Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized

A mathematical programming approach to SVM-based classification with label noise

The authors of this research acknowledge financial support by the Spanish Ministerio de Ciencia y Tecnologia, Agencia Estatal de Investigacion and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020114594GB-C21. The authors also acknowledge partial support from projects FEDER-US-1256951, Junta de Andalucía P18-FR-1422, CEI-3-FQM331, NetmeetData: Ayudas Fundación BBVA a equipos de investigación científica 2019. The first author was also supported by projects P18-FR-2369 (Junta de Andalucía) and IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033. (Spanish Ministerio de Ciencia y Tecnologia).In this paper we propose novel methodologies to optimally construct Support Vector Machine-based classifiers that take into account that label noise occur in the training sample. We propose different alternatives based on solving Mixed Integer Linear and Non Linear models by incorporating decisions on relabeling some of the observations in the training dataset. The first method incorporates relabeling directly in the SVM model while a second family of methods combines clustering with classification at the same time, giving rise to a model that applies simultaneously similarity measures and SVM. Extensive computational experiments are reported based on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of the proposed approaches.Spanish Ministerio de Ciencia y Tecnologia, Agencia Estatal de Investigacion and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020114594GB-C21FEDER-US-1256951Junta de Andalucía P18-FR-1422CEI-3-FQM331NetmeetData: Ayudas Fundación BBVA a equipos de investigación científica 2019Project P18-FR-2369 Junta de AndalucíaIMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033. (Spanish Ministerio de Ciencia y Tecnologia

Solution Path Algorithm for Twin Multi-class Support Vector Machine

The twin support vector machine and its extensions have made great achievements in dealing with binary classification problems, however, which is faced with some difficulties such as model selection and solving multi-classification problems quickly. This paper is devoted to the fast regularization parameter tuning algorithm for the twin multi-class support vector machine. A new sample dataset division method is adopted and the Lagrangian multipliers are proved to be piecewise linear with respect to the regularization parameters by combining the linear equations and block matrix theory. Eight kinds of events are defined to seek for the starting event and then the solution path algorithm is designed, which greatly reduces the computational cost. In addition, only few points are combined to complete the initialization and Lagrangian multipliers are proved to be 1 as the regularization parameter tends to infinity. Simulation results based on UCI datasets show that the proposed method can achieve good classification performance with reducing the computational cost of grid search method from exponential level to the constant level

ICASE semiannual report, April 1 - September 30, 1989

The Institute conducts unclassified basic research in applied mathematics, numerical analysis, and computer science in order to extend and improve problem-solving capabilities in science and engineering, particularly in aeronautics and space. The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers. ICASE reports are considered to be primarily preprints of manuscripts that have been submitted to appropriate research journals or that are to appear in conference proceedings

Hypersonic Boundary-Layer Stability Across a Compression Corner

Stability of a hypersonic boundary-layer over a compression corner was investigated numerically. The three-dimensional compressible Navier-Stokes equations were solved using a fifth-order weighted essentially non-oscillating (ArENO) shock capturing scheme to study the shock wave and boundary-layer interactions. The boundary-layer stability was studied in three distinct regions: upstream of the separation region, inside the separation region and downstream of the separation region. After the mean flow field was computed, linear stability theory was employed to predict the unstable disturbance modes in different flow regions and also to find the most amplified disturbance frequency across the compression corner. Gortler instability computations were performed to study the influence of the streamline curvatures on boundary-layer stability, and PSE(parabolized stability equation) method was employed to obtain the initial disturbances for direct numerical simulation. To study the boundary-layer stability by direct numerical simulation, two- or three-dimensional initial disturbances were introduced at the initial streamwise location of the computational domain. Two-dimensional disturbance evolution simulation shows that two-dimensional high frequency linear disturbances grow exponentially upstream and downstream of the separation region and remain neutral in the separation region, but two-dimensional low frequency linear disturbances only grow in a narrow area inside the separation region and remain neutral upstream and downstream of the separation region. Two-dimensional nonlinear disturbances will saturate downstream of the separation region when their amplitudes reach quit large amplitude. The three-dimensional disturbance evolution simulations show that three-dimensional linear mono-frequency disturbances are less amplified than its two-dimensional counterpart across the compression corner. The three-dimensional nonlinear mono-frequency disturbance evolution indicates that mode (0,2) is responsible for the oblique breakdown. Three-dimensional disturbances are much more amplified with the presence of two-dimensional primary disturbance due to the secondary instability. Finally, the simulations of three-dimensional random frequency disturbance evolution with the presence of a two-dimensional primary disturbance show that the secondary instability first occurs downstream of the separation region and a fundamental or K-type breakdown will be triggered by this secondary instability

Modal Analysis of Fluid Flows: An Overview

Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flow field, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades. For a non-expert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis in a presentation that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (Balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis