Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 8513652, 6 pages

https://doi.org/10.1155/2017/8513652

## A Deep Learning Prediction Model Based on Extreme-Point Symmetric Mode Decomposition and Cluster Analysis

School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, China

Correspondence should be addressed to Hong Yang

Received 14 July 2017; Accepted 5 December 2017; Published 27 December 2017

Academic Editor: Simone Bianco

Copyright © 2017 Guohui Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Aiming at the irregularity of nonlinear signal and its predicting difficulty, a deep learning prediction model based on extreme-point symmetric mode decomposition (ESMD) and clustering analysis is proposed. Firstly, the original data is decomposed by ESMD to obtain the finite number of intrinsic mode functions (IMFs) and residuals. Secondly, the fuzzy -means is used to cluster the decomposed components, and then the deep belief network (DBN) is used to predict it. Finally, the reconstructed IMFs and residuals are the final prediction results. Six kinds of prediction models are compared, which are DBN prediction model, EMD-DBN prediction model, EEMD-DBN prediction model, CEEMD-DBN prediction model, ESMD-DBN prediction model, and the proposed model in this paper. The same sunspots time series are predicted with six kinds of prediction models. The experimental results show that the proposed model has better prediction accuracy and smaller error.

#### 1. Introduction

At present, there are still many difficulties in predicting nonlinear signal such as sunspots and underwater acoustic signal. Sunspots are the basic parameters of the solar activity level. They are closely related to the geomagnetic disturbance and ionospheric electron concentration. Prediction of sunspots is an important part of spatial forecast which can provide important reference information for communication, navigation, and positioning. Some scholars have conducted extensive research on the theory of forecasting [1, 2]. In the time-frequency signal analysis, the commonly used method is Fourier transform which is mainly mapping the time domain signal to the frequency domain energy spectrum space, but Fourier transform only applies to the stationary signal. Artificial neural network has the characteristics of independent learning compared with the previous regression analysis which is especially suitable for nonlinear signal processing. However, due to the limitation of synchronous instantaneous input, the time cumulative effect of continuous signal cannot be reflected, and the prediction accuracy is low [3]. Wavelet neural network is combined with the characteristics of artificial neural network and wavelet analysis which has been widely applied to the processing of nonlinear signal. Li and Wang [1] propose the prediction model based on complementary ensemble empirical mode decomposition and wavelet neural network. Although its prediction accuracy is improved to a certain extent, there is room for further improvement. The emergence of empirical mode decomposition [4] (EMD) provides an idea for the processing of nonlinear signal. It does not need to select a basis function, but it is difficult to determine the number of screenings and there are many defects in Hilbert spectral analysis. The extreme-point symmetric mode decomposition [5–7] (ESMD) method is a further improvement of the EMD, whose envelope interpolation from extreme points of the original external changes to internal upper and lower extreme symmetric interpolation. The residual modal component is optimized by the least squares method, which has the characteristics of adaptive global to determine the number of screenings. ESMD uses the direct interpolation (DI) method, which is different from Fourier transform only by the idea of transformation of the integral algorithm. In view of the advantages of ESMD, this paper selects the ESMD method to decompose the nonlinear time series. Then, fuzzy -means [8, 9] clustering analysis is used to aggregate the data of the same membership to facilitate the prediction analysis of the model. Finally, the deep belief network [10–13] (DBN) is trained to achieve the expected output value, and then the predicted output value is reconstructed to obtain the final predicted value.

#### 2. ESMD Method

ESMD is a new development of the Hilbert-Huang transform, and its algorithm is as follows:(1)Find all the extreme points (maximum and minimum) of the data and record them as .(2)Connect the adjacent poles with lines, and the midpoint is recorded as .(3)Supplement the left and right border midpoint by certain methods.(4)Use the obtained midpoints to construct bar differential lines and calculate their mean curves .(5)Repeat the above steps until the number of screenings reaches the preset maximum value; then the first decomposed empirical mode is recorded as .(6)Repeat the above steps for to obtain until the final margin only has a certain number of poles.(7)Let the maximum number of screenings process and cycle of the above process in the integer interval to get some components, and then calculate the variance ratio and draw it with the change map, where is the relative standard deviation of and is the standard deviation of the original data.(8)Select the maximum number of screenings which corresponded to the minimum variance ratio in the interval , and repeat the first six steps to output the decomposition results.

#### 3. Clustering Algorithm

The fuzzy clustering algorithm was originally proposed by Dunn [14] and further introduced by Bezdek [15], which is now being applied to many fields. Its operation steps can be expressed as follows: the sample set is divided into class. Membership degree of any element in the sample on the class is recorded as . The fuzzy membership matrix is used in the matrix after clustering, which is recorded as and satisfies the following conditions:

The fuzzy -means clustering is obtained by minimizing the purpose function . The purpose function is as follows:where is the membership matrix, represents clustering center point sets, and is the weighted index. The fuzzy clustering is transformed into hard mean clustering [14] when is 1. The ideal range of is , usually .

The distance from the th sample to the th class center iswhere is the positive definite matrix of , special conditions , and (3) is the Euclidean distance. FCM [16] is achieved by continuously optimizing the objective function. FCM algorithm process is as follows:(1)Initialize the cluster center .(2)Calculate membership matrix:(3)Calculate the new cluster center:(4)Repeat steps and until (2) reaches convergence. When , a singular value is generated, and membership cannot be calculated by (4). A class of nonsingular values will appear when the membership value is 0. The class of singular value appears, and then the membership is calculated according to (1).

#### 4. Forecasting Model

##### 4.1. DBN Network Structure

DBN [17, 18] is organized by a number of restricted Boltzmann machine (RBM) models. The visual layer of the RBM model is similar to the input layer, and the hidden layer is similar to the output layer. Learning between layers and layers of a large numbers of RBM models is used to end the final operation. The specific structure of RBM model is shown in Figure 1. The unit of the visual layer and the unit of the hidden layer can be interconnected with each other. The elements inside the layers are not connected. The units of the hidden layer can obtain a close correlation between the units of the visual layer.