Multiclass Weighted Least Squares Twin Bounded Support Vector Machine for Intelligent Water Leakage Diagnosis

Abstract

Monitoring the operating status of the pipeline and determining the location of the leak in time are very important to ensure the safe operation of the pipeline. Least squares twin support vector machine (LSTSVM) is a classic fast classification method, which has been used to identify different pipeline conditions. However, LSTSVM assumes that all samples share the same weight when generating the hyperplane, including data points that may be polluted in the sample (i.e., outliers), and outlier samples with equal weights will mislead the generation of the hyperplane. Inspired by the above research, this paper proposes a weighted least squares twin bounded support vector machine based on Gaussian mixture models (GMM), referred to as G-WLSTSVM. The proposed G-WLSTSVM introduces a weight matrix for the objective function through GMM, and assigns a larger weight to the normal samples and a smaller weight to the outliers, which reduces the impact effect of the outliers on the generation of the classification hyperplane. Furthermore, since LSTSVM only considers the empirical risk minimization principle, it may lead to overfitting. The proposed G-WLSTSVM introduces an extra regularization term based on the margin maximization idea to realize the principle of structural risk minimization, which improves the generalization performance of the model. Finally, since the practical problems are mostly multi-classification problems, the G-WLSTSVM for binary classification cannot be satisfied. Therefore, the proposed G-WLSTSVM combined with a "One-versus-One" strategy is extended to handle multi-classification problems, namely the multi-class G-WLSTSVM. We evaluate the effectiveness of the multi-class G-WLSTSVM in identifying different pipeline conditions and localize the identified leakage. Numerical experimental results on several UCI datasets further demonstrate that compared with other related methods, the proposed G-WLSTSVM not only retains the advantages of simplicity and speed of the LSTSVM, but also improves the classification accuracy and generalization ability. The code for this article is available at https://github.com/cmq-456/glstsvm.