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A Sparse Fixed-Point online KPCA Extraction Algorithm

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2024年 72卷 4604-4617页

作者： Souza Filho, Joao B. O. Diniz, Paulo S. R. Univ Fed Rio de Janeiro Dept Elect & Comp Engn DEL POLI BR-21941972 Rio De Janeiro Brazil Univ Fed Rio de Janeiro Elect Engn Program PEE COPPE BR-21941972 Rio De Janeiro Brazil

kernel principal component analysis (KPCA) is a powerful tool for nonlinear feature extraction, but its standard formulation is not well-suited for streaming data. Although there are efficient online KPCA solutions, there is a gap in the literature regarding genuinely sparse online KPCA algorithms. This paper introduces a novel, fast, and accurate online fixedpoint algorithm designed for sparse kernel principal component extraction. Utilizing a two-level sparsifying strategy, the proposed algorithm efficiently handles streaming data and large datasets within minimal computing and memory requirements, achieving both higher accuracy and sparser components compared to existing online KPCA methods.

关键词： kernel principal component analysis kernel methods online kernel algorithms sparse kernel techniques.

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Improving KPCA online Extraction by Orthonormalization in the Feature Space

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018年第4期29卷 1382-1387页

作者： Souza Filho, Joao B. O. Diniz, Paulo S. R. Univ Fed Rio de Janeiro Elect Engn Program COPPE POLI BR-21941972 Rio De Janeiro Brazil

Recently, some online kernel principal component analysis (KPCA) techniques based on the generalized Hebbian algorithm (GHA) were proposed for use in large data sets, defining kernel components using concise dictionaries automatically extracted from data. This brief proposes two new online KPCA extraction algorithms, exploiting orthogonalized versions of the GHA rule. In both the cases, the orthogonalization of kernel components is achieved by the inclusion of some low complexity additional steps to the kernel Hebbian algorithm, thus not substantially affecting the computational cost of the algorithm. Results show improved convergence speed and accuracy of components extracted by the proposed methods, as compared with the state-of-the-art online KPCA extraction algorithms.

关键词： kernel methods machine learning and generalized Hebbian algorithm (GHA) online kernel algorithms principal component analysis (PCA)

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A recursive least square algorithm for online kernel principal component extraction

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NEUROCOMPUTING 2017年 237卷 255-264页

作者： Souza Filho, Joao B. O. Diniz, Paulo S. R. Univ Fed Rio de Janeiro Polytech Sch Dept Elect & Comp Engn Technol Ctr Ave Athos Silveira Ramos 149Bldg H2nd Floor Rio De Janeiro Brazil Fed Ctr Technol Educ Celso Suckow Fonseca Elect Engn Postgrad Program PPEEL Ave Maracana 229Bldg E5th Floor Rio De Janeiro Brazil Univ Fed Rio de Janeiro Alberto Luiz Coimbra Inst COPPE Elect Engn Program PEE Rio De Janeiro Brazil

The online extraction of kernel principal components has gained increased attention, and several algorithms proposed recently explore kernelized versions of the generalized Hebbian algorithm (GHA) [1], a well-known principal component analysis (PCA) extraction rule. Corisequently, the convergence speed of such algorithms and the accuracy of the extracted components are highly dependent on a proper choice of the learning rate, a problem dependent factor. This paper proposes a new online fixed-point kerriel principal component extraction algorithm, exploring the minimization of a recursive least-square error function, conjugated with an approximated deflation transform using component estimates obtained by the algorithm, implicitly applied upon data. The proposed technique automatically builds a concise dictionary to expand kernel components, involves simple recursive equations to dynamically define a specific learning rate to each component under extraction, and has a linear computational complexity regarding dictionary size. As compared to state-of-art kernel principal component extraction algorithms, results show improved convergence speed and accuracy of the components produced by the proposed method in five open-access databases.

关键词： kernel principal components analysis kernel methods online kernel algorithms Machine learning Generalized Hebbian algorithm

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A Fixed-Point online kernel Principal Component Extraction Algorithm

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第23期65卷 6244-6259页

作者： Souza Filho, Joao B. O. Diniz, Paulo S. R. Univ Fed Rio de Janeiro Dept Elect & Comp Engn BR-68504 Rio De Janeiro Brazil

kernel principal component analysis (KPCA) is a powerful and widely applied nonlinear feature extraction technique. However, as originally proposed, KPCA may be cumbersome or infeasible in large-scale datasets, which motivated the development of low-complexity iterative extraction algorithms, mainly aiming image processing applications. Recently, some online KPCA extraction algorithms were proposed, but most of them suffer from low-convergence speed. This paper proposes a new algorithm based on fixed-point iterative equations for KPCA extraction, expanding kernel components using a compact dictionary, dynamically built from data, according to a user-defined accuracy parameter. The algorithm relies on simple equations, can track nonstationary environments, and requires reduced storage, enabling its use in real-time applications operating in low-cost embedded hardware. Results involving open-access image datasets show improved accuracy and convergence speed, as well as permitted effective improvements in practical image applications, as compared to state-of-art online KPCA techniques.

关键词： Principal component analysis kernel methods online kernel algorithms machine learning generalized Hebbian algorithm

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