Radar HRRP statistical recognition with temporal factor analysis by automatic Bayesian Ying-Yang harmony learning

Abstract

Radar high-resolution range profiles (HRRPs) are typical high-dimensional and interdimension dependently distributed data, the statistical modeling of which is a challenging task for HRRP-based target recognition. Supposing that HRRP samples are independent and jointly Gaussian distributed, a recent work [Du L, Liu H W, Bao Z. IEEE Transactions on Signal Processing, 2008, 56(5): 1931-1944] applied factor analysis (FA) to model HRRP data with a two-phase approach for model selection, which achieved satisfactory recognition performance. The theoretical analysis and experimental results reveal that there exists high temporal correlation among adjacent HRRPs. This paper is thus motivated to model the spatial and temporal structure of HRRP data simultaneously by employing temporal factor analysis (TFA) model. For a limited size of high-dimensional HRRP data, the two-phase approach for parameter learning and model selection suffers from intensive computation burden and deteriorated evaluation. To tackle these problems, this work adopts the Bayesian Ying-Yang (BYY) harmony learning that has automatic model selection ability during parameter learning. Experimental results show stepwise improved recognition and rejection performances from the two-phase learning based FA, to the two-phase learning based TFA and to the BYY harmony learning based TFA with automatic model selection. In addition, adding many extra free parameters to the classic FA model and thus becoming even worse in identifiability, the model of a general linear dynamical system is even inferior to the classic FA model.

Key words： radar automatic target recognition (RATR); high-resolution range profile (HRRP); temporal factor analysis (TFA); Bayesian Ying-Yang (BYY) harmony learning; automatic model selection

References

1 Kosir P, DeWal R. Feature alignment techniques for pattern recognition. In: Proceedings of IEEE National Conference on Aerospace and Electronics. 1994, 1: 128-132

2 Webb A R. Gamma mixture models for target recognition. Pattern Recognition, 2000, 33(12): 2045-2054

3 Copsey K, Webb A R. Bayesian Gamma mixture model approach to radar target recognition. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1201-1217

4 Seibert M, Waxman A M. Adaptive 3-D object recognition from multiple views. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14(2): 107-124

5 Jacobs S P. Automatic target recognition using highresolution radar range profiles. Dissertation for the Doctoral Degree. St. Louis: Washington University, 1999

6 Du L, Liu H W, Bao Z, Zhang J Y. A two-distribution compounded statistical model for radar HRRP target recognition. IEEE Transactions on Signal Processing, 2006, 54(6): 2226-2238

7 Du L, Liu H W, Bao Z. Radar HRRP statistical recognition based on hypersphere model. Signal Processing, 2008, 88(5): 1176-1190

8 Du L, Liu H W, Bao Z. Radar HRRP statistical recognition: parametric model and model selection. IEEE Transactions on Signal Processing, 2008, 56(5): 1931-1944

9 Zhu F, Zhang X D, Hu Y F. Gabor filter approach to joint feature extraction and target recognition. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(1): 17-30

10 Wong S K. High range resolution profiles as motion-invariant features for moving ground targets identification in SAR based automatic target recognition. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(3): 1017-1039

11 Xu L. Bayesian Ying-Yang system and theory as a unified statistical learning approach: (v) temporal modeling for temporal perception and control. In: Proceedings of the International Conference on Neural Information Processing. 1998, 2: 877-884

12 Xu L. Temporal Bayesian Ying-Yang dependence reduction, blind source separation and principal independent components. In: Proceedings of International Joint Conference on Neural Networks. 1999, 2: 1071-1076

13 Xu L. Temporal BYY learning for state space approach, hidden Markov model, and blind source separation. IEEE Transactions on Signal Processing, 2000, 48(7): 2132-2144

14 Xu L. BYY harmony learning, independent state space, and generalized APT financial analyses. IEEE Transactions on Neural Networks, 2001, 12(4): 822-849

15 Xu L. Temporal factor analysis: stable-identifiable family, orthogonal flow learning, and automated model selection. In: Proceedings of International Joint Conference on Neural Networks. 2002, 472-476

16 Xu L. Independent component analysis and extensions with noise and time: a Bayesian Ying-Yang learning perspective. Neural Information Processing—Letters and Reviews, 2003, 1(1): 1-52

17 Xu L. Temporal BYY encoding, Markovian state spaces, and space dimension determination. IEEE Transactions on Neural Networks, 2004, 15(5): 1276-1295

18 Xu L. Learning algorithms for RBF functions and subspace based functions. Handbook of Research on Machine Learning, Applications and Trends: Algorithms, Methods and Techniques. Hershey: IGI Global, 2009, 60-94

19 Xu L. Bayesian Ying-Yang system, best harmony learning and five action circling. Frontiers of Electrical and Electronic Engineering in China, 2010, 5(3): 281-328

20 Chiu K C, Xu L. Arbitrage pricing theory based Gaussian temporal factor analysis for adaptive portfolio management. Decision Support Systems, 2004, 37(4): 485-500

21 Chiu K C, Xu L. Optimizing financial portfolios from the perspective of mining temporal structures of stock returns. In: Proceedings of the 3rd International Conference on Machine Learning. 2003, 266-275

22 Burnham K P, Anderson D. Model Selection and Multi-Model Inference. New York: Springer, 2002

23 Akaike H. Factor analysis and AIC. Psychometrika, 1987, 52(3): 317-332

24 Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1974, 19(6): 714-723

25 Bozdogan H. Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extension. Psychometrika, 1987, 52(3): 345-370

26 Anderson T W, Rubin H. Statistical inference in factor analysis. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. 1956, 5: 111-150

27 Ghahramani Z, Hinton G. Parameter estimation for linear dynamical systems. Technical Report CRG-TR-96-2, 1996

28 Roweis S, Ghahramani Z. A unifying review of linear Gaussian models. Neural Computation, 1999, 11(2): 305-345

29 Ghahramani Z, Hinton G E. Variational learning for switching state-space models. Neural Computation, 2000, 12(4): 831-864

30 Carrara W G, Goodman R S, Majewski R M. Spotlight Synthetic Aperture Radar — Signal Processing Algorithms. Boston: Arthech House, 1995

31 Parzen E. On the estimation of a probability density function and mode. Annals of Mathematical Statistics, 1962, 33(3): 1065-1076

32 Rubin D B, Thayer D T. EM algorithms for ML factor analysis. Psychometrika, 1982, 47(1): 69-76

33 Schwarz G. Estimating the dimension of a model. Annals of Statistics, 1978, 6(2): 461-464

34 Shi L, Wang P, Liu H, Xu L, Bao Z. Radar HRRP statistical recognition with local factor analysis by automatic Bayesian Ying-Yang harmony learning. IEEE Transactions on Signal Processing, 2011, 59(2): 610-617

35 Salah A A, Alpaydin E. Incremental mixtures of factor analyzers. In: Proceedings of the 17th International Conference on Pattern Recognition. 2004, 1: 276-279

36 Tipping M E, Bishop C M. Mixtures of probabilistic principal component analyzers. Neural Computation, 1999, 11(2): 443-482

37 Shumway R H, Stoffer D S. An approach to time series smoothing and forecasting using the EM algorithm. Journal of Time Series Analysis, 1982, 3(4): 253-264

38 Xu L. YING-YANG machine for temporal signals. In: Proceedings of 1995 IEEE International Conference on Neural Networks and Signal Processing. 1995, I: 644-651

39 Xu L. Bayesian Ying Yang system and theory as a unified statistical learning approach: (ii) from unsupervised learning to supervised learning and temporal modeling. In: Wong K M, King I, Yeung D Y, eds. Proceedings of Theoretical Aspects of Neural Computation: A Multidisciplinary Perspective. 1997, 25-42

40 Xu L. Temporal BYY learning and its applications to extended Kalman filtering, hidden Markov model, and sensormotor integration. In: Proceedings of International Joint Conference on Neural Networks. 1999, 2: 949-954

41 Shumway R H, Stoffer D S. Dynamic linear models with switching. Journal of the American Statistical Association, 1991, 86(415): 763-769

42 Elliott R J, Aggoun L, Moore J B. Hidden Markov Models: Estimation and Control. New York: Springer-Verlag, 1995

43 Digalakis V, Rohlicek J R, Ostendorf M. ML estimation of a stochastic linear system with the EM algorithm and its application to speech recognition. IEEE Transactions on Speech and Audio Processing, 1993, 1(4): 431-442

44 Xu L. Bayesian-Kullback coupled YING-YANG machines: unified learning and new results on vector quantization. In: Proceedings of the International Conference on Neural Information Processing. 1995, 977-988 (A further version in NIPS8. In: Touretzky D S, . eds. Cambridge: MIT Press, 444-450)

45 Xu L. Another perspective of BYY harmony learning: representation in multiple layers, co-decomposition of data covariance matrices, and applications to network biology. Frontiers of Electrical and Electronic Engineering in China, 2011, 6(1): 86-119

46 Xu L. Bayesian Ying Yang system and theory as a unified statistical learning approach: (i) unsupervised and semiunsupervised learning. In: Amari S, Kassabov N, eds. Brain-Like Computing and Intelligent Information Systems. New Zealand: Springer-Verlag, 1997, 241-274

47 Tu S, Xu L. Parameterizations make different model selections: empirical findings from factor analysis. Frontiers of Electrical and Electronic Engineering in China, 2011 (in Press)

48 Xu L. Data smoothing regularization, multi-sets-learning, and problem solving strategies. Neural Networks, 2003, 16(5-6): 817-825

49 Egan J P. Signal Detection Theory and ROC Analysis. San Diego: Academic Press, 1975