Fuzzy Least Squares Twin Support Vector Machines

Least Squares Twin Support Vector Machine (LSTSVM) is an extremely efficient and fast version of SVM algorithm for binary classification. LSTSVM combines the idea of Least Squares SVM and Twin SVM in which two non-parallel hyperplanes are found by solving two systems of linear equations. Although the algorithm is very fast and efficient in many classification tasks, it is unable to cope with two features of real-world problems. First, in many real-world classification problems, it is almost impossible to assign data points to a single class. Second, data points in real-world problems may have different importance. In this study, we propose a novel version of LSTSVM based on fuzzy concepts to deal with these two characteristics of real-world data. The algorithm is called Fuzzy LSTSVM (FLSTSVM) which provides more flexibility than the binary classification of LSTSVM. Two models are proposed for the algorithm. In the first model, a fuzzy membership value is assigned to each data point and the hyperplanes are optimized based on these fuzzy samples. In the second model we construct fuzzy hyperplanes to classify data. Finally, we apply our proposed FLSTSVM to an artificial as well as three real-world datasets. Results demonstrate that FLSTSVM obtains better performance than SVM and LSTSVM.