This paper proposes a new reduced kernel method for monitoring nonlinear dynamic systems on reproducing kernel Hilbert space (RKHS). Here, the proposed method is a concatenation of two techniques proposed in our previous studies, the reduced kernel principal component (RKPCA) Taouali et al. (Int J Adv Manuf Technol, 2015) and the singular value decomposition-kernel principal component (SVD-KPCA) (Elaissi et al. (ISA Trans, 52 (1), 96-104, 2013)) The proposed method is entitled SVD-RKPCA. It consists at first to identify an implicit RKPCA model, that approaches "properly" the system behavior, and after that to update this RKPCA model by SVD of an incremented and decremented kernel matrix using a moving data window. The proposed SVD-RKPCA has been applied successfully for monitoring of a continuous stirred tank reactor (CSTR) as well as a Tennessee Eastman process (TEP).
Alzheimer's disease (AD), a neurodegenerative disorder, is a very serious illness that cannot be cured, but the early diagnosis allows precautionary measures to be taken. The current used methods to detect Alzheimer's disease are based on tests of cognitive impairment, which does not provide an exact diagnosis before the patient passes a moderate stage of AD. In this article, a novel classifier of brain magnetic resonance images (MRI) based on the new downsized kernel principal component analysis (DKPCA) and multiclass support vector machine (SVM) is proposed. The suggested scheme classifies AD MRIs. First, a multiobjective optimization technique is used to determine the optimal parameter of the kernel function in order to ensure good classification results and to minimize the number of retained principle components simultaneously. The optimal parameter is used to build the optimized DKPCA model. Second, DKPCA is applied to normalized features. Downsized features are then fed to the classifier to output the prediction. To validate the effectiveness of the proposed method, DKPCA was tested using synthetic data to demonstrate its efficiency on dimensionality reduction, then the DKPCA based technique was tested on the OASIS MRI database and the results were satisfactory compared to conventional approaches.
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