Fuzzy Least Squares Twin Support Vector Machines

Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an efficient and fast algorithm for binary classification. It combines the operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still unable to cope with two features of real-world problems. First, in many real-world applications, labels of samples are not deterministic; they come naturally with their associated membership degrees. Second, samples in real-world applications may not be equally important and their importance degrees affect the classification. In this paper, we propose Fuzzy LST-SVM (FLST-SVM) to deal with these two characteristics of real-world data. Two models are introduced for FLST-SVM: the first model builds up crisp hyperplanes using training samples and their corresponding membership degrees. The second model, on the other hand, constructs fuzzy hyperplanes using training samples and their membership degrees. Numerical evaluation of the proposed method with synthetic and real datasets demonstrate significant improvement in the classification accuracy of FLST-SVM when compared to well-known existing versions of SVM

Support matrix machine: A review

Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists in matrix format, which is given as input to SVM by reshaping the matrices into vectors. The process of reshaping disrupts the spatial correlations inherent in the matrix data. Also, converting matrices into vectors results in input data with a high dimensionality, which introduces significant computational complexity. To overcome these issues in classifying matrix input data, support matrix machine (SMM) is proposed. It represents one of the emerging methodologies tailored for handling matrix input data. The SMM method preserves the structural information of the matrix data by using the spectral elastic net property which is a combination of the nuclear norm and Frobenius norm. This article provides the first in-depth analysis of the development of the SMM model, which can be used as a thorough summary by both novices and experts. We discuss numerous SMM variants, such as robust, sparse, class imbalance, and multi-class classification models. We also analyze the applications of the SMM model and conclude the article by outlining potential future research avenues and possibilities that may motivate academics to advance the SMM algorithm

Support vector machines to detect physiological patterns for EEG and EMG-based human-computer interaction:a review

Support vector machines (SVMs) are widely used classifiers for detecting physiological patterns in human-computer interaction (HCI). Their success is due to their versatility, robustness and large availability of free dedicated toolboxes. Frequently in the literature, insufficient details about the SVM implementation and/or parameters selection are reported, making it impossible to reproduce study analysis and results. In order to perform an optimized classification and report a proper description of the results, it is necessary to have a comprehensive critical overview of the applications of SVM. The aim of this paper is to provide a review of the usage of SVM in the determination of brain and muscle patterns for HCI, by focusing on electroencephalography (EEG) and electromyography (EMG) techniques. In particular, an overview of the basic principles of SVM theory is outlined, together with a description of several relevant literature implementations. Furthermore, details concerning reviewed papers are listed in tables and statistics of SVM use in the literature are presented. Suitability of SVM for HCI is discussed and critical comparisons with other classifiers are reported

Nonparallel support vector machines for pattern classification

We propose a novel nonparallel classifier, called nonparallel support vector machine (NPSVM), for binary classification. Our NPSVM that is fully different from the existing nonparallel classifiers, such as the generalized eigenvalue proximal support vector machine (GEPSVM) and the twin support vector machine (TWSVM), has several incomparable advantages: 1) two primal problems are constructed implementing the structural risk minimization principle; 2) the dual problems of these two primal problems have the same advantages as that of the standard SVMs, so that the kernel trick can be applied directly, while existing TWSVMs have to construct another two primal problems for nonlinear cases based on the approximate kernel-generated surfaces, furthermore, their nonlinear problems cannot degenerate to the linear case even the linear kernel is used; 3) the dual problems have the same elegant formulation with that of standard SVMs and can certainly be solved efficiently by sequential minimization optimization algorithm, while existing GEPSVM or TWSVMs are not suitable for large scale problems; 4) it has the inherent sparseness as standard SVMs; 5) existing TWSVMs are only the special cases of the NPSVM when the parameters of which are appropriately chosen. Experimental results on lots of datasets show the effectiveness of our method in both sparseness and classification accuracy, and therefore, confirm the above conclusion further. In some sense, our NPSVM is a new starting point of nonparallel classifiers