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Juyang Weng, Yilu Zhang, WeyShiuan Hwang, "Candid CovarianceFree Incremental Principal Component Analysis," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 8, pp. 10341040, August, 2003.  
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@article{ 10.1109/TPAMI.2003.1217609, author = {Juyang Weng and Yilu Zhang and WeyShiuan Hwang}, title = {Candid CovarianceFree Incremental Principal Component Analysis}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {25}, number = {8}, issn = {01628828}, year = {2003}, pages = {10341040}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2003.1217609}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Candid CovarianceFree Incremental Principal Component Analysis IS  8 SN  01628828 SP1034 EP1040 EPD  10341040 A1  Juyang Weng, A1  Yilu Zhang, A1  WeyShiuan Hwang, PY  2003 KW  Principal component analysis KW  incremental principal component analysis KW  stochastic gradient ascent (SGA) KW  generalized hebbian algorithm (GHA) KW  orthogonal complement. VL  25 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—Appearancebased image analysis techniques require fast computation of principal components of highdimensional image vectors. We introduce a fast incremental principal component analysis (IPCA) algorithm, called candid covariancefree IPCA (CCIPCA), used to compute the principal components of a sequence of samples incrementally without estimating the covariance matrix (so covariancefree). The new method is motivated by the concept of statistical efficiency (the estimate has the smallest variance given the observed data). To do this, it keeps the scale of observations and computes the mean of observations incrementally, which is an efficient estimate for some wellknown distributions (e.g., Gaussian), although the highest possible efficiency is not guaranteed in our case because of unknown sample distribution. The method is for realtime applications and, thus, it does not allow iterations. It converges very fast for highdimensional image vectors. Some links between IPCA and the development of the cerebral cortex are also discussed.
[1] I. Sirovich and M. Kirby, LowDimensional Procedure for the Characterization of Human Faces J. Optical Soc. Am. A, vol. 4, no. 3, pp. 519524, Mar. 1987.
[2] M. Turk and A. Pentland, Eigenfaces for Recognition J. Cognitive Neuroscience, vol. 3, no. 1, pp. 7186, 1991.
[3] H. Murase and S.K. Nayar, “Visual Learning and Recognition of 3D Objects from Appearance,” Int'l J. Computer Vision, vol. 14, pp. 524, 1995.
[4] Y. Cui and J. Weng, AppearanceBase Hand Sign Recognition from Intensity Image Sequences Computer Vision and Image Understanding, vol. 78, pp. 157176, 2000.
[5] S. Chen and J. Weng, StateBased SHOSLIF for Indoor Visual Navigation IEEE Trans. Neural Networks, vol. 11, no. 6, pp. 13001314, 2000.
[6] G.H. Golub and C.F. vanLoan, Matrix Computations. Baltimore, Md.: The Johns Hopkins Univ. Press, 1989.
[7] Proc. NSF/DARPA Workshop Development and Learning, J. Weng and I. Stockman, eds., Apr. 2000.
[8] J. Hertz, A. Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation. AddisonWesley, 1991.
[9] E. Oja, Subspace Methods of Pattern Recognition. Letchworth, U.K.: Research Studies Press, 1983.
[10] E. Oja and J. Karhunen, On Stochastic Approximation of the Eigenvectors and Eigenvalues of the Expectation of a Random Matrix J. Math. Analysis and Application, vol. 106, pp. 6984, 1985.
[11] T.D. Sanger, Optimal Unsupervised Learning in a SingleLayer Linear Feedforward Neural Network IEEE Trans. Neural Networks, vol. 2, pp. 459473, 1989.
[12] Y. Zhang and J. Weng, Convergence Analysis of Complementary Candid Incremental Principal Component Analysis Technical Report MSUCSE0123, Dept. of Computer Science and Eng., Michigan State Univ., East Lansing, Aug. 2001.
[13] M. Fisz, Probability Theory and Mathematical Statistics, third ed. John Wiley&Sons, 1963.
[14] J. Weng,T. S. Huang,, and N. Ahuja,Motion and Structure from Image Sequences, Springer Series on Information Sciences. Berlin: SpringerVerlag, 1993.
[15] N.L. Owsley, Adaptive Data Orthogonalization Proc. IEEE Int'l Conf. Acoustics, Speech, and Signal Processing, pp. 109112, Apr. 1978.
[16] P.A. Thompson, An Adaptive Spectral Analysis Technique for Unbiased Frequency Estimation in the Presence of White Noise Proc. 13th Asilomar Conf. Circuits, Systems, and Computers, pp. 529533, 1979.
[17] E. Kreyszig, Advanced Engineering Mathematics, John Wiley&Sons, New York, 1983.
[18] P.J. Phillips, H. Moon, P. Rauss, and S.A. Rizvi, "The FERET Evaluation Methodology for FaceRecognition Algorithms," Computer Vision and Pattern Recognition, pp. 137143, 1997.
[19] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in C, second ed. Cambridge Univ. Press, 1986.
[20] J. Weng, W.S. Hwang, Y. Zhang, C. Yang, and R. Smith, Developmental Humanoids: Humanoids that Develop Skills Automatically Proc. First IEEERAS Int'l Conf. Humanoid Robots, Sept. 2000.
[21] J. Rubner and K. Schulten, Development of Feature Detectors by SelfOrganization Biological Cybernetics, vol. 62, pp. 193199, 1990.
[22] Principles of Neural Science, third ed. E.R. Kandel, J.H. Schwartz, and T.M. Jessell, eds., Norwalk, Conn.: Appleton and Lange, 1991.