Optimization Method for Cross-domain Coupled Graph Online Anomaly Detection Model

doi:10.12382/bgxb.2024.0076

Abstract

Abstract:

The graph online anomaly detection model plays a vital role in a wide range of application fields, including the network communication mode monitoring of missile system, the malicious attack ide.pngication of radar system, and the network activity monitoring of fighter aircraft control system. The detection model couples the spectral domain signal processing model with the time domain detection model, which involves the high-order nonlinear signal processing and introduces the space-time correlation, posing a significant challenge in achieving the robust and high-precision detection through the optimization of cross-domain coupled graph online anomaly detection model. An optimization method is proposed for the cross-domain coupled graph online anomaly detection model. The spatial-temporal signal correlation generated during signal processing is considered in the proposed optimization method. The spatial-temporal coupling mechanism and the impact of coupling process on detection performance are studied by intricately deriving the statistical characteristics, providing the basis for selecting the key parameter values in the anomaly detection model, and addressing the disadvantage of relying solely on approximation and empirical methods for parameter selection. Simulated results demonstrate that the proposed optimization method enhances detection accuracy while preserving the robustness of anomaly detection within graph networks.

Key words: graph signal processing, anomaly detection, cross-domain coupling, spatial-temporal correlation, model optimization

CLC Number:

TN911.7

SUN Xuandi, SHEN Xiaohong, WANG Haiyan, YAN Yongsheng, SUO Jian. Optimization Method for Cross-domain Coupled Graph Online Anomaly Detection Model[J]. Acta Armamentarii, 2024, 45(9): 3261-3273.

Figures/Tables 13

Fig.1 Influences of graph filter parameters on detection performance

Fig.2 Influences of asynchronous learning rates on detection performance

Fig.3 Influence of graph topology on detection performance

Fig.4 Graph topology

Fig.5 Anomaly signal on graph network

Fig.6 Influence of graph filter coefficient regularization on the detection performance of cross-domain coupling model

Table 1 Influence of graph filter coefficient regularization on detection performance

图滤波器截止频率	正则处理	h₀	h₁	h₂	h₃	h₄	h₅	h₆	AUC
λ_c=0.37	无正则	0.83	5.99	-38.17	71.48	-60.68	24.27	-3.71	0.56
	含正则	1.18	-2.01	-0.15	1.02	0.46	0.76	0.188	0.77
λ_c=1.20	无正则	0.91	2.71	-18.09	44.99	-49.18	23.74	-4.16	0.41
	含正则	0.92	0.37	0.29	-0.59	-0.65	0.52	-0.06	0.63

Fig.7 Coupling relationship between B value and asynchronous learning rate

Fig.8 Influence of B value on detection performance

Fig.9 Experimental equipment

Fig.10 Temporal signal of L-type network with 8 channels

Fig.11 Received signal time-frequency representations on Node 2(upper)and Node 3(below)

Fig.12 Detection performance enhancement of the proposed model optimization method

References 28

[1]	ISUFI E, GAMA F, SHUMAN D I, et al. Graph filters for signal processing and machine learning on graphs[J/OL]. IEEE Transactions on Signal Processing, 2024,arXiv: 2211.08854.
[2]	LEUS G, MARQUES A G, MOURA J M F, et al. Graph signal processing: history, development, impact, and outlook[J]. IEEE Signal Processing Magazine, 2023, 40(4): 49-60.
[3]	滕克难, 盛安冬. 舰艇编队协同反导作战网络效果度量方法研究[J]. 兵工学报, 2010, 31(9):1247-1253.
	TENG K N, SHENG A D. Research on metric of network effect in ship formation cooperation anti-missile operation[J]. Acta Armamentarii, 2010, 31(9):1247-1253. (in Chinese)
[4]	ORTEGA A. Introduction to graph signal processing[M]. Cambridge, UK: Cambridge University Press, 2022.
[5]	徐冰冰, 岑科廷, 黄俊杰, 等. 图卷积神经网络综述[J]. 计算机学报, 2020, 43(5): 755-780.
	XU B B, CEN K T, HUANG J J, et al. Overview of graph convolutional neural networks[J]. Chinese Journal of Computers, 2020, 43(5): 755-780. (in Chinese)
[6]	COLUCCIA A, D’ALCONZO A, RICCIATO F. Distribution-based anomaly detection via generalized likelihood ratio test: a general maximum entropy approach[J]. Computer Networks, 2013, 57(17): 3446-3462.
[7]	SHARPNACK J, SINGH A, RINALDO A. Changepoint detection over graphs with the spectral scan statistic[C]//Proceedings of A.pngicial Intelligence and Statistics. Brookline, MA, US:PMLR, 2013: 545-553.
[8]	SHARPNACK J, RINALDO A, SINGH A. Detecting anomalous activity on networks with the graph Fourier scan statistic[J]. IEEE Transactions on Signal Processing, 2015, 64(2): 364-379.
[9]	FERRARI A, RICHARD C, VERDUCI L. Distributed change detection in streaming graph signals[C]// Proceedings of 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. Piscataway, NJ, US:IEEE, 2019: 166-170.
[10]	KERIVEN N, GARREAU D, POLI I. NEWMA:a new method for scalable model-free online change-point detection[J]. IEEE Transactions on Signal Processing, 2020, 68: 3515-3528.
[11]	LIU Y, YANG X H, ZHOU S H, et al. Simple contrastive graph clustering[J]. IEEE Transactions on Neural Networks and Learning Systems, 2023, 34(5): 2243-2256.
[12]	BECK A. Introduction to nonlinear optimization:theory, algorithms, and applications with MATLAB[M]. Philadelphia, PA, US: Society for Industrial and Applied Mathematics, 2014.
[13]	DIWEKAR U M. Introduction to applied optimization[M].New York, NY, US:Springer, 2020.
[14]	AKOGLU L, TONG H, KOUTRA D. Graph based anomaly detection and description: a survey[J]. Data Mining and Knowledge Discovery, 2015, 29: 626-688.
[15]	PIMENTEL M A F, CLIFTON D A, CLIFTON L, et al. A review of novelty detection[J]. Signal Processing, 2014, 99: 215-249.
[16]	DONG X W, THANOU D, TONI L, et al. Graph signal processing for machine learning: a review and new perspectives[J]. IEEE Signal Processing Magazine, 2020, 37(6): 117-127.
[17]	COUTINO M, ISUFI E, LEUS G. Advances in distributed graph filtering[J]. IEEE Transactions on Signal Processing, 2019, 67(9):2320-2333.
[18]	SHUMAN D I, NARANG S K, FROSSARD P, et al. The emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains[J]. IEEE Signal Processing Magazine, 2013, 30(3): 83-98.
[19]	BREST J, MAUČEC M S, BOŠKOVIĆ B. Single objective real-parameter optimization: algorithm jSO[C]//Proceedings of 2017 IEEE Congress on Evolutionary Computation. Piscataway, NJ, US:IEEE, 2017: 1311-1318.
[20]	MA X X, WU J, XUE S, et al. A comprehensive survey on graph anomaly detection with deep learning[J]. IEEE Transactions on Knowledge and Data Engineering, 2021, 35(12): 12012-12038.
[21]	JAHN J. Introduction to the theory of nonlinear optimization[M].Berlin, Germany:Springer, 2020.
[22]	NT H, MAEHARA T. Revisiting graph neural networks:all we haveislow-pass filters:arXiv:1905.09550[R]. Ithaca, US: Cornell University, 2019:1905.09550.
[23]	STANKOVIĆ L, MANDIC D, DAKOVIĆ M, et al. Vertex-frequency graph signal processing: a comprehensive review[J]. Digital Signal Processing, 2020, 107: 102802.
[24]	WAN L, ZEILER M, ZHANG S X, et al. Regularization of neural networks using dropconnect[C]//Proceedings of International Conference on Machine Learning. Brookline,MA, US:PMLR, 2013: 1058-1066.
[25]	MATNI N, CHANDRASEKARAN V. Regularization for design[J]. IEEE Transactions on Automatic Control, 2016, 61(12):3991-4006.
[26]	THAYYIL J, BIJOY K E. Digital image forgery detection using graph fourier transform[C]//Proceedings of 2020 International Conference on Futuristic Technologies in Control Systems & Renewable Energy. Piscataway, NJ, US: IEEE, 2020: 1-5.
[27]	SHANG C, YANG F, GAO X, et al. Concurrent monitoring of operating condition deviations and process dynamics anomalies with slow feature analysis[J]. AICHE Journal, 2015, 61(11): 3666-3682.
[28]	PERRAUDIN N, PARATTE J, SHUMAN D, et al. GSPBOX:a toolbox for signal processing on graphs:arXiv:1408.5781[R]. Ithaca, US: Cornell University, 2014:1408.5781.