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

Senyue Zhang,Wenan Tan

doi:10.1155/2016/7293278

Abstract

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.

Highlights

The kernel extreme learning machine (KELM) is proposed by Huang et al in 2010 by applying the kernel functions to ELM algorithm [1, 2] and where the random hidden layer feature mapping in ELM is substituted by the kernel mapping [3]
References [12,13,14,15,16] constructed the weighting function as KGau(x, z) = exp (−‖x − z‖2/d), where d denotes the dimension of vector x, z, in which since the parameter σ of Gaussian kernel KRBF is directly set with √d/2, the data structure information is lost the parameter optimization is simplified
In order to test the performance of Generalized Triangular Hermite kernel extreme learning machine (Tri-H KELM) algorithms, this section compares it concerning testing accuracy, training time, and regression determination coefficient

Summary

Introduction

The kernel extreme learning machine (KELM) is proposed by Huang et al in 2010 by applying the kernel functions to ELM algorithm [1, 2] and where the random hidden layer feature mapping in ELM is substituted by the kernel mapping [3]. According to above analysis, based on Hermite orthogonal polynomials, a mixed kernel function called Generalized Triangular Hermite kernel function is constructed by using the product of triangular kernel and generalized Hermite Dirichlet kernel This kernel function has only one parameter chosen from a small range of integer numbers, the parameter optimization is facilitated greatly, and more structure information of sample data is retained. The effectiveness of the proposed method for regression and binary, multiclass classification problems is demonstrated by performing numerical experiments on a number of real-world datasets from the UCI benchmark repository and comparing their results with SVM and other extreme learning machines with different kernels

Kernel Extreme Learning Machine

Triangular Hermite Kernel Extreme Learning Machine

Experiments and Analysis

Conclusion