Zheng, W.: Fisher discriminant analysis with L1-norm. IEEE Trans. Cybern. 44(6), 828–842 (2014)
Yang, J., Zhang, D., Yang, J.Y.: Median LDA: a robust feature extraction method for face recognition. In: IEEE International Conference on Systems, Man and Cybernetics, SMC 2006, vol. 5, pp. 4208–4213. IEEE (2006)
Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Hopkins University Press, Baltimore (1996)
Sugiyama, M., Idé, T., Nakajima, S., Sese, J.: Semi-supervised local fisher discriminant analysis for dimensionality reduction. Mach. Learn. 78(1–2), 35–61 (2010)
Chen, H.T., Chang, H.W., Liu, T.L.: Local discriminant embedding and its variants. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, vol. 2, pp. 846–853. IEEE (2005)
Wang, H., Chen, S., Hu, Z., Zheng, W.: Locality-preserved maximum information projection. IEEE Trans. Neural Netw. 19(4), 571–585 (2008)
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Elkhadir, Z., Chougdali, K., Benattou, M. (2017). A Median Nearest Neighbors LDA for Anomaly Network Detection. In: El Hajji, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2017. Lecture Notes in Computer Science(), vol 10194. Springer, Cham. https://doi.org/10.1007/978-3-319-55589-8_9
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