A fuzzy universum least squares twin support vector machine (FULSTSVM)

Universum based twin support vector machines give prior information about the distribution of data to the classifier. This leads to better generalization performance of the model, due to the universum. However, in many applications the data points are not equally useful for the classification task. This leads to the use of fuzzy membership functions for the datasets. Similarly, in universum based algorithms, all the universum data points are not equally important for the classifier. To solve these problems, a novel fuzzy universum least squares twin support vector machine (FULSTSVM) is proposed in this work. In FULSTSVM, the membership values are used to provide weights for the data samples of the classes, as well as to the universum data. Further, the optimization problem of proposed FULSTSVM is obtained by solving a system of linear equations. This leads to an efficient fuzzy based algorithm. Numerical experiments are performed on various benchmark datasets, with discussions on generalization performance, and computational cost of the algorithms. The proposed FULSTSVM outperformed the existing algorithms on most datasets. A comparison is presented for the performance of the proposed and other baseline algorithms using statistical significance tests. To show the applicability of FULSTSVM, applications are also presented, such as detection of Alzheimer's disease, and breast cancer.