Relevant bibliographies by topics / Linear programming-based discriminant analysis

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Linear programming-based discriminant analysis'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Linear programming-based discriminant analysis"

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Liu, Yi‐Hsin, and John Maloney. "Discriminant analysis and linear programming." International Journal of Mathematical Education in Science and Technology 28, no. 2 (March 1997): 207–10. http://dx.doi.org/10.1080/0020739970280204.

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Gochet, Willy, Antonie Stam, V. Srinivasan, and Shaoxiang Chen. "Multigroup Discriminant Analysis Using Linear Programming." Operations Research 45, no. 2 (April 1997): 213–25. http://dx.doi.org/10.1287/opre.45.2.213.

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Ubi, Jaan, Evald Ubi, Innar Liiv, and Kristina Murtazin. "Predicting Student Retention by Linear Programming Discriminant Analysis." International Journal of Technology and Educational Marketing 4, no. 2 (July 2014): 43–53. http://dx.doi.org/10.4018/ijtem.2014070104.

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The goal of the paper is to predict student retention with an ensemble method by combining linear programming (LP) discriminant analysis approaches together with bootstrapping and feature salience detection. In order to perform discriminant analysis, we linearize a fractional programming method by using Charnes-Cooper transformation (CCT) and apply linear programming, while comparing with an approach that uses deviation variables (DV) to tackle a similar multiple criteria optimization problem. We train a discriminatory hyperplane family and make the decision based on the average of the histograms created, thereby reducing variability of predictions. Feature salience detection is performed by using the peeling method, which makes the selection based on the proportion of variance explained in the correlation matrix. While the CCT method is superior in detecting true-positives, DV method excels in finding true-negatives. The authors obtain optimal results by selecting either all 14 (CCT) or the 8 (DV) most important student study related and demographic dimensions. They also create an ensemble. A quantitative course along with the age at accession are deemed to be the most important, whereas the two courses resulting in less than 2% of failures are amongst the least important, according to peeling. A five-fold Kolmogorov-Smirnov test is undertaken, in order to help university staff in devising intervention measures.
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Youssef, Slah Ben, and Abdelwaheb Rebai. "Discriminant analysis using fuzzy linear programming models." International Journal of Knowledge Management Studies 2, no. 4 (2008): 445. http://dx.doi.org/10.1504/ijkms.2008.019751.

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Glover, Fred. "Improved Linear Programming Models for Discriminant Analysis." Decision Sciences 21, no. 4 (December 1990): 771–85. http://dx.doi.org/10.1111/j.1540-5915.1990.tb01249.x.

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Glen, J. J. "Mathematical programming models for piecewise-linear discriminant analysis." Journal of the Operational Research Society 56, no. 3 (March 2005): 331–41. http://dx.doi.org/10.1057/palgrave.jors.2601818.

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SUN, MINGHE. "A MIXED INTEGER PROGRAMMING MODEL FOR MULTIPLE-CLASS DISCRIMINANT ANALYSIS." International Journal of Information Technology & Decision Making 10, no. 04 (July 2011): 589–612. http://dx.doi.org/10.1142/s0219622011004476.

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A mixed integer programming model is proposed for multiple-class discriminant and classification analysis. When multiple discriminant functions, one for each class, are constructed with the mixed integer programming model, the number of misclassified observations in the sample is minimized. This model is an extension of the linear programming models for multiple-class discriminant analysis but may be considered as a generalization of mixed integer programming formulations for two-class classification analysis. Properties of the model are studied. The model is immune from any difficulties of many mathematical programming formulations for two-class classification analysis, such as nonexistence of optimal solutions, improper solutions, and instability under linear data transformation. In addition, meaningful discriminant functions can be generated under conditions where other techniques fail. Examples are provided. Results on publically accessible datasets show that this model is very effective in generating powerful discriminant functions.
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Gordon, Kenneth R., Michael Palmer, and Fred Glover. "Modeling international loan portfolios through Linear Programming Discriminant Analysis." Journal of Policy Modeling 15, no. 3 (June 1993): 297–312. http://dx.doi.org/10.1016/0161-8938(93)90034-n.

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Retzlaff-Roberts, Donna L. "A ratio model for discriminant analysis using linear programming." European Journal of Operational Research 94, no. 1 (October 1996): 112–21. http://dx.doi.org/10.1016/0377-2217(95)00196-4.

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Sun, Minghe. "Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis." International Journal of Strategic Decision Sciences 1, no. 1 (January 2010): 57–80. http://dx.doi.org/10.4018/jsds.2010103004.

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New linear programming approaches are proposed as nonparametric procedures for multiple-class discriminant and classification analysis. A new MSD model minimizing the sum of the classification errors is formulated to construct discriminant functions. This model has desirable properties because it is versatile and is immune to the pathologies of some of the earlier mathematical programming models for two-class classification. It is also purely systematic and algorithmic and no user ad hoc and trial judgment is required. Furthermore, it can be used as the basis to develop other models, such as a multiple-class support vector machine and a mixed integer programming model, for discrimination and classification. A MMD model minimizing the maximum of the classification errors, although with very limited use, is also studied. These models may also be considered as generalizations of mathematical programming formulations for two-class classification. By the same approach, other mathematical programming formulations for two-class classification can be easily generalized to multiple-class formulations. Results on standard as well as randomly generated test datasets show that the MSD model is very effective in generating powerful discriminant functions.
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Dissertations / Theses on the topic "Linear programming-based discriminant analysis"

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Wilgenbus, Erich Feodor. "The file fragment classification problem : a combined neural network and linear programming discriminant model approach / Erich Feodor Wilgenbus." Thesis, North-West University, 2013. http://hdl.handle.net/10394/10215.

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The increased use of digital media to store legal, as well as illegal data, has created the need for specialized tools that can monitor, control and even recover this data. An important task in computer forensics and security is to identify the true le type to which a computer le or computer le fragment belongs. File type identi cation is traditionally done by means of metadata, such as le extensions and le header and footer signatures. As a result, traditional metadata-based le object type identi cation techniques work well in cases where the required metadata is available and unaltered. However, traditional approaches are not reliable when the integrity of metadata is not guaranteed or metadata is unavailable. As an alternative, any pattern in the content of a le object can be used to determine the associated le type. This is called content-based le object type identi cation. Supervised learning techniques can be used to infer a le object type classi er by exploiting some unique pattern that underlies a le type's common le structure. This study builds on existing literature regarding the use of supervised learning techniques for content-based le object type identi cation, and explores the combined use of multilayer perceptron neural network classi ers and linear programming-based discriminant classi ers as a solution to the multiple class le fragment type identi cation problem. The purpose of this study was to investigate and compare the use of a single multilayer perceptron neural network classi er, a single linear programming-based discriminant classi- er and a combined ensemble of these classi ers in the eld of le type identi cation. The ability of each individual classi er and the ensemble of these classi ers to accurately predict the le type to which a le fragment belongs were tested empirically. The study found that both a multilayer perceptron neural network and a linear programming- based discriminant classi er (used in a round robin) seemed to perform well in solving the multiple class le fragment type identi cation problem. The results of combining multilayer perceptron neural network classi ers and linear programming-based discriminant classi ers in an ensemble were not better than those of the single optimized classi ers.
MSc (Computer Science), North-West University, Potchefstroom Campus, 2013
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Zaeri, Naser. "Computation and memory efficient face recognition using binarized eigenphases and component-based linear discriminant analysis for wide range applications." Thesis, University of Surrey, 2007. http://epubs.surrey.ac.uk/844078/.

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Face recognition finds many important applications in many life sectors and in particular in commercial and law enforcement. This thesis presents two novel methods which make face recognition more practical. In the first method, we propose an attractive solution for efficient face recognition systems that utilize low memory devices. The new technique applies the principal component analysis to the binarized phase spectrum of the Fourier transform of the covariance matrix constructed from the MPEG-7 Fourier Feature Descriptor vectors of the face images. Most of the algorithms proposed for face recognition are computationally exhaustive and hence they can not be used on devices constrained with limited memory; hence our method may play an important role in this area. The second method presented in this thesis proposes a new approach for efficient face representation and recognition by finding the best location component-based linear discriminant analysis. In this regard, the face image is decomposed into a number of components of certain size. Then the proposed scheme finds the best representation of the face image in most efficient way, taking into consideration both the recognition rate and the processing time. Note that the effect of the variation in a face image, when it is taken as a whole, is reduced when it is divided into components. As a result the performance of the system is enhanced. This method should find applications in systems requiring very high recognition and verification rates. Further, we demonstrate a solution to the problem of face occlusion using this method. The experimental results show that both proposed methods enhance the performance of the face recognition system and achieve a substantial saving in the computation time when compared to other known methods. It will be shown that the two proposed methods are very attractive for a wide range of applications for face recognition.
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Umunoza, Gasana Emelyne. "Misclassification Probabilities through Edgeworth-type Expansion for the Distribution of the Maximum Likelihood based Discriminant Function." Licentiate thesis, Linköpings universitet, Tillämpad matematik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-175873.

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This thesis covers misclassification probabilities via an Edgeworth-type expansion of the maximum likelihood based discriminant function. When deriving misclassification errors, first the expectation and variance in the population are assumed to be known where the variance is the same across populations and thereafter we consider the case where those parameters are unknown. Cumulants of the discriminant function for discriminating between two multivariate normal populations are derived. Approximate probabilities of the misclassification errors are established via an Edgeworth-type expansion using a standard normal distribution.
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Phan, Duy Nhat. "Algorithmes basés sur la programmation DC et DCA pour l’apprentissage avec la parcimonie et l’apprentissage stochastique en grande dimension." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0235/document.

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De nos jours, avec l'abondance croissante de données de très grande taille, les problèmes de classification de grande dimension ont été mis en évidence comme un challenge dans la communauté d'apprentissage automatique et ont beaucoup attiré l'attention des chercheurs dans le domaine. Au cours des dernières années, les techniques d'apprentissage avec la parcimonie et l'optimisation stochastique se sont prouvées être efficaces pour ce type de problèmes. Dans cette thèse, nous nous concentrons sur le développement des méthodes d'optimisation pour résoudre certaines classes de problèmes concernant ces deux sujets. Nos méthodes sont basées sur la programmation DC (Difference of Convex functions) et DCA (DC Algorithm) étant reconnues comme des outils puissants d'optimisation non convexe. La thèse est composée de trois parties. La première partie aborde le problème de la sélection des variables. La deuxième partie étudie le problème de la sélection de groupes de variables. La dernière partie de la thèse liée à l'apprentissage stochastique. Dans la première partie, nous commençons par la sélection des variables dans le problème discriminant de Fisher (Chapitre 2) et le problème de scoring optimal (Chapitre 3), qui sont les deux approches différentes pour la classification supervisée dans l'espace de grande dimension, dans lequel le nombre de variables est beaucoup plus grand que le nombre d'observations. Poursuivant cette étude, nous étudions la structure du problème d'estimation de matrice de covariance parcimonieuse et fournissons les quatre algorithmes appropriés basés sur la programmation DC et DCA (Chapitre 4). Deux applications en finance et en classification sont étudiées pour illustrer l'efficacité de nos méthodes. La deuxième partie étudie la L_p,0régularisation pour la sélection de groupes de variables (Chapitre 5). En utilisant une approximation DC de la L_p,0norme, nous prouvons que le problème approché, avec des paramètres appropriés, est équivalent au problème original. Considérant deux reformulations équivalentes du problème approché, nous développons différents algorithmes basés sur la programmation DC et DCA pour les résoudre. Comme applications, nous mettons en pratique nos méthodes pour la sélection de groupes de variables dans les problèmes de scoring optimal et d'estimation de multiples matrices de covariance. Dans la troisième partie de la thèse, nous introduisons un DCA stochastique pour des problèmes d'estimation des paramètres à grande échelle (Chapitre 6) dans lesquelles la fonction objectif est la somme d'une grande famille des fonctions non convexes. Comme une étude de cas, nous proposons un schéma DCA stochastique spécial pour le modèle loglinéaire incorporant des variables latentes
These days with the increasing abundance of data with high dimensionality, high dimensional classification problems have been highlighted as a challenge in machine learning community and have attracted a great deal of attention from researchers in the field. In recent years, sparse and stochastic learning techniques have been proven to be useful for this kind of problem. In this thesis, we focus on developing optimization approaches for solving some classes of optimization problems in these two topics. Our methods are based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) which are wellknown as one of the most powerful tools in optimization. The thesis is composed of three parts. The first part tackles the issue of variable selection. The second part studies the problem of group variable selection. The final part of the thesis concerns the stochastic learning. In the first part, we start with the variable selection in the Fisher's discriminant problem (Chapter 2) and the optimal scoring problem (Chapter 3), which are two different approaches for the supervised classification in the high dimensional setting, in which the number of features is much larger than the number of observations. Continuing this study, we study the structure of the sparse covariance matrix estimation problem and propose four appropriate DCA based algorithms (Chapter 4). Two applications in finance and classification are conducted to illustrate the efficiency of our methods. The second part studies the L_p,0regularization for the group variable selection (Chapter 5). Using a DC approximation of the L_p,0norm, we indicate that the approximate problem is equivalent to the original problem with suitable parameters. Considering two equivalent reformulations of the approximate problem we develop DCA based algorithms to solve them. Regarding applications, we implement the proposed algorithms for group feature selection in optimal scoring problem and estimation problem of multiple covariance matrices. In the third part of the thesis, we introduce a stochastic DCA for large scale parameter estimation problems (Chapter 6) in which the objective function is a large sum of nonconvex components. As an application, we propose a special stochastic DCA for the loglinear model incorporating latent variables
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Einestam, Ragnar, and Karl Casserfelt. "PiEye in the Wild: Exploring Eye Contact Detection for Small Inexpensive Hardware." Thesis, Malmö högskola, Fakulteten för teknik och samhälle (TS), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-20696.

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Ögonkontakt-sensorer skapar möjligheten att tolka användarens uppmärksamhet, vilketkan användas av system på en mängd olika vis. Dessa inkluderar att skapa nya möjligheterför människa-dator-interaktion och mäta mönster i uppmärksamhet hos individer.I den här uppsatsen gör vi ett försök till att konstruera en ögonkontakt-sensor med hjälpav en Raspberry Pi, med målet att göra den praktisk i verkliga scenarion. För att fastställaatt den är praktisk satte vi upp ett antal kriterier baserat på tidigare användning avögonkontakt-sensorer. För att möta dessa kriterier valde vi att använda en maskininlärningsmetodför att träna en klassificerare med bilder för att lära systemet att upptäcka omen användare har ögonkontakt eller ej. Vårt mål var att undersöka hur god prestanda vikunde uppnå gällande precision, hastighet och avstånd. Efter att ha testat kombinationerav fyra olika metoder för feature extraction kunde vi fastslå att den bästa övergripandeprecisionen uppnåddes genom att använda LDA-komprimering på pixeldatan från varjebild, medan PCA-komprimering var bäst när input-bilderna liknande de från träningen.När vi undersökte systemets hastighet fann vi att nedskalning av bilder hade en stor effektpå hastigheten, men detta sänkte också både precision och maximalt avstånd. Vi lyckadesminska den negativa effekten som en minskad skala hos en bild hade på precisionen, mendet maximala avståndet som sensorn fungerade på var fortfarande relativ till skalan och iförlängningen hastigheten.
Eye contact detection sensors have the possibility of inferring user attention, which can beutilized by a system in a multitude of different ways, including supporting human-computerinteraction and measuring human attention patterns. In this thesis we attempt to builda versatile eye contact sensor using a Raspberry Pi that is suited for real world practicalusage. In order to ensure practicality, we constructed a set of criteria for the system basedon previous implementations. To meet these criteria, we opted to use an appearance-basedmachine learning method where we train a classifier with training images in order to inferif users look at the camera or not. Our aim was to investigate how well we could detecteye contacts on the Raspberry Pi in terms of accuracy, speed and range. After extensivetesting on combinations of four different feature extraction methods, we found that LinearDiscriminant Analysis compression of pixel data provided the best overall accuracy, butPrincipal Component Analysis compression performed the best when tested on imagesfrom the same dataset as the training data. When investigating the speed of the system,we found that down-scaling input images had a huge effect on the speed, but also loweredthe accuracy and range. While we managed to mitigate the effects the scale had on theaccuracy, the range of the system is still relative to the scale of input images and byextension speed.
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Spinnato, Juliette. "Modèles de covariance pour l'analyse et la classification de signaux électroencéphalogrammes." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4727/document.

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Cette thèse s’inscrit dans le contexte de l’analyse et de la classification de signaux électroencéphalogrammes (EEG) par des méthodes d’analyse discriminante. Ces signaux multi-capteurs qui sont, par nature, très fortement corrélés spatialement et temporellement sont considérés dans le plan temps-fréquence. En particulier, nous nous intéressons à des signaux de type potentiels évoqués qui sont bien représentés dans l’espace des ondelettes. Par la suite, nous considérons donc les signaux représentés par des coefficients multi-échelles et qui ont une structure matricielle électrodes × coefficients. Les signaux EEG sont considérés comme un mélange entre l’activité d’intérêt que l’on souhaite extraire et l’activité spontanée (ou "bruit de fond"), qui est largement prépondérante. La problématique principale est ici de distinguer des signaux issus de différentes conditions expérimentales (classes). Dans le cas binaire, nous nous focalisons sur l’approche probabiliste de l’analyse discriminante et des modèles de mélange gaussien sont considérés, décrivant dans chaque classe les signaux en termes de composantes fixes (moyenne) et aléatoires. Cette dernière, caractérisée par sa matrice de covariance, permet de modéliser différentes sources de variabilité. Essentielle à la mise en oeuvre de l’analyse discriminante, l’estimation de cette matrice (et de son inverse) peut être dégradée dans le cas de grandes dimensions et/ou de faibles échantillons d’apprentissage, cadre applicatif de cette thèse. Nous nous intéressons aux alternatives qui se basent sur la définition de modèle(s) de covariance(s) particulier(s) et qui permettent de réduire le nombre de paramètres à estimer
The present thesis finds itself within the framework of analyzing and classifying electroencephalogram signals (EEG) using discriminant analysis. Those multi-sensor signals which are, by nature, highly correlated spatially and temporally are considered, in this work, in the timefrequency domain. In particular, we focus on low-frequency evoked-related potential-type signals (ERPs) that are well described in the wavelet domain. Thereafter, we will consider signals represented by multi-scale coefficients and that have a matrix structure electrodes × coefficients. Moreover, EEG signals are seen as a mixture between the signal of interest that we want to extract and spontaneous activity (also called "background noise") which is overriding. The main problematic is here to distinguish signals from different experimental conditions (class). In the binary case, we focus on the probabilistic approach of the discriminant analysis and Gaussian mixtures are used, describing in each class the signals in terms of fixed (mean) and random components. The latter, characterized by its covariance matrix, allow to model different variability sources. The estimation of this matrix (and of its inverse) is essential for the implementation of the discriminant analysis and can be deteriorated by high-dimensional data and/or by small learning samples, which is the application framework of this thesis. We are interested in alternatives that are based on specific covariance model(s) and that allow to decrease the number of parameters to estimate
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Marinósson, Sigurour Freyr. "Stability analysis of nonlinear systems with linear programming a Lyapunov functions based approach /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=982323697.

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LoPinto, Frank Anthony. "An Agent-Based Distributed Decision Support System Framework for Mediated Negotiation." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/27401.

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Implementing an e-market for limited supply perishable asset (LiSPA) products is a problem at the intersection of online purchasing and distributed decision support systems (DistDSS). In this dissertation, we introduce and define LiSPA products, provide real-world examples, develop a framework for a distributed system to implement an e-market for LiSPA products, and provide proof-of-concept for the two major components of the framework. The DistDSS framework requires customers to instantiate agents that learn their preferences and evaluate products on their behalf. Accurately eliciting and modeling customer preferences in a quick and easy manner is a major hurdle for implementing this agent-based system. A methodology is developed for this problem using conjoint analysis and neural networks. The framework also contains a model component that is addressed in this work. The model component is presented as a mediator of customer negotiation that uses the agent-based preference models mentioned above and employs a linear programming model to maximize overall satisfaction of the total market.
Ph. D.
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Pal, Anamitra. "PMU-Based Applications for Improved Monitoring and Protection of Power Systems." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/51093.

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Monitoring and protection of power systems is a task that has manifold objectives. Amongst others, it involves performing data mining, optimizing available resources, assessing system stresses, and doing data conditioning. The role of PMUs in fulfilling these four objectives forms the basis of this dissertation. Classification and regression tree (CART) built using phasor data has been extensively used in power systems. The splits in CART are based on a single attribute or a combination of variables chosen by CART itself rather than the user. But as PMU data consists of complex numbers, both the attributes, should be considered simultaneously for making critical decisions. An algorithm is proposed here that expresses high dimensional, multivariate data as a single attribute in order to successfully perform splits in CART. In order to reap maximum benefits from placement of PMUs in the power grid, their locations must be selected judiciously. A gradual PMU placement scheme is developed here that ensures observability as well as protects critical parts of the system. In order to circumvent the computational burden of the optimization, this scheme is combined with a topology-based system partitioning technique to make it applicable to virtually any sized system. A power system is a dynamic being, and its health needs to be monitored at all times. Two metrics are proposed here to monitor stress of a power system in real-time. Angle difference between buses located across the network and voltage sensitivity of buses lying in the middle are found to accurately reflect the static and dynamic stress of the system. The results indicate that by setting appropriate alerts/alarm limits based on these two metrics, a more secure power system operation can be realized. A PMU-only linear state estimator is intrinsically superior to its predecessors with respect to performance and reliability. However, ensuring quality of the data stream that leaves this estimator is crucial. A methodology for performing synchrophasor data conditioning and validation that fits neatly into the existing linear state estimation formulation is developed here. The results indicate that the proposed methodology provides a computationally simple, elegant solution to the synchrophasor data quality problem.
Ph. D.
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Nguyen, Ngoc Anh. "Explicit robust constrained control for linear systems : analysis, implementation and design based on optimization." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLC012/document.

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Les lois de commande affines par morceaux ont attiré une grande attention de la communauté d'automatique de contrôle grâce à leur pertinence pour des systèmes contraints, systèmes hybrides; également pour l'approximation de commandes nonlinéaires. Pourtant, leur mise en oeuvre est soumise à quelques difficultés. Motivé par l'intérêt à cette classe de commandes, cette thèse porte sur leur analyse, mise en oeuvre et synthèse.La première partie de cette thèse a pour but le calcul de la marge de robustesse et de la marge de fragilité pour une loi de commande affine par morceaux donnée et un système linéaire discret. Plus précisément, la marge de robustesse est définie comme l'ensemble des systèmes linéaires à paramètres variants que la loi de commande donnée garde les trajectoires dans de la région faisable. D'ailleurs, la marge de fragilité comprend toutes les variations des coefficients de la commande donnée telle que l'invariance de la région faisable soit encore garantie. Il est montré que si la région faisable donnée est un polytope, ces marges sont aussi des polytopes.La deuxième partie de ce manuscrit est consacrée au problème de l'optimalité inverse pour la classe des fonctions affines par morceaux. C'est-à-dire, l'objective est de définir un problème d'optimisation pour lequel la solution optimale est équivalente à la fonction affine par morceaux donnée. La méthodologie est fondée sur le convex lifting, i.e., un variable auxiliaire, scalaire, qui permet de définir un ensemble convex à partir de la partition d'état de la fonction affine par morceaux donnée. Il est montré que si la fonction affine par morceaux donnée est continue, la solution optimale de ce problème redéfini sera unique. Par contre, si la continuité n'est pas satisfaite, cette fonction affine par morceaux sera une solution optimale parmi les autres du problème redéfini.En ce qui concerne l’application dans la commande prédictive, il sera montré que n'importe quelle loi de commande affine par morceaux continue peut être obtenue par un autre problème de commande prédictive avec l'horizon de prédiction au plus égal à 2. A côté de cet aspect théorique, ce résultat sera utile pour faciliter la mise en oeuvre des lois de commandes affines par morceaux en évitant l'enregistrement de la partition de l'espace d'état. Dans la dernière partie de ce rapport, une famille de convex liftings servira comme des fonctions de Lyapunov. En conséquence, ce "convex lifting" sera déployé pour synthétiser des lois de commande robustes pour des systèmes linéaires incertains, également en présence de perturbations additives bornées. Des lois implicites et explicites seront obtenues en même temps. Cette méthode permet de garantir la faisabilité récursive et la stabilité robuste. Cependant, cette fonction de Lyapunov est limitée à l'ensemble λ −contractive maximal avec une constante scalaire 0 ≤ λ < 1 qui est plus petit que l'ensemble contrôlable maximal. Pour cette raison, une extension de cette méthode pour l'ensemble contrôlable de N − pas, sera présentée. Cette méthode est fondée sur des convex liftings en cascade où une variable auxiliaire sera utilisée pour servir comme une fonction de Lyapunov. Plus précisément, cette variable est non-négative, strictement décroissante pour les N premiers pas et égale toujours à 0 − après. Par conséquent, la stabilité robuste est garantie
Piecewise affine (PWA) feedback control laws have received significant attention due to their relevance for the control of constrained systems, hybrid systems; equally for the approximation of nonlinear control. However, they are associated with serious implementation issues. Motivated from the interest in this class of particular controllers, this thesis is mostly related to their analysis and design.The first part of this thesis aims to compute the robustness and fragility margins for a given PWA control law and a linear discrete-time system. More precisely, the robustness margin is defined as the set of linear time-varying systems such that the given PWA control law keeps the trajectories inside a given feasible set. On a different perspective, the fragility margin contains all the admissible variations of the control law coefficients such that the positive invariance of the given feasible set is still guaranteed. It will be shown that if the given feasible set is a polytope, then so are these robustness/fragility margins.The second part of this thesis focuses on inverse optimality problem for the class of PWA controllers. Namely, the goal is to construct an optimization problem whose optimal solution is equivalent to the given PWA function. The methodology is based on emph convex lifting: an auxiliary 1− dimensional variable which enhances the convexity characterization into recovered optimization problem. Accordingly, if the given PWA function is continuous, the optimal solution to this reconstructed optimization problem will be shown to be unique. Otherwise, if the continuity of this given PWA function is not fulfilled, this function will be shown to be one optimal solution to the recovered problem.In view of applications in linear model predictive control (MPC), it will be shown that any continuous PWA control law can be obtained by a linear MPC problem with the prediction horizon at most equal to 2 prediction steps. Aside from the theoretical meaning, this result can also be of help to facilitate implementation of PWA control laws by avoiding storing state space partition. Another utility of convex liftings will be shown in the last part of this thesis to be a control Lyapunov function. Accordingly, this convex lifting will be deployed in the so-called robust control design based on convex liftings for linear system affected by bounded additive disturbances and polytopic uncertainties. Both implicit and explicit controllers can be obtained. This method can also guarantee the recursive feasibility and robust stability. However, this control Lyapunov function is only defined over the maximal λ −contractive set for a given 0 ≤ λ < 1 which is known to be smaller than the maximal controllable set. Therefore, an extension of the above method to the N-steps controllable set will be presented. This method is based on a cascade of convex liftings where an auxiliary variable will be used to emulate a Lyapunov function. Namely, this variable will be shown to be non-negative, to strictly decrease for N first steps and to stay at 0 afterwards. Accordingly, robust stability is sought
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Books on the topic "Linear programming-based discriminant analysis"

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Baillo, Amparo, Antonio Cuevas, and Ricardo Fraiman. Classification methods for functional data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.10.

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This article reviews the literature concerning supervised and unsupervised classification of functional data. It first explains the meaning of unsupervised classification vs. supervised classification before discussing the supervised classification problem in the infinite-dimensional case, showing that its formal statement generally coincides with that of discriminant analysis in the classical multivariate case. It then considers the optimal classifier and plug-in rules, empirical risk and empirical minimization rules, linear discrimination rules, the k nearest neighbor (k-NN) method, and kernel rules. It also describes classification based on partial least squares, classification based on reproducing kernels, and depth-based classification. Finally, it examines unsupervised classification methods, focusing on K-means for functional data, K-means for data in a Hilbert space, and impartial trimmed K-means for functional data. Some practical issues, in particular real-data examples and simulations, are reviewed and some selected proofs are given.
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Hector, Andy. The New Statistics with R. 2nd ed. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198798170.001.0001.

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Statistics is a fundamental component of the scientific toolbox, but learning the basics of this area of mathematics is one of the most challenging parts of a research training. This book gives an up-to-date introduction to the classical techniques and modern extensions of linear-model analysis—one of the most useful approaches in the analysis of scientific data in the life and environmental sciences. The book emphasizes an estimation-based approach that takes account of recent criticisms of overuse of probability values and introduces the alternative approach using information criteria. The book is based on the use of the open-source R programming language for statistics and graphics, which is rapidly becoming the lingua franca in many areas of science. This second edition adds new chapters, including one discussing some of the complexities of linear-model analysis and another introducing reproducible research documents using the R Markdown package. Statistics is introduced through worked analyses performed in R using interesting data sets from ecology, evolutionary biology, and environmental science. The data sets and R scripts are available as supporting material.
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Book chapters on the topic "Linear programming-based discriminant analysis"

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Nhat, Phan Duy, Manh Cuong Nguyen, and Hoai An Le Thi. "A DC Programming Approach for Sparse Linear Discriminant Analysis." In Advanced Computational Methods for Knowledge Engineering, 65–74. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06569-4_4.

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Gonzalez-Reyna, Sheila Esmeralda, Juan Gabriel Avina-Cervantes, Sergio Eduardo Ledesma-Orozco, Ivan Cruz-Aceves, and M. de Guadalupe Garcia-Hernandez. "Traffic Sign Recognition Based on Linear Discriminant Analysis." In Lecture Notes in Computer Science, 185–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-45111-9_16.

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Joachimsthaler, Erich A. "Linear Programming as an Alternative to Standard Discriminant Function Analysis." In Proceedings of the 1984 Academy of Marketing Science (AMS) Annual Conference, 460–64. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16973-6_99.

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Loog, Marco, and Are C. Jensen. "Constrained Log-Likelihood-Based Semi-supervised Linear Discriminant Analysis." In Lecture Notes in Computer Science, 327–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34166-3_36.

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Zhang, Wenchao, Shiguang Shan, Wen Gao, Yizheng Chang, and Bo Cao. "Component-Based Cascade Linear Discriminant Analysis for Face Recognition." In Advances in Biometric Person Authentication, 288–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-30548-4_33.

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Dong, Weijun, Mingquan Zhou, and Guohua Geng. "Face Recognition Based on DWT and Improved Linear Discriminant Analysis." In Recent Advances in Computer Science and Information Engineering, 699–704. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25781-0_102.

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Punithavathi, P., and S. Geetha. "Random Permutation-Based Linear Discriminant Analysis for Cancelable Biometric Recognition." In Lecture Notes in Electrical Engineering, 593–603. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-6977-1_43.

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Du, Minggang, and Shanwen Zhang. "Plant Classification Using Leaf Image Based on 2D Linear Discriminant Analysis." In Lecture Notes in Computer Science, 454–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14922-1_56.

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Chen, Lijiang, Wentao Dou, and Xia Mao. "Schatten-p Norm Based Linear Regression Discriminant Analysis for Face Recognition." In Image and Graphics Technologies and Applications, 45–56. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1702-6_5.

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Pan, I.-Hui, Ping Sheng Huang, and Te-Jen Chang. "DCT-Based Watermarking for Color Images via Two-Dimensional Linear Discriminant Analysis." In Lecture Notes in Electrical Engineering, 57–65. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6996-0_7.

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Conference papers on the topic "Linear programming-based discriminant analysis"

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Junoh, Ahmad Kadri, and Muhammad Naufal Mansor. "Safety system based on Linear Discriminant Analysis." In 2012 International Symposium on Instrumentation & Measurement, Sensor Network and Automation (IMSNA). IEEE, 2012. http://dx.doi.org/10.1109/msna.2012.6324510.

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Song, Fengxi, Dayong Mei, and Hongfeng Li. "Feature Selection Based on Linear Discriminant Analysis." In 2010 International Conference on Intelligent System Design and Engineering Application (ISDEA). IEEE, 2010. http://dx.doi.org/10.1109/isdea.2010.311.

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An, Lei-Lei, and Hong-Jie Xing. "Linear discriminant analysis based on Zp-norm maximization." In 2014 2nd International Conference on Information Technology and Electronic Commerce (ICITEC). IEEE, 2014. http://dx.doi.org/10.1109/icitec.2014.7105578.

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Lee, Hung-Shin, and Berlin Chen. "Empirical error rate minimization based linear discriminant analysis." In ICASSP 2009 - 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009. http://dx.doi.org/10.1109/icassp.2009.4959955.

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Elhadji Ille Gado, Nassara, Edith Grall-Maës, and Malika Kharouf. "Linear Discriminant Analysis based on Fast Approximate SVD." In 6th International Conference on Pattern Recognition Applications and Methods. SCITEPRESS - Science and Technology Publications, 2017. http://dx.doi.org/10.5220/0006148603590365.

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Lim, Yai-Fung, Sharipah Soaad Syed Yahaya, and Hazlina Ali. "Robust linear discriminant analysis with distance based estimators." In PROCEEDINGS OF THE 13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5012246.

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Mehrabani, Mahnoosh, Ozlem Kalinli, and Ruxin Chen. "Emotion clustering based on probabilistic linear discriminant analysis." In Interspeech 2015. ISCA: ISCA, 2015. http://dx.doi.org/10.21437/interspeech.2015-327.

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Min, Hwang-Ki, Yuxi Hou, Iickho Song, Seungwon Lee, and Hyun Gu Kang. "Complexity reduction for null space-based linear discriminant analysis." In 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim). IEEE, 2011. http://dx.doi.org/10.1109/pacrim.2011.6032989.

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Kan, Meina, Shiguang Shan, Dong Xu, and Xilin Chen. "Side-Information based Linear Discriminant Analysis for Face Recognition." In British Machine Vision Conference 2011. British Machine Vision Association, 2011. http://dx.doi.org/10.5244/c.25.125.

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Gao, Changxin, Feifei Chen, Jin-Gang Yu, Rui Huang, and Nong Sang. "Exemplar-based linear discriminant analysis for robust object tracking." In 2014 IEEE International Conference on Image Processing (ICIP). IEEE, 2014. http://dx.doi.org/10.1109/icip.2014.7025077.

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