Model-Based Online Learning With Kernels

• Published in: IEEE transaction on neural networks and learning systems Vol. 24; no. 3; pp. 356 - 369
• Main Authors: Li, Guoqi, Wen, Changyun, Li, Zheng Guo, Zhang, Aimin, Yang, Feng, Mao, Kezhi
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2013; Institute of Electrical and Electronics Engineers
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Artificial intelligence; Artificial Intelligence - trends; Classification; Computer science; control theory; systems; Computer Simulation - trends; Data processing. List processing. Character string processing; Exact sciences and technology; Humans; Kernel; Kernels; Learning and adaptive systems; Memory organisation. Data processing; Models, Theoretical; Neural Networks (Computer); novelty detection; online learning; Optimization; regression; reproducing Kernel Hilbert space; Signal processing algorithms; Software; Stochastic processes; Support vector machines; Theoretical computing; Vectors; On line; Event detection; Modeling; Gradient descent; Efficiency; Least squares method; Classification; Vector support machine; Anomaly; Hilbert space; Learning algorithm; Novelty; Mathematical programming; reproducing Kernel Hilbert Space; Non stationary condition; Minimization; Regression analysis; Real time; Depth of field; Kernel method; Constrained optimization; Kernels; Image segmentation; Experimental result; novelty detection; regression; Recursive method; Artificial intelligence; online learning
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2012.2229293

New optimization models and algorithms for online learning with Kernels (OLK) in classification, regression, and novelty detection are proposed in a reproducing Kernel Hilbert space. Unlike the stochastic gradient descent algorithm, called the naive online Reg minimization algorithm (NORMA), OLK algorithms are obtained by solving a constrained optimization problem based on the proposed models. By exploiting the techniques of the Lagrange dual problem like Vapnik's support vector machine (SVM), the solution of the optimization problem can be obtained iteratively and the iteration process is similar to that of the NORMA. This further strengthens the foundation of OLK and enriches the research area of SVM. We also apply the obtained OLK algorithms to problems in classification, regression, and novelty detection, including real time background substraction, to show their effectiveness. It is illustrated that, based on the experimental results of both classification and regression, the accuracy of OLK algorithms is comparable with traditional SVM-based algorithms, such as SVM and least square SVM (LS-SVM), and with the state-ofthe-art algorithms, such as Kernel recursive least square (KRLS) method and projectron method, while it is slightly higher than that of NORMA. On the other hand, the computational cost of the OLK algorithm is comparable with or slightly lower than existing online methods, such as above mentioned NORMA, KRLS, and projectron methods, but much lower than that of SVM-based algorithms. In addition, different from SVM and LS-SVM, it is possible for OLK algorithms to be applied to non-stationary problems. Also, the applicability of OLK in novelty detection is illustrated by simulation results.