Abstract
Multiple SVR based on ensemble learning could be enhanced from the viewpoint of the performance, but the performance of modeling closely depends on the initial condition of the partitioning method and they are easily affected by noise and outliers. In this study, a multi-linear fuzzy support vector regression (MFSVR) robust to noise is proposed with the aid of the composite kernel function and $\varepsilon $ -fuzzy c-means (FCM) clustering based on insensitive data information. Here insensitive data information stands for the interval data information of “$\varepsilon $ ” which stands for insensitive loss parameter used in the $\varepsilon $ - insensitive loss function. The objective of this study is to reduce the effect of noise and to alleviate the overfitting problem through the synergistic effect of the following methods: First, $\varepsilon $ -FCM clustering based on insensitive data information is used for considering more impact on decision boundary and reducing the effect of noise. Second, the composite kernel based on multiple linear kernel expression is proposed for implementing multi-linear decision boundary to alleviate overfitting problem. In more detail, each training data point is assigned with corresponding membership degrees in the $\varepsilon $ -FCM clustering. Some data which are potentially to be noise or outlier are assigned with lower membership degrees and given small contribution (compensation) considered in composite kernel function. Then, the composite kernel function for multiple local SVRs is constructed according to the distribution characteristics of $\varepsilon $ -FCM clustering. The proposed MFSVR is tested with both synthetic and UCI data sets in order to verify the effectiveness as well as efficient performance improvement. Experimental results demonstrate that the proposed method shows the better performance when compared to other some methods studied so far.
Highlights
During the past two decades, an identification of nonlinear models (NM) has received much attention
The proposed ε-fuzzy c-means (FCM) is a data pre-processing algorithm based on existing Support Vector Regression (SVR), which limit the effect of data points away from the decision boundary [23]
EXPERIMENTAL STUDIES the conventional SVR with three types of kernel functions, proposed multi-linear fuzzy support vector regression (MFSVR) based on FCM and proposed MFSVR based on ε-FCM are used for comparing the performance
Summary
During the past two decades, an identification of nonlinear models (NM) has received much attention. A multiple fuzzy SVR (MFSVR) based on ε-FCM and the composite kernel function is proposed for alleviating the overfitting problem. In the composite kernel function, the membership degrees obtained by ε-FCM are considered to provide the regression model with more compensation. Ε-FCM alleviates the effect of uncorrelated data through assigning more compensation (through the corresponding membership degrees) on decision boundary (regression model). The purpose of the composite kernel function is to alleviate the overfitting problem with multiple local linear decision boundaries. The main contributions of our work can be summarized in a concise way as follows: First, The local linear decision boundary obtained by local clusters can be adjusted by the fuzzy clusters for alleviating the overfitting problem.
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