Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Sliding Window Generalized Kernel Affine Projection Algorithm Using Projection Mappings | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2008 Article ID 735351 16 pages doi 2008 735351 Research Article Sliding Window Generalized Kernel Affine Projection Algorithm Using Projection Mappings Konstantinos Slavakis1 and Sergios Theodoridis2 1 Department of Telecommunications Science and Technology University of Peloponnese Karaiskaki St. Tripoli 22100 Greece 2 Department of Informatics and Telecommunications University of Athens Ilissia Athens 15784 Greece Correspondence should be addressed to Konstantinos Slavakis slavakis@ Received 8 October 2007 Revised 25 January 2008 Accepted 17 March 2008 Recommended by Theodoros Evgeniou Very recently a solution to the kernel-based online classification problem has been given by the adaptive projected subgradient method APSM . The developed algorithm can be considered as a generalization of a kernel affine projection algorithm APA and the kernel normalized least mean squares NLMS . Furthermore sparsification of the resulting kernel series expansion was achieved by imposing a closed ball convex set constraint on the norm of the classifiers. This paper presents another sparsification method for the APSM approach to the online classification task by generating a sequence of linear subspaces in a reproducing kernel Hilbert space RKHS . To cope with the inherent memory limitations of online systems and to embed tracking capabilities to the design an upper bound on the dimension of the linear subspaces is imposed. The underlying principle of the design is the notion of projection mappings. Classification is performed by metric projection mappings sparsification is achieved by orthogonal projections while the online system s memory requirements and tracking are attained by oblique projections. The resulting sparsification scheme shows strong similarities with the classical sliding window adaptive schemes. The proposed design is validated by the adaptive equalization .
