scholarly journals Quasi-invariance of fermion processes with J-Hermitian kernel

2014 ◽  
Vol 8 (2) ◽  
Author(s):  
Giovanni Luca Torrisi
Keyword(s):  
Hermitian Kernel

scholarly journals An Extreme Learning Machine Based on the Mixed Kernel Function of Triangular Kernel and Generalized Hermite Dirichlet Kernel

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Senyue Zhang ◽  
Wenan Tan
Keyword(s):  
Extreme Learning Machine ◽  
Kernel Function ◽  
Binary Classification ◽  
Dirichlet Kernel ◽  
Computational Time ◽  
Support Vector ◽  
Structure Information ◽  
Kernel Parameter ◽  
Hermitian Kernel ◽  
Learning Machine

According to the characteristics that the kernel function of extreme learning machine (ELM) and its performance have a strong correlation, a novel extreme learning machine based on a generalized triangle Hermitian kernel function was proposed in this paper. First, the generalized triangle Hermitian kernel function was constructed by using the product of triangular kernel and generalized Hermite Dirichlet kernel, and the proposed kernel function was proved as a valid kernel function of extreme learning machine. Then, the learning methodology of the extreme learning machine based on the proposed kernel function was presented. The biggest advantage of the proposed kernel is its kernel parameter values only chosen in the natural numbers, which thus can greatly shorten the computational time of parameter optimization and retain more of its sample data structure information. Experiments were performed on a number of binary classification, multiclassification, and regression datasets from the UCI benchmark repository. The experiment results demonstrated that the robustness and generalization performance of the proposed method are outperformed compared to other extreme learning machines with different kernels. Furthermore, the learning speed of proposed method is faster than support vector machine (SVM) methods.

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