Optimizing the Gaussian kernel function with the formulated kernel target alignment criterion for two-class pattern classification

Zhong, Shangping; Da-ya, Chen; Xu, Qiaofen; Chen, Tianshun

doi:10.1016/j.patcog.2012.12.012

Cited by 34 publications

(16 citation statements)

References 18 publications

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“…The difference between the centered alignment of two kernel matrices and the alignment of the corresponding kernel functions can be bounded by a term in Oð1= ffiffiffi n p Þ [8]. Generally speaking, centered kernel polarization, kernel target alignment and kernel polarization have the same property that: the alignment value will increase when we keep within-class data pairs close and between-class data pairs apart in the feature space [8,20,29,34]. The only difference between kernel target alignment and centered kernel alignment, by comparing Eq.…”

Section: Review Of Three Kinds Of Alignment Criteriamentioning

confidence: 99%

“…Observe that when the number of positive samples equals to the one of negative samples, i.e. n þ ¼ n À , the optimization problem here is identical to that in [34]. Thus, centered kernel polarization is a general extension of kernel polarization.…”

Section: The ''Centered Kernel Polarization'' Criterionmentioning

confidence: 99%

“…Ref. [34] examined the local and global extremal properties of the approximate formulate kernel polarization. However, on four out of thirteen data sets in [34], the objective function curves depending on the kernel parameter were found to monotonically increase very slowly when r is greater than r opt .…”

Section: Sðrþmentioning

confidence: 99%

“…The approximate criterion function can be proved to have a determined global minimum point for two-class pattern classification tasks under weaker constraint conditions than those in [34]. We note that the proposed criterion is similar to the Hilbert-Schmidt Independence Criterion (HSIC) [13], which is a practical criterion for independence test in the context of independent component analysis (ICA).…”

Section: Introductionmentioning

confidence: 97%

“…[34] proposed an efficient Gaussian kernel optimization method, which works by maximizing the formulated kernel target alignment (in fact, it is the formulated kernel polarization). The contribution of this work lies in obtaining a differentiable objective function having a determined minimum point.…”

Section: Introductionmentioning

confidence: 99%

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An efficient Gaussian kernel optimization based on centered kernel polarization criterion

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Section: Review Of Three Kinds Of Alignment Criteriamentioning

confidence: 99%

Section: The ''Centered Kernel Polarization'' Criterionmentioning

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Section: Sðrþmentioning

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Section: Introductionmentioning

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An efficient Gaussian kernel optimization based on centered kernel polarization criterion

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An interval support vector domain description based on the dynamic decreasing inertia weight particle swarm optimization

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Chen

2019

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For the fault diagnosis of the interval rotor crack fault samples, this paper proposes an interval support vector domain description method through using the dynamic decreasing inertia weight particle swarm optimization (DDIWPSO). Firstly, the interval Gauss function is constructed by using the interval midpoint and interval radius. Applying the interval Gauss kernel function as the kernel, the interval support vector domain description is proposed and can realize the classification of interval samples. Secondly, the DDIWPSO is applied to select the optimal penalty parameter C, the Gauss interval kernel width parameter , and the factor of the proposed method. Finally, interval University of California Irvine (UCI) samples and the interval rotor crack data are used to verify the advantages of this method. The experimental verification shows that the interval support vector domain description method has the higher accuracy compared with the traditional interval fault classification methods because this method owns the empirical risk minimization of SVM and the optimal parameters selection based on the DDIWPSO.

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A Semi-supervised Low Rank Kernel Learning Algorithm via Extreme Learning Machine

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et al. 2016

Proceedings of ELM-2015 Volume 1

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Optimizing the Gaussian kernel function with the formulated kernel target alignment criterion for two-class pattern classification

Cited by 34 publications

References 18 publications

An efficient Gaussian kernel optimization based on centered kernel polarization criterion

An efficient Gaussian kernel optimization based on centered kernel polarization criterion

An interval support vector domain description based on the dynamic decreasing inertia weight particle swarm optimization

A Semi-supervised Low Rank Kernel Learning Algorithm via Extreme Learning Machine

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