Abstract
Despite the popularity of principal component analysis (PCA) as an anomaly detection technique, the main shortage of PCA-based anomaly detection models is their interpretability. Constructing the abnormal subspace of PCA (i.e., the subspace spanned by the least significant principal components (PCs)), with sparse and orthogonal loading vectors provides a means of anomaly interpretation. However, solving all abnormal sparse PCs one by one through semi-definite programming is time consuming. In this paper, we derive an adapted projection deflation method for extracting least significant PCs and propose an alternating direction method of multipliers (ADMM) solution for constructing the sparse abnormal subspace. Our experiments on two real world datasets showed that the proposed ADMM solution achieved comparable detection accuracy and sparsity as the SDP solution and is 10 times more efficient, which makes it more suitable for application domains with higher dimensions.
This work is funded by the National Key Research and Development Program of China (Grant No. 2016YFB0200100).
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Chandola, V., Banerjee, A., Kumar, V.: Anomaly detection: a survey. ACM Comput. Surv. 41(3), 1–58 (2009)
Ringberg, H., Soule, A., Rexford, J., Diot, C.: Sensitivity of PCA for traffic anomaly detection. In: The 2007 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, pp. 109–120. ACM (2007)
Jiang, R., Fei, H., Huan, J.: A family of joint sparse PCA algorithms for anomaly localization in network data streams. IEEE Trans. Knowl. Data Eng. 25(11), 2421–2433 (2013)
Bin, X., Zhao, Y., Shen, B.: Abnormal subspace sparse PCA for anomaly detection and intepretation. In: The ACM SIGKDD Workshop on Outlier Detection and Description, ODD 2015, pp. 1–10 (2015)
Jolliffe, I.: Principal Component Analysis. Wiley Online Library, Hoboken (2002)
Jolliffe, I.T., Trendafilov, N.T., Uddin, M.: A modified principal component technique based on the LASSO. J. Comput. Graph. Stat. 12(3), 531–547 (2003)
Luo, L., Bao, S., Mao, J., Tang, D.: Fault detection and diagnosis based on sparse PCA and two-level contribution plots. Ind. Eng. Chem. Res. 56(1), 225–240 (2017)
Yu, H., Khan, F., Garaniya, V.: A sparse PCA for nonlinear fault diagnosis and robust feature discovery of industrial processes. AIChE J. 62(5), 1494–1513 (2016)
Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. J. Comput. Graph. Stat. 15(2), 265–286 (2006)
d’Aspremont, A., El Ghaoui, L., Jordan, M.I., Lanckriet, G.R.G.: A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49(3), 434–448 (2007)
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1–122 (2011)
Ma, S.: Alternating direction method for multipliers for sparse principal component analysis. J. Oper. Res. Soc. China 1, 253–274 (2013)
Vu, V.Q., Cho, J., Lei, J., Rohe, K.: Fantope projection and selection: a near-optimal convex relaxation of sparse PCA. In: Advances in Neural Information Processing Systems, vol. 26, pp. 2670–2678 (2013)
Mackey, L.: Deflation methods for sparse PCA. In: Advances in Neural Information Processing Systems, vol. 22, pp. 1017–1024 (2009)
Breast Cancer Wisconsin (Diagnostic) Data Set (1995)
KDD Cup 1999 Data (1999)
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Jiang, W., Zhao, Y., Adnan, K.A. (2020). An ADMM Approach for Constructing Abnormal Subspace of Sparse PCA. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12253. Springer, Cham. https://doi.org/10.1007/978-3-030-58814-4_58
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