A deep residual compensation extreme learning machine and applications

• Author: Xiaoliang Xie,Tianle Zhang,Muzhou Hou,Jiaxian Bai,Yinghao Chen
• Date: 01 September 2020
• Published date: 01 September 2020
• DOI: http://doi.org/10.1002/for.2663

RESEARCH ARTICLE

A deep residual compensation extreme learning machine

and applications

Yinghao Chen

1

| Xiaoliang Xie

2

| Tianle Zhang

1

| Jiaxian Bai

3

|

Muzhou Hou

1

1

College of Mathematics and Statistics,

Central South University, Changsha,

China

2

School of Mathematics and Statistics,

Hunan University of Technology and

Business, Changsha, China

3

College of Finance and Statistics, Hunan

University, Changsha, China

Correspondence

Muzhou Hou, College of Mathematics and

Statistics, Central South University.

Changsha 410083, China.

Email: houmuzhou@sina.com

Funding information

The Projects of the National Social Science

Foundation of China, Grant/Award

Number: 19BTJ011

Abstract

The extreme learning machine (ELM) is a type of machine learning algorithm

for training a single hidden layer feedforward neural network. Randomly ini-

tializing the weight between the input layer and the hidden layer and the

threshold of each hidden layer neuron, the weight matrix of the hidden layer

can be calculated by the least squares method. The efficient learning ability in

ELM makes it widely applicable in classification, regression, and more. How-

ever, owing to some unutilized information in the residual, there are relatively

huge prediction errors involving ELM. In this paper, a deep residual compen-

sation extreme learning machine model (DRC-ELM) of multilayer structures

applied to regression is presented. The first layer is the basic ELM layer, which

helps in obtaining an approximation of the objective function by learning the

characteristics of the sample. The other layers are the residual compensation

layers in which the learned residual is corrected layer by layer to the predicted

value obtained in the previous layer by constructing a feature mapping

between the input layer and the output of the upper layer. This model is

applied to two practical problems: gold price forecasting and airfoil self-noise

prediction. We used the DRC-ELM with 50, 100, and 200 residual compensa-

tion layers respectively for experiments, which show that DRC-ELM does bet-

ter in generalization and robustness than classical ELM, improved ELM

models such as GA-RELM and OS-ELM, and other traditional machine learn-

ing algorithms such as support vector machine (SVM) and back-propagation

neural network (BPNN).

KEYWORDS

airfoil self-noise, deep residual compensation extreme learning machine, extreme learning

machine, gold price forecasting, regression problem

1|INTRODUCTION

Single hidden layer feedforward neural networks

(SLFNs) have been proved to approximate nonlinear fea-

ture mapping with any precision (Hornik, 1991). How-

ever, the traditional single hidden layer neural network

based on the gradient descent algorithm can easily fall

into local minimum and bring greater computational

time complexity. In 2005 Huang et al. released a new

machine learning algorithm to solve several problems

(Huang, Zhu & Siew, 2004). As an improvement to the

training method of the single hidden layer neural

Received: 13 August 2019 Accepted: 12 January 2020

DOI: 10.1002/for.2663

986 © 2020 John Wiley & Sons, Ltd. Journal of Forecasting. 2020;39:986–999.wileyonlinelibrary.com/journal/for