简介: |
摘要：
Subspace projection methods have played a central role in feature dimension-reduction in machine learning. Two such methods, PCA and DCA, share the same type of trace-norm optimization formulation; consequently their optimal solutions can be derived from the (principal or mixed) eigenvectors of their respective discriminant matrices.
The discriminant matrix of PCA is its (center-adjusted) scatter matrix, whose m principal eigenvectors are known to lead to the optimal reconstruction error among all m-dimensional subspaces. Unfortunately, PCA fails to make use of the teacher's information made available in supervised applications aiming at discriminating distinctive classes.
To rectify this problem, DCA incorporates the teacher's information into the trace-norm optimizer. More exactly, incorporated ito DCA's discriminant matrix is a "pre-whitening" operation based on a regularized ``within-class" scatter matrix. The optimal DCA solution in the original (resp. kernel) space is then formed from the (L-1) principal eigenvectors, here L denotes the number of classes, and (m-L+1) minor eigenvectors of the original (resp. kernel-domain ) discriminating matrix.
DCA can be viewed as a hybrid of PCA and Fisher's FDA. Another hybrid is SODA (Successively Orthogonal Discriminant Analysis) which is computationally efficient for deriving an SoSNR-optimal solution. Via numerical examples, DCA can be shown to be superior to SODA, with PCA falling way behind, in terms of a classifier-independent performance metric: OSNR (omnidirectional SNR). Furthermore, the subspace methods have been successfully applied to high dimensional medical data for brain stroke detection. Finally, DCA's mixed minimizer/maximizer formulation is potentially appealing to extracting components which accentuate the signal subspace while suppressing the interference subspace.
简历：
S.Y. Kung is a Professor at Department of Electrical Engineering in Princeton University. His research areas include VLSI array processors, system modeling and identification, machine learning, wireless communication, sensor array processing, multimedia signal processing, and genomic signal processing and data mining. He was a founding member of several Technical Committees (TC) of the IEEE Signal Processing Society, and was appointed as the first Associate Editor in VLSI Area (1984) and later the first Associate Editor in Neural Network (1991) for the IEEE Transactions on Signal Processing. He has been a Fellow of IEEE since 1988. He served as a Member of the Board of Governors of the IEEE Signal Processing Society (1989-1991). Since 1990, he has been the Editor-In-Chief of the Journal of VLSI Signal Processing Systems. He was a recipient of IEEE Signal Processing Society's Technical Achievement Award for the contributions on "parallel processing and neural network algorithms for signal processing" (1992); a Distinguished Lecturer of IEEE Signal Processing Society (1994); a recipient of IEEE Signal Processing Society's Best Paper Award for his publication on principal component neural networks (1996); and a recipient of the IEEE Third Millennium Medal (2000). He has authored and co-authored more than 500 technical publications and numerous textbooks including ``VLSI Array Processors'', Prentice-Hall (1988); ``Digital Neural Networks'', Prentice-Hall (1993) ; ``Principal Component Neural Networks'', John-Wiley (1996); ``Biometric Authentication: A Machine Learning Approach'', Prentice-Hall (2004); and ``Kernel Methods and Machine Learning”. Cambridge University Press (2014). |
