Papers by Theodore Trafalis
Proceedings of the 2021 SIAM International Conference on Data Mining (SDM), 2021
Оптимальное ядро матрицы регрессии рассчитано методом полуопределенногопрограммирования с использ... more Оптимальное ядро матрицы регрессии рассчитано методом полуопределенногопрограммирования с использованием трех базисных матриц. В работе представле-ны предварительные результаты, использующие стандартные реперные данные, длякоторых выявлены оптимальные параметры линейной комбинации трех базисных ма-триц ядра.
Lecture Notes in Computer Science, 2022
Lecture Notes in Computer Science, 2022
arXiv (Cornell University), Jul 9, 2021
In this work, we present a learning-based nonlinear H ∞ control algorithm that guarantee system p... more In this work, we present a learning-based nonlinear H ∞ control algorithm that guarantee system performance under learned dynamics and disturbance estimate. The Gaussian Process (GP) regression is utilized to update the nominal dynamics of the system and provide disturbance estimate based on data gathered through interaction with the system. A softconstrained differential game associated with the disturbance attenuation problem in nonlinear H ∞ control is then formulated to obtain the nonlinear H ∞ controller. The differential game is solved through the min-max Game-Theoretic Differential Dynamic Programming (GT-DDP) algorithm in continuous time. Simulation results on a quadcopter system demonstrate the efficiency of the learning-based control algorithm in handling external disturbances.
Tables S1-S5 with deterministic system information for integrated refinery model. Appendix A. The... more Tables S1-S5 with deterministic system information for integrated refinery model. Appendix A. The crude unloading model constraints, Appendix B. The refinery production model constraints, Appendix C. The final product pooling problem constraints, Appendix D. The pipeline distribution model constraints, Appendix E. The utility system model constraints, Appendix F. Implementation of the proposed global optimization algorithm and Normalized multiparametric disaggregation techniques (NMDT).
Support Vector Machines (SVM) can be constructed with the selection of an appropriate kernel func... more Support Vector Machines (SVM) can be constructed with the selection of an appropriate kernel function to solve an optimization problem. Algorithmic approaches can be taken to solve problems related to SVM which are used for regression analysis and data classi
cation of a data set. The (inhomogeneous) polynomial kernel k (x; y) = 1 + x y d is useful for non-linear data set classi
cation. In this work, the SVM QP problem with (inhomogeneous) polynomial kernel k (x; y) is expressed as a mixed convex optimization problem with respect to the real variables 2 R and b 2 R; and the integer variable d 2 Z. Several examples of mixed convexity and computational results are given. In addition, we introduce the de
nitions of unimodal and semi-unimodal mixed variable functions with the corresponding minimization results. Key-Words: SVM, Inhomogeneous Polynomial Kernel Map, Unimodal Function, Mixed Convex Function, Minimization.
2017 IEEE 17th International Conference on Bioinformatics and Bioengineering (BIBE), 2017
Thyroid nodules are a common pathology which are fortunately usually benign. However, current ima... more Thyroid nodules are a common pathology which are fortunately usually benign. However, current image characterization is limited in accurately differentiating benign from malignant nodules. Consequently, a percutaneous biopsy is often necessary to determine if a nodule is benign or malignant. We hypothesized that deep learning in conjunction with professional image characterization could improve nodule characterization and reduce benign biopsies. We extracted our features using convolutional auto-encoders, local binary patterns as well as histogram of oriented gradients descriptors in association with medical professional thyroid image characterization. The experiment showed the classifiers using these features can improve negative predictive value of thyroid nodule evaluation using ultrasound.
International Journal of Mathematics in Operational Research, 2021
Symmetry, 2020
The limitations and high false-negative rates (30%) of COVID-19 test kits have been a prominent c... more The limitations and high false-negative rates (30%) of COVID-19 test kits have been a prominent challenge during the 2020 coronavirus pandemic. Manufacturing those kits and performing the tests require extensive resources and time. Recent studies show that radiological images like chest X-rays can offer a more efficient solution and faster initial screening of COVID-19 patients. In this study, we develop a COVID-19 diagnosis model using Multilayer Perceptron and Convolutional Neural Network (MLP-CNN) for mixed-data (numerical/categorical and image data). The model predicts and differentiates between COVID-19 and non-COVID-19 patients, such that early diagnosis of the virus can be initiated, leading to timely isolation and treatments to stop further spread of the disease. We also explore the benefits of using numerical/categorical data in association with chest X-ray images for screening COVID-19 patients considering both balanced and imbalanced datasets. Three different optimization...
Optimization Methods and Software, 2016
Incorporating the quantity and variety of observations in atmospheric and oceanographic assimilat... more Incorporating the quantity and variety of observations in atmospheric and oceanographic assimilation and prediction models has become an increasingly complex task. Data assimilation allows for uneven spatial and temporal data distribution and redundancy to be addressed so that the models can ingest massive data sets. Traditional data assimilation methods introduce Kalman filters and variational approaches. This study introduces a family of algorithms, motivated by advances in machine learning. These algorithms provide an alternative approach to incorporating new observations into the analysis forecast cycle. The application of kernel methods to processing the states of a quasi-geostrophic numerical model is intended to demonstrate the feasibility of the method as a proof-of-concept. The speed, efficiency, accuracy and scalability in recovering unperturbed state trajectories establishes the viability of machine learning for data assimilation.
Proceedings of the 15th Wseas International Conference on Computers, Jul 15, 2011
The main objective of this talk is to present recent developments in the applications of kernel m... more The main objective of this talk is to present recent developments in the applications of kernel methods and Support Vector Machines (SVMs) to severe weather prediction. I will also discuss how kernel methods can be used to uncover physically meaningful, predictive patterns in weather radar data that alert to severe weather before the severe weather occurs. Specific indices related to the analysis of imbalanced weather data (for example tornado data) using kernel methods will be also discussed. In addition a family of learning algorithms, motivated by Support Vector Machines, capable of replacing traditional methods for assimilating data and generating forecasts, without requiring the assumptions made by the assimilation methods (Kalman filters) and an application of kernel methods to processing the states of a Quasi-Geostrophic (QG) numerical model will be presented. Extensions of those techniques to other areas of applications will be investigated.
Springer Proceedings in Mathematics & Statistics, 2015
Let measurements of a real function of one variable be given. If the function is convex but conve... more Let measurements of a real function of one variable be given. If the function is convex but convexity has been lost due to errors of measurement, then we make the least sum of squares change to the data so that the second divided differences of the smoothed values are nonnegative. The underlying calculation is a quadratic programming algorithm and the piecewise linear interpolant to the solution components is a convex curve. Problems of this structure arise in various contexts in research and applications in science, engineering and social sciences. The sensitivity of the solution is investigated when the data are slightly altered. The sensitivity question arises in the utilization of the method. First some theory is presented and then an illustrative example shows the effect of specific as well as random changes of the data to the solution. As an application to real data, an experiment on the sensitivity of the convex estimate to the Gini coefficient in the USA for the time period 1947–1996 is presented. The measurements of the Gini coefficient are considered uncertain, with a uniform probability distribution over a certain interval. Some consequences of this uncertainty are investigated with the aid of a simulation technique.
Recently a lot of attention has been given to applications of mathematical programming to machine... more Recently a lot of attention has been given to applications of mathematical programming to machine learning and neural networks. In this tutorial we i n vestigate the use of Interior Point Methods (IPMs) to Support Vector Machines (SVMs) and Arti cial Neural Networks (ANNs) training. The training of ANNs is a highly nonconvex optimization problem in contrast to the SVMs training problem which i s a c o n vex optimization problem. Speci cally, training a SVM is equivalent to solving a linearly constrained quadratic programming (QP) problem in a number of variables equal to the number of data points. This problem becomes quite challenging when the size of the data becomes of the order of some thousands. IPMs have b e e n s h o wn quite promising for solving large scale linear and quadratic programming problems. We focus on primal-dual IPMs applied to SVMs and neural networks and investigate the problem of reducing its computational complexity. W e also develop a new class of incremental nonlinear primal-dual techniques for arti cial neural training and provide preliminary experimental results for nancial forecasting problems.
Wseas Transactions on Systems, 2005
The binary support vector machines (SVMs) have been extensively investigated. However their exten... more The binary support vector machines (SVMs) have been extensively investigated. However their extension to a multi-classification model is still an ongoing research. In this paper we present an extension of the binary support vector machines (SVMs) for the k > 2 class problems. The SVM model as originally proposed requires the construction of several binary SVM classifiers to solve the multi-class problem. We propose a single quadratic optimization problem called a pairwise multi-classification support vector machines (P A MSVMs) for constructing a pairwise linear and nonlinear classification decision functions. A kernel approach is also discussed for nonlinear classification problems. Computational results are presented for two real data sets.
AIP Conference Proceedings, 2004
In the last two decades, there has been significant interest in using mean field theory coming fr... more In the last two decades, there has been significant interest in using mean field theory coming from statistical physics in combinatorial optimization, neural networks, image processing, and engineering. This has led to the development of powerful optimization techniques such as neural networks (NNs), simulated annealing (SA), and mean field annealing (MFA). MFA combines many characteristics of SA and NNs. MFA replaces the stochastic nature of SA with a set of deterministic equations named as mean field equations. The mean field equations depend on the energy function of the NNs and are solved at each temperature during the annealing process of SA. MFA advances to the optimal solution in a fundamentally different way than stochastic methods. The use of mean field techniques for the combinatorial optimization problems are reviewed extensively in this study.
AIP Conference Proceedings, 2004
Primal dual Interior Point Methods (IPMs) generate points that lie in the neighborhood of the cen... more Primal dual Interior Point Methods (IPMs) generate points that lie in the neighborhood of the central trajectory. The key ingredient of the primal dual IPMs is the parameterization of the central trajectory. A new approach to the parameterization of the central trajectory is presented. Instead of parameterizing the central trajectory by the barrier parameter, it is parameterized by the time
Contributions to Management Science, 1997
This paper proposes a portfolio selection model for common stock investments. Although the usage ... more This paper proposes a portfolio selection model for common stock investments. Although the usage of the beta coefficient in the capital asset pricing model (CAPM) has its limitations, still it is one of the most powerful tools in financial planning. In the proposed model, individual beta has a range described as a tolerance and the different combinations of betas form scenarios. The objective of the model is to find the portfolio with the lowest unsystematic risk and the least conflicting solution among scenarios at the investor’s best knowledge. The problem is solved through an interactive multiobjective programming approach based on a circum scribed ellipsoid interior point algorithm. In the process of solving the problem, the investor can appropriately incorporate any information regarding the securities and the investor’s preference.
International Journal of Smart Engineering System Design, 2003
... rep-resent the variability of Doppler velocity values due to turbulence within and velocity s... more ... rep-resent the variability of Doppler velocity values due to turbulence within and velocity shear across the sam-pling volume ... atmospheric circulation events identified by the mesocyclone detection algorithm (MDA) as having characteristics consistent with pre-tornado conditions. ...
Uploads
Papers by Theodore Trafalis