Abstract：Kernel principal component analysis(KPCA) can extract nonlinear features of datasets. However,its efficiency is inversely proportional to the size of the training sample set. In this paper,an adaptive kernel feature subspace method is proposed to extract features efficiently. This method is methodologically consistent with KPCA,and it improves the efficiency by adaptively selecting the spanning vectors of the KPCA without losing accuracy. Experimental results on two-dimensional data and MNIST datasets show that the proposed method is better than the one associated with KPCA and reference methods.
[1] Scholkopf B,Smola A,Muller K R. Kernel Principal Component Analysis // Proc of the International Conference on Artificial Neural Networks. Lausanne,Switzerland,1997: 583-588 [2] Pokharel P P,Liu W F,Principe J C. Kernel Least Mean Square Algorithm with Constrained Growth. Signal Processing,2009,89(3): 257-265 [3] Bian Zhaoqi. Pattern Recognition. 2nd Edition. Beijing,China: Tsinghua University Press,2000(in Chinese) (边肇祺.模式识别.第2版.北京:清华大学出版社,2000) [4] Yang Jian,Jin Zhong,Yang Jingyu. Essence of Kernel Fisher Discriminant: KPCA Plus LDA. Pattern Recognition,2004,37(10):2097-2100 [5] Rosipal R,Girolami M,Trejo L J,et al. Kernel PCA for Feature Extraction and De-Noising in Nonlinear Regression. Neural Computing and Application,2001,10(3): 231-243 [6] Kim K L,Franz M O,Scholkopf B. Iterative Kernel Principal Component Analysis for Image Modeling. IEEE Trans on Pattern Analysis and Machine Intelligence,2005,27(9): 1351-1366 [7] Günter S,Schraudolph N N,Vishwanathan S V N. Fast Iterative Kernel Principal Component Analysis. Journal of Machine Learning Research,2007,8: 1893-1918 [8] Chin T J,Schindler K,Suter D. Incremental Kernel SVD for Face Recognition with Image Sets // Proc of the 7th International Conference on Automatic Face and Gesture Recognition. Southampton,UK,2006: 461-466 [9] Chin T J,Suter D. Incremental Kernel PCA for Efficient Non-Linear Feature Extraction // Proc of the 17th British Machine Vision Conference. Edinburgh,UK,2006,III: 939-948 [10] Chin T J,Suter D. Incremental Kernel Principal Component Analysis. IEEE Trans on Image Processing,2007,16(6): 1662-1674 [11] Fan V,Hlavac V. Greedy Algorithm for a Training Set Reduction in the Kernel Method // Proc of the 10th International Conference on Computer Analysis of Images and Patterns. Groningen,Netherlands,2003: 426-433 [12] Fan V. Optimization Algorithm for Kernel Methods. Ph.D Dissertation. Prague,Czech: Czech Technical University,2005 [13] Xu Yong,Zhang D,Song Fengxi,et al. A Method for Speeding up Feature Extraction Based on KPCA. Neural Computing,2007,70(4/5/6): 1056-1061 [14] Ding Mingtao. Tian Zheng,Xu Haixia. Adaptive Kernel Principal Component Analysis. Signal Processing,2010,90(5): 1542-1553 [15] Chen Chunyuan,Hsu C C,Chen Muchen. Adaptive Kernel Principal Component Analysis for Monitoring Small Disturbances of Nonlinear Process. Industrial and Engineering Chemistry Research,2010,49(5): 2254-2262 [16] Pang Yanwei,Wang Lei,Yuan Yuan. Generalized KPCA by Adaptive Rules in Feature Space. International Journal of Computer Mathematics,2010,87(5): 956-968 [17] Engel Y. Algorithms and Representations for Reinforcement Learning. Ph.D Dissertation. Doktorarbeit,Israel: Hebrew University,2005 [18] Scholkopf B,Mika S,Burges C J C,et al. Input Space versus Feature Space in Kernel-Based Methods. IEEE Trans on Neural Networks,1999,10(5): 1000-1017 [19] Scholkopf B,Smola A,Muller K R. Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation,1998,10(5): 1299-1319
2013, Vol. 26 
