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Approximation of large-scale dynamical systems: an overview

100%
Antoulas A. C., Sorensen D. C.
International Journal of Applied Mathematics and Computer Science
|
2001
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tom 11
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nr 5
1093-1121
EN
In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two.
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A practical application of kernel-based fuzzy discriminant analysis

86%
Gao J.-Q., Fan L.-Y., Li L., Xu L.-Z.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 4
887-903
EN
A novel method for feature extraction and recognition called Kernel Fuzzy Discriminant Analysis (KFDA) is proposed in this paper to deal with recognition problems, e.g., for images. The KFDA method is obtained by combining the advantages of fuzzy methods and a kernel trick. Based on the orthogonal-triangular decomposition of a matrix and Singular Value Decomposition (SVD), two different variants, KFDA/QR and KFDA/SVD, of KFDA are obtained. In the proposed method, the membership degree is incorporated into the definition of between-class and within-class scatter matrices to get fuzzy between-class and within-class scatter matrices. The membership degree is obtained by combining the measures of features of samples data. In addition, the effects of employing different measures is investigated from a pure mathematical point of view, and the t-test statistical method is used for comparing the robustness of the learning algorithm. Experimental results on ORL and FERET face databases show that KFDA/QR and KFDA/SVD are more effective and feasible than Fuzzy Discriminant Analysis (FDA) and Kernel Discriminant Analysis (KDA) in terms of the mean correct recognition rate.
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