The use of grossone in elastic net regularization and sparse support vector machines

Effective common spatial pattern (CSP) feature extraction for motor-imagery (MI) EEG recordings usually depends on the filter band selection to a large extent. However, the most proper filter band can hardly be determined manually due to its subject-specific property. This study introduces a sparse support vector machine (SSVM) approach to implement simultaneous CSP feature selection and classification for MI-based brain–computer interface (BCI). In SSVM, CSP features are first extracted on multiple signals that are filtered from raw EEG data at a set of overlapping subbands. SVM with l 1-norm regularization is then proposed to classify MI tasks with automatic selection of filter bands giving the significant CSP features. The effectiveness of SSVM for MI classification is demonstrated on the BCI Competition III dataset IVa, in comparison with several other competing methods. Experimental results indicate that the proposed SSVM method is promising for development of an improved MI-based BCI.

Twin support vector machine (TSVM) has been widely applied to classification problems. But TSVM is sensitive to outliers and is not efficient enough to realize feature selection. To overcome the shortcomings of TSVM, we propose a novel sparse twin support vector machine with the correntropy-induced loss (C-STSVM), which is inspired by the robustness of the correntropy-induced loss and the sparsity of the \(\ell _1\)-norm regularization. The objective function of C-STSVM includes the correntropy-induced loss that replaces the hinge loss, and the \(\ell _1\)-norm regularization that can make the decision model sparse to realize feature selection. Experiments on real-world datasets with label noise and noise features demonstrate the effectiveness of C-STSVM in classification accuracy and confirm the above conclusion further.

Sparse pinball twin support vector machines

Melt index is one of the most important quality variables to determine product specifications in the polymer processing, which cannot be real-time measured by ordinary method. In order to estimate the melt index, a soft sensor method using sparse least square support vector machine based on genetic algorithm is proposed. In the proposed method, genetic algorithm is used to realize the sparseness of least square support vector machine and the optimization of its parameters. Simulation results of industrial data show that the proposed method can reduce the model scale which has better generalization capability than that of the non-sparse model.

Capturing CO2 from the flue gas of a power plant based on chemical absorption method is an effective way to cut down the emission of CO2. However, the principal components in the solvent are very difficult to be measured online. Therefore an online measurement and control system was designed for the process of capturing CO2 by MEA chemical absorption. The feature selection was done according to Bayesian networks. Furthermore based on the principle of a new sparse support vector machine (SLS-SVM), the measurement of ionic species distribution in the absorption solution was predicted, and the results agreed well with the data obtained by Nuclear Magnetic Resonance (NMR) measurement. The mean square error is 3.8645×10-7. The measurement of solution species distribution was carried out online by using infrared sensors and NMR technology. Meanwhile the sampling system and NMR unit were linked for the online analysis based on variable-temperature and variable-pressure NMR technology. Finally a measurement and control platform was constructed based on VI technology. It shows that the performance of traditional equipment can be improved by the novel system, which will provide a more effective method for CO2 capture process.

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer—the Infinity Computer—able to work with all these types of numbers. The new computational tools both give possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given.

Sparse elastic net multi-label rank support vector machine with pinball loss and its applications

We introduce a family of Newton-type greedy selection methods for -constrained minimization problems. The basic idea is to construct a quadratic function to approximate the original objective function around the current iterate and solve the constructed quadratic program over the cardinality constraint. The next iterate is then estimated via a line search operation between the current iterate and the solution of the sparse quadratic program. This iterative procedure can be interpreted as an extension of the constrained Newton methods from convex minimization to non-convex -constrained minimization. We show that the proposed algorithms converge asymptotically and the rate of local convergence is superlinear up to certain estimation error. Our methods compare favorably against several state-of-the-art greedy selection methods when applied to sparse logistic regression and sparse support vector machines.

The mutation status of KRAS is a significant biomarker in the prognosis of rectal cancer. This study investigated the feasibility of MRI-based radiomics in predicting the mutation status of KRAS with a composite index which could be an important criterion for KRAS mutation in clinical practice. In this retrospective study, a total of 127 patients with rectal cancer were enrolled. The 3D Slicer was used to extract the radiomics features from the MRI images, and sparse support vector machine (SVM) with linear kernel was applied for feature reduction. The radiomics classifier for predicting the KRAS status was then constructed by Linear Discriminant Analysis (LDA) and its performance was evaluated. The composite index was determined with LDA model. Out of 127 rectal cancer subjects, there were 44 KRAS mutation cases and 83 wild cases. A total of 104 radiomics features were extracted, 54 features were filtered by linear SVM with L1-norm regularization and 6 features that had no significant correlations within them were finally selected. The radiomics classifier constructed using the 6 features featured an AUC value of 0.669 (specificity: 0.506; sensitivity: 0.773) with LDA. Furthermore, the composite index (Radscore) had statistically significant difference between the KRAS mutation and wild groups. It is suggested that the MRI-based radiomics has the potential in predicting the KRAS status in patients with rectal cancer, which may enhance the diagnostic value of MRI in rectal cancer.

Algorithms for the numerical solution of optimal control problems with bounded state variables are developed. Two main cases are considered: either the control variable appears nonlinearly or the control variable appears linearly. In the first case, an extremal are touching the boundary or containing a boundary arc, is shown to satisfy a suitable two-point boundary value problem. In the second case, a numerical idea for solving the problem in statespace is presented which dispenses with the Lagrange-multipliers. Three numerical examples are discussed illustrating the efficiency of the different algorithms. The encountered two-point boundary value problems are solved with the method of multiple shooting.

SUMMARYThis paper presents an algorithm for the indirect solution of optimal control problems that contain mixed state and control variable inequality constraints. The necessary conditions for optimality lead to an inequality constrained two‐point BVP with index‐1 differential‐algebraic equations (BVP‐DAEs). These BVP‐DAEs are solved using a multiple shooting method where the DAEs are approximated using a single‐step linearly implicit Runge–Kutta (Rosenbrock–Wanner) method. An interior‐point Newton method is used to solve the residual equations associated with the multiple shooting discretization. The elements of the residual equations, and the Jacobian of the residual equations, are constructed in parallel. The search direction for the interior‐point method is computed by solving a sparse bordered almost block diagonal (BABD) linear system. Here, a parallel‐structured orthogonal factorization algorithm is used to solve the BABD system. Examples are presented to illustrate the efficiency of the parallel algorithm. It is shown that an American National Standards Institute C implementation of the parallel algorithm achieves significant speedup with the increase in the number of processors used. Copyright © 2013 John Wiley & Sons, Ltd.

Three algorithms for efficient solution of optimal control problems for high-dimensional systems are presented. Each bypasses the intermediate (and, unnecessary) step of open-loop model reduction. Each also bypasses the solution of the full Riccati equation corresponding to the LQR problem, which is numerically intractable for large n. Motivation for this effort comes from the field of model-based flow control, where open-loop model reduction often fails to capture the dynamics of interest (governed by the Navier–Stokes equation). Our minimum control energy method is a simplified expression for the well-known minimum-energy stabilizing control feedback that depends only on the left eigenvectors corresponding to the unstable eigenvalues of the system matrix A. Our Adjoint of the Direct-Adjoint method is based on the repeated iterative computation of the adjoint of a forward problem, itself defined to be the direct-adjoint vector pair associated with the LQR problem. Our oppositely-shifted subspace iteration (OSSI, the main new result of the present paper) method is based on our new subspace iteration method for computing the Schur vectors corresponding, notably, to the \(m\ll n\) central eigenvalues (near the imaginary axis) of the Hamiltonian matrix related to the Riccati equation of interest. Prototype OSSI implementations are tested on a low-order control problem to illustrate its behavior.

This paper is devoted to the algorithm of the linear Cauchy problem solution for large systems of first-order ordinary differential equations using parallel calculations. The proof of the convergence of the iteration process using the solution as expansion over orthogonal polynomials for the interval [0,1] is presented. The features of this algorithm are its simplicity, the opportunity to get a solution by parallel calculations, and also the possibility to get a solution for nonlinear problems by changing the operator using the solution from the iteration process.

Scene classification based on single-layer SAE and SVM

Due to the limited resolution of hyperspectral sensors, anomalous targets expressed with subpixels are often mixed with nonhomogeneous backgrounds. This fact makes anomalies difficult to be distinguished from the surrounding background. From this perspective, we propose a novel hyperspectral anomaly detection (AD) algorithm based on low-rank & sparse matrix decomposition (LRaSMD) and support vector machine (SVM). First, based on the LRaSMD technique, the Go decomposition (GoDec) model is utilized to decompose the original image into three components: background, anomalies and noise. In this way, the robust background can be obtained. Subsequently, a clustering algorithm is employed to pick some obvious anomalies. Accordingly, we use both samples of background and anomaly to train an SVM model. The original dataset is sent into the SVM model and both anomalous components and background components can be classified. Experiments on a synthetic hyperspectral image validate the performance of the proposed method.