Computer Science ›› 2022, Vol. 49 ›› Issue (8): 267-272.doi: 10.11896/jsjkx.210700175

• Artificial Intelligence • Previous Articles     Next Articles

KPCA Based Novelty Detection Method Using Maximum Correntropy Criterion

LI Qi-ye, XING Hong-jie   

  1. Hebei Key Laboratory of Machine Learning and Computational Intelligence,College of Mathematics and Information Science,Hebei University,Baoding,Hebei 071002,China
  • Received:2021-07-18 Revised:2022-02-28 Published:2022-08-02
  • About author:LI Qi-ye,born in 1995,postgraduate.His main research interests include novelty detection and kernel methods.
    XING Hong-jie,born in 1976,Ph.D,professor,master supervisor.His main research interests include kernel me-thods,neural networks,novelty detection and ensemble learning.
  • Supported by:
    National Natural Science Foundation of China(61672205), Natural Science Foundation of Hebei Province(F2017201020) and High-Level Talents Research Start-Up Project of Hebei University(521100222002).

Abstract: Novelty detection is an important research issue in the field of machine learning.Till now,there exist lots of novelty detection approaches.As a commonly used kernel method,kernel principal component analysis(KPCA)has been successfully applied to deal with the problem of novelty detection.However,the traditional KPCA based novelty detection method is very sensitive to noise.If there exist noise in the given training samples,the detection performance of KPCA based novelty detection method may be decreased.To enhance the anti-noise ability of KPCA based novelty detection method,a maximum correntropy criterion(MCC)based novelty detection method is proposed.Correntropy in information theoretic learning is utilized to substitute the 2-norm based measure in KPCA based novelty detection method.By adjusting the width parameter of the correntropy function,the adverse effect of noise can be alleviated.The half-quadratic optimization technique is used to solve the optimization problem of the proposed method.The local optimal solution can thus be obtained after a few iterations.Moreover,the algorithmic description of the proposed method is provided,and the computational complexity of the corresponding algorithm is analyzed.Experimental results on the 16 UCI benchmark data sets demonstrate that the proposed method obtains better anti-noise and generalization performance in comparison with the other four related approaches.

Key words: Correntropy, Half-quadratic optimization, Information theoretic learning, Kernel principal component analysis, Novelty detection

CLC Number: 

  • TP391.4
[1]TAX D M J.One-class classification:concept learning in the absence of counter examples[D].Delft:Delf University of Technology,2001.
[2]PENNY K I,JOLLIFFE I T.A comparison of multivariate outlier detection methods for clinical laboratory safety data[J].The Statistician,2001,50(3):295-307.
[3]OH C K,SOHN H,BAE I H.Statistical novelty detection within the Yeongjong suspension bridge under environmental and operational variations[J].Smart Materials and Structures,2009,18(12):5022-5029.
[4]SCHÖLKOPF B,WILLIAMSON R C,SMOLA A J.Support vector method for novelty detection[C]//Advances in Neural Information Processing Systems.2000:582-588.
[5]TAX D M J,DUIN R P W.Support vector data description[J].Machine Learning,2004,54(1):45-66.
[6]SCHÖLKOPF B,SMOLA A,MÜLLER K R.Nonlinear component analysis as a kernel eigenvalue problem[J].Neural Computation,1998,10(5):1299-1319.
[7]JOLLIFFE I T.Principal Component Analysis[M].Berlin:Springer-Verlag,2005.
[8]TEIXEIRA A R,TOMÉ A M,STADLTHANNER K,et al.KPCA denosing and the pre-image problem revisited[J].Digital Signal Processing,2008,18(4):568-580.
[9]LIAN H.On feature selection with principal component analysis for one-class SVM[J].Pattern Recognition Letters,2012,33(9):1027-1031.
[10]HILL J,CORONA E,AO J,et al.Information Theoretic Clustering for Medical Image Segmentation[M].Berlin:Springer-Verlag,2014.
[11]DEBRUYNE M,VERDONCK T.Robust kernel principal component and classification[J].Advances in Data Analysis and Classification,2010,4(2):151-167.
[12]KIM C,KLABIAN D.A simple and fast algorithm for L1-norm kernel PCA[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2019,42(8):1842-1855.
[13]DUAN X,QI P,TIAN Z.Registration for variform object of remote-sensing image using improved robust weighted kernel principal component analysis[J].Journal of The Indian Society of Remote Sensing,2016,44(5):675-686.
[14]FAN J,CHOW T W S.Exactly robust kernel principal component analysis[J].IEEE Transactions on Neural Networks and Learning Systems,2020,31(3):749-761.
[15]HOFFMANN H.Kernel PCA for novelty detection[J].Pattern Recognition,2007,40(3):863-874.
[16]DUDA R O,HART P E,STORK D G.Pattern Classification.2nd Ed.[M].New York:Wiley Press,2001.
[17]XIAO Y,WANG H,XU W,et al.L1 norm based KPCA for novelty detection[J].Pattern Recognition,2013,46(1):389-396.
[18]ALZATE C,SUYKES J.Kernel component analysis using anepsilon-insensitive robust loss function[J].IEEE Transactions on Neural Networks,2008,19(9):1583-1598.
[19]WANG D,TANAKA T.Robust kernel principal componentanalysis with l2,1-regularized loss minimization[J].IEEE Access,2020,8(81):864-875.
[20]PRINCIPE J C.Information Theoretic Learning:Renyi’s Entropy and Kernel Perspectives[M].New York:Springer,2010.
[21]LIU W,POKHAREL P P,PRINCIPE J C.Correntropy:properties and applications in non-Gaussian signal processing[J].IEEE Transactions on Signal Processing,2007,55(11):5286-5298.
[22]HE R,HU B,ZHENG W,et al.Robust principal componentanalysis based on maximum correntropy criterion[J].IEEE Transactions on Image Processing,2011,20(6):1485-1494.
[23]YUAN X,HU B.Robust feature extraction via information theoretic learning[C]//International Conference on Machine Learning,Montreal.2009:1193-1200.
[24]KWAK N.Principal component analysis based on L1-norm maxi-mization[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2008,30(9):1672-1680.
[25]VAPNIK V N.The Nature of Statistical Learning Theory[M].New York:Springer,2000.
[26]ZHOU Z.Machine Learning[M].Beijing:Tsinghua University Press,2016.
[27]GÜLER O.Convex Analysis[M].New York:Springer,2010.
[28]SUN Q,ZHANG H,WANG X,et al.Sparsity constrained recursive generalized maximum correntropy criterion with variable center algorithm[J].IEEE Transactions on Circuits and Systems II:Express Briefs,2020,67(12):3517-3521.
[29]GAUTAM C,BALAJI R,SUDHARSAN K,et al.Localizedmultiple kernel learning for anomaly detection:one-class classification[J].Knowledge Based Systems,2019,165:241-252.
[30]LICHMAN M.UCI Machine Learning Repository[EB/OL].University of California,Irvine,School of Information and Computer Sciences,2019.
[31]WU M,YE J.A small sphere and large margin approach for novelty detection using training data with outliers[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(11):2088-2092.
[32]DENG H,XU R.Model selection for anomaly detection in wireless ad hoc networks[C]//2007 IEEE Symposium on Computational Intelligence and Data Mining.2007:540-546.
[33]WANG S,YU J,LAPIRA E,et al.A modified support vector data description based novelty detection approach for machinery components[J].Applied Soft Computing,2013,13(2):1193-1205.
[34]XIAO Y,WANG H,XU W.Parameter selection of Gaussiankernel for one-class SVM[J].IEEE Transactions on Cyberne-tics,2015,45:941-953.
[35]SILVERMAN B W.Density Estimation for Statistics and Data Analysis[M].London:Chapman and Hall,1986.
[36]LI Y,WANG Y,WANG Y,et al.Quantum clustering using kernel entropy component analysis[J].Neurocomputing,2016,202:36-48.
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