In this thesis, cluster analysis was applied to data comprising of customer spending habits at a retail chain in order to perform customer segmentation. The method used was a two-step cluster procedure in which the first step consisted of feature engineering, a square root transformation of the data in order to handle big spenders in the data set and finally principal component analysis in order to reduce the dimensionality of the data set. This was done to reduce the effects of high dimensionality. The second step consisted of applying clustering algorithms to the transformed data. The methods used were K-means clustering, Gaussian mixture models in the MCLUST family, t-distributed mixture models in the tEIGEN family and non-negative matrix factorization (NMF). For the NMF clustering a slightly different data pre-processing step was taken, specifically no PCA was performed. Clustering partitions were compared on the basis of the Silhouette index, Davies-Bouldin index and subject matter knowledge, which revealed that K-means clustering with K = 3 produces the most reasonable clusters. This algorithm was able to separate the customer into different segments depending on how many purchases they made overall and in these clusters some minor differences in spending habits are also evident. In other words there is some support for the claim that the customer segments have some variation in their spending habits. / I denna uppsats har klusteranalys tillämpats på data bestående av kunders konsumtionsvanor hos en detaljhandelskedja för att utföra kundsegmentering. Metoden som använts bestod av en två-stegs klusterprocedur där det första steget bestod av att skapa variabler, tillämpa en kvadratrotstransformation av datan för att hantera kunder som spenderar långt mer än genomsnittet och slutligen principalkomponentanalys för att reducera datans dimension. Detta gjordes för att mildra effekterna av att använda en högdimensionell datamängd. Det andra steget bestod av att tillämpa klusteralgoritmer på den transformerade datan. Metoderna som användes var K-means klustring, gaussiska blandningsmodeller i MCLUST-familjen, t-fördelade blandningsmodeller från tEIGEN-familjen och icke-negativ matrisfaktorisering (NMF). För klustring med NMF användes förbehandling av datan, mer specifikt genomfördes ingen PCA. Klusterpartitioner jämfördes baserat på silhuettvärden, Davies-Bouldin-indexet och ämneskunskap, som avslöjade att K-means klustring med K=3 producerar de rimligaste resultaten. Denna algoritm lyckades separera kunderna i olika segment beroende på hur många köp de gjort överlag och i dessa segment finns vissa skillnader i konsumtionsvanor. Med andra ord finns visst stöd för påståendet att kundsegmenten har en del variation i sina konsumtionsvanor.

L’avantage du train depuis sa création est sa faible résistance à l’avancement du fait du contact fer-fer de la roue sur le rail conduisant à une adhérence réduite. Cependant cette adhérence faible est aussi un inconvénient majeur : étant dépendante des conditions environnementales, elle est facilement altérée lors d’une pollution du rail (végétaux, corps gras, eau, etc.). Aujourd’hui, les mesures prises face à des situations d'adhérence dégradée impactent directement les performances du système et conduisent notamment à une perte de capacité de transport. L’objectif du projet est d’utiliser les nouvelles technologies d’imagerie spectrale pour identifier sur les rails les zones à adhérence réduite et leur cause afin d’alerter et d’adapter rapidement les comportements. La stratégie d’étude a pris en compte les trois points suivants : • Le système de détection, installé à bord de trains commerciaux, doit être indépendant du train. • La détection et l’identification ne doivent pas interagir avec la pollution pour ne pas rendre la mesure obsolète. Pour ce faire le principe d’un Contrôle Non Destructif est retenu. • La technologie d’imagerie spectrale permet de travailler à la fois dans le domaine spatial (mesure de distance, détection d’objet) et dans le domaine fréquentiel (détection et reconnaissance de matériaux par analyse de signatures spectrales). Dans le temps imparti des trois ans de thèse, nous nous sommes focalisés sur la validation du concept par des études et analyses en laboratoire, réalisables dans les locaux de SNCF Ingénierie & Projets. Les étapes clés ont été la réalisation d’un banc d’évaluation et le choix du système de vision, la création d'une bibliothèque de signatures spectrales de référence et le développement d'algorithmes classification supervisées et non supervisées des pixels. Ces travaux ont été valorisés par le dépôt d'un brevet et la publication d'articles dans des conférences IEEE. / The advantage of the train since its creation is in its low resistance to the motion, due to the contact iron-iron of the wheel on the rail leading to low adherence. However this low adherence is also a major drawback : being dependent on the environmental conditions, it is easily deteriorated when the rail is polluted (vegetation, grease, water, etc). Nowadays, strategies to face a deteriorated adherence impact the performance of the system and lead to a loss of transport capacity. The objective of the project is to use a new spectral imaging technology to identify on the rails areas with reduced adherence and their cause in order to quickly alert and adapt the train's behaviour. The study’s strategy took into account the three following points : -The detection system, installed on board of commercial trains, must be independent of the train. - The detection and identification process should not interact with pollution in order to keep the measurements unbiased. To do so, we chose a Non Destructive Control method. - Spectral imaging technology makes it possible to work with both spatial information (distance’s measurement, target detection) and spectral information (material detection and recognition by analysis of spectral signatures). In the assigned time, we focused on the validation of the concept by studies and analyses in laboratory, workable in the office at SNCF Ingénierie & Projets. The key steps were the creation of the concept's evaluation bench and the choice of a Vision system, the creation of a library containing reference spectral signatures and the development of supervised and unsupervised pixels classification. A patent describing the method and process has been filed and published.

Raman spectroscopy provides a powerful means of chemical identification in a variety of fields, partly because of its non-contact nature and the speed at which measurements can be taken. The development of powerful, inexpensive lasers and sensitive charge-coupled device (CCD) detectors has led to widespread use of commercial and scientific Raman systems. However, relatively little work has been done developing physics-based probabilistic models for Raman measurement systems and crafting inference algorithms within the framework of statistical estimation and detection theory. The objective of this thesis is to develop algorithms and performance bounds for the identification of chemicals from their Raman spectra. First, a Poisson measurement model based on the physics of a dispersive Raman device is presented. The problem is then expressed as one of deterministic parameter estimation, and several methods are analyzed for computing the maximum-likelihood (ML) estimates of the mixing coefficients under our data model. The performance of these algorithms is compared against the Cramer-Rao lower bound (CRLB). Next, the Raman detection problem is formulated as one of multiple hypothesis detection (MHD), and an approximation to the optimal decision rule is presented. The resulting approximations are related to the minimum description length (MDL) approach to inference. In our simulations, this method is seen to outperform two common general detection approaches, the spectral unmixing approach and the generalized likelihood ratio test (GLRT). The MHD framework is applied naturally to both the detection of individual target chemicals and to the detection of chemicals from a given class. The common, yet vexing, scenario is then considered in which chemicals are present that are not in the known reference library. A novel variation of nonnegative matrix factorization (NMF) is developed to address this problem. Our simulations indicate that this algorithm gives better estimation performance than the standard two-stage NMF approach and the fully supervised approach when there are chemicals present that are not in the library. Finally, estimation algorithms are developed that take into account errors that may be present in the reference library. In particular, an algorithm is presented for ML estimation under a Poisson errors-in-variables (EIV) model. It is shown that this same basic approach can also be applied to the nonnegative total least squares (NNTLS) problem. Most of the techniques developed in this thesis are applicable to other problems in which an object is to be identified by comparing some measurement of it to a library of known constituent signatures.

Reducing interference noise in a noisy speech recording has been a challenging task for many years yet has a variety of applications, for example, in handsfree mobile communications, in speech recognition, and in hearing aids. Traditional single-channel noise reduction schemes, such as Wiener filtering, do not work satisfactorily in the presence of non-stationary background noise. Alternatively, supervised approaches, where the noise type is known in advance, lead to higher-quality enhanced speech signals. This dissertation proposes supervised and unsupervised single-channel noise reduction algorithms. We consider two classes of methods for this purpose: approaches based on nonnegative matrix factorization (NMF) and methods based on hidden Markov models (HMM).  The contributions of this dissertation can be divided into three main (overlapping) parts. First, we propose NMF-based enhancement approaches that use temporal dependencies of the speech signals. In a standard NMF, the important temporal correlations between consecutive short-time frames are ignored. We propose both continuous and discrete state-space nonnegative dynamical models. These approaches are used to describe the dynamics of the NMF coefficients or activations. We derive optimal minimum mean squared error (MMSE) or linear MMSE estimates of the speech signal using the probabilistic formulations of NMF. Our experiments show that using temporal dynamics in the NMF-based denoising systems improves the performance greatly. Additionally, this dissertation proposes an approach to learn the noise basis matrix online from the noisy observations. This relaxes the assumption of an a-priori specified noise type and enables us to use the NMF-based denoising method in an unsupervised manner. Our experiments show that the proposed approach with online noise basis learning considerably outperforms state-of-the-art methods in different noise conditions.  Second, this thesis proposes two methods for NMF-based separation of sources with similar dictionaries. We suggest a nonnegative HMM (NHMM) for babble noise that is derived from a speech HMM. In this approach, speech and babble signals share the same basis vectors, whereas the activation of the basis vectors are different for the two signals over time. We derive an MMSE estimator for the clean speech signal using the proposed NHMM. The objective evaluations and performed subjective listening test show that the proposed babble model and the final noise reduction algorithm outperform the conventional methods noticeably. Moreover, the dissertation proposes another solution to separate a desired source from a mixture with arbitrarily low artifacts.  Third, an HMM-based algorithm to enhance the speech spectra using super-Gaussian priors is proposed. Our experiments show that speech discrete Fourier transform (DFT) coefficients have super-Gaussian rather than Gaussian distributions even if we limit the speech data to come from a specific phoneme. We derive a new MMSE estimator for the speech spectra that uses super-Gaussian priors. The results of our evaluations using the developed noise reduction algorithm support the super-Gaussianity hypothesis. / <p>QC 20130916</p>

Le phénomène du cocktail party fait référence à notre remarquable capacité à nous concentrer sur une seule voix dans des environnements bruyants. Dans cette thèse, nous concevons, implémentons et évaluons une approche computationnelle nommée GCC-NMF pour résoudre ce problème. GCC-NMF combine l’apprentissage automatique non supervisé par la factorisation matricielle non négative (NMF) avec la méthode de localisation spatiale à corrélation croisée généralisée (GCC). Les atomes du dictionnaire NMF sont attribués au locuteur cible ou à l’interférence à chaque instant en fonction de leurs emplacements spatiaux estimés. Nous commençons par étudier GCC-NMF dans le contexte hors ligne, où des mélanges de 10 secondes sont traités à la fois. Nous développons ensuite une variante temps réel de GCC-NMF et réduisons par la suite sa latence algorithmique inhérente de 64 ms à 2 ms avec une méthode asymétrique de transformée de Fourier de courte durée (STFT). Nous montrons que des latences aussi faibles que 6 ms, dans la plage des délais tolérables pour les aides auditives, sont possibles sur les plateformes embarquées actuelles. Nous évaluons la performance de GCC-NMF sur des données publiquement disponibles de la campagne d’évaluation de séparation des signaux SiSEC. La qualité de séparation objective est quantifiée avec les méthodes PEASS, estimant les évaluations subjectives humaines, ainsi que BSS Eval basée sur le rapport signal sur bruit (SNR) traditionnel. Bien que GCC-NMF hors ligne ait moins bien performé que d’autres méthodes du défi SiSEC en termes de métriques SNR, ses scores PEASS sont comparables aux meilleurs résultats. Dans le cas de GCC-NMF en ligne, alors que les métriques basées sur le SNR favorisent à nouveau d’autres méthodes, GCC-NMF surpasse toutes les approches précédentes sauf une en termes de scores PEASS globaux, obtenant des résultats comparables au masque binaire idéale. Nous montrons que GCC-NMF augmente la qualité objective et les métriques d’intelligibilité STOI et ESTOI sur une large gamme de SNR d’entrée de -30 à 20 dB, avec seulement des réductions mineures pour les SNR d’entrée supérieurs à 20 dB. GCC-NMF présente plusieurs caractéristiques souhaitables lorsqu’on le compare aux approches existantes. Contrairement aux méthodes d’analyse de scène auditive computationnelle (CASA), GCC-NMF ne nécessite aucune connaissance préalable sur la nature des signaux d’entrée et pourrait donc convenir aux applications de séparation et de débruitage de source dans un grand nombre de domaines. Dans le cas de GCC-NMF en ligne, seule une petite quantité de données non étiquetées est nécessaire pour apprendre le dictionnaire NMF. Cela se traduit par une plus grande flexibilité et un apprentissage beaucoup plus rapide par rapport aux approches supervisées, y compris les solutions basées sur NMF et les réseaux neuronaux profonds qui reposent sur de grands ensembles de données étiquetées. Enfin, contrairement aux méthodes de séparation de source aveugle (BSS) qui reposent sur des statistiques de signal accumulées, GCC-NMF fonctionne indépendamment pour chaque trame, ce qui permet des applications en temps réel à faible latence. / Abstract: The cocktail party phenomenon refers to our remarkable ability to focus on a single voice in noisy environments. In this thesis, we design, implement, and evaluate a computational approach to solving this problem named GCC-NMF. GCC-NMF combines unsupervised machine learning via non-negative matrix factorization (NMF) with the generalized cross-correlation (GCC) spatial localization method. Individual NMF dictionary atoms are attributed to the target speaker or background interference at each point in time based on their estimated spatial locations. We begin by studying GCC-NMF in the offline context, where entire 10-second mixtures are treated at once. We then develop an online, instantaneous variant of GCC-NMF and subsequently reduce its inherent algorithmic latency from 64 ms to 2 ms with an asymmetric short-time Fourier transform (STFT) windowing method. We show that latencies as low as 6 ms, within the range of tolerable delays for hearing aids, are possible on current hardware platforms. We evaluate the performance of GCC-NMF on publicly available data from the Signal Separation Evaluation Campaign (SiSEC), where objective separation quality is quantified using the signal-to-noise ratio (SNR)-based BSS Eval and perceptually-motivated PEASS toolboxes. Though offline GCC-NMF underperformed other methods from the SiSEC challenge in terms of the SNR-based metrics, its PEASS scores were comparable with the best results. In the case of online GCC-NMF, while SNR-based metrics again favoured other methods, GCC-NMF outperformed all but one of the previous approaches in terms of overall PEASS scores, achieving comparable results to the ideal binary mask (IBM) baseline. Furthermore, we show that GCC-NMF increases objective speech quality and the STOI and ETOI speech intelligibility metrics over a wide range of input SNRs from -30 dB to 20 dB, with only minor reductions for input SNRs greater than 20 dB. GCC-NMF exhibits a number of desirable characteristics when compared existing approaches. Unlike computational auditory scene analysis (CASA) methods, GCC-NMF requires no prior knowledge about the nature of the input signals, and may thus be suitable for source separation and denoising applications in a wide range of fields. In the case of online GCC-NMF, only a small amount of unlabeled data is required to pre-train the NMF dictionary. This results in much greater flexibility and significantly faster training when compared to supervised approaches including NMF and deep neural network-based solutions that rely on large, supervised datasets. Finally, in contrast with blind source separation (BSS) methods that rely on accumulated signal statistics, GCC-NMF operates independently for each time frame, allowing for low latency, real-time applications.

The ability to automatically analyze and segment news articles by their content is a growing research field. This thesis explores the unsupervised machine learning method topic modeling applied on Swedish news articles for generating topics to describe and segment articles. Specifically, the algorithms non-negative matrix factorization (NMF) and the latent Dirichlet allocation (LDA) are implemented and evaluated. Their usefulness in the news media industry is assessed by its ability to serve as a uniform categorization framework for news articles. This thesis fills a research gap by studying the application of topic modeling on Swedish news articles and contributes by showing that this can yield meaningful results. It is shown that Swedish text data requires extensive data preparation for successful topic models and that nouns exclusively and especially common nouns are the most suitable words to use. Furthermore, the results show that both NMF and LDA are valuable as content analysis tools and categorization frameworks, but they have different characteristics, hence optimal for different use cases. Lastly, the conclusion is that topic models have issues since they can generate unreliable topics that could be misleading for news consumers, but that they nonetheless can be powerful methods for analyzing and segmenting articles efficiently on a grand scale by organizations internally. The thesis project is a collaboration with one of Sweden’s largest media groups and its results have led to a topic modeling implementation for large-scale content analysis to gain insight into readers’ interests.

The purpose of this study was to examine the trends, attrition and retention rates of National Merit Finalists at the University of Central Florida between the years of 1997 to 2005. This study was intended to provide information for higher education practitioners, faculty, and administrators to help them better understand the expectations and current trends of National Merit Finalists. The problem was to determine how to increase recruitment and retention while decreasing the attrition rates of these highly desirable students. The importance of this study includes identifying trends that may aid in future recruitment efforts for National Merit Finalists; finding the causes of dissatisfaction towards the University among these students; and identifying specific areas in which to alleviate those dissatisfactions. The results will hopefully provide insight into specific recruitment, services, and programming options for these students. The study examined data that was collected from the University of Central Florida's Burnett Honors College database known as FileMaker 8.0. The data examined characteristics such as grade point averages (high school and college); valedictorian and salutatorian status; test scores (SAT and ACT); Honors in the Major (undergraduate thesis) students; Honors and university status (withdrawn, probation, removed, disqualified, enrolled, graduated); Honors college attrition; university attrition; ethnicity; gender ratios; majors; and, prestigious scholarships awarded in college (such as the Rhodes, Truman, Marshall). The actual size of the sample was one hundred ninety-eight National Merit Finalists. Data was also collected from a survey given to all University of Central Florida National Merit Finalists. Descriptive statistics were reported for each of the components examined. This data examined the types of scholarship packages that National Merit Finalists were offered; the reasons students chose the University of Central Florida over other universities; the college recruitment process; hours studied for the PSAT; siblings; perceptions on being a National Merit Finalist; the number of times students changed their majors; job status; transportation; computer attainment; disabilities; and the potential disadvantages of being labeled as a National Merit Finalist. The data could be utilized to examine the trends of our National Merit Finalists, in order to see what is working and what is not in terms or recruitment and retention; and also to further examine what these students want from their institutions. Findings indicated that problems exist in regard to the following: the recruitment of female and minority National Merit Finalists; males historically score higher on the SAT than females; decreasing the attrition rates of this population at the University of Central Florida; the majority of National Merit Finalists at the University of Central Florida come from Florida; the majority of National Merit Finalists at the University of Central Florida do not tend to be high school salutatorians or valedictorians; high school counselors seem to be the least effective tool for recruiting National Merit Finalists at the University of Central Florida; and the majority of National Merit Finalists at the University of Central Florida did not study at all for the PSAT test. However, the University of Central Florida is extremely competitive with other institutions of higher education with regard to scholarship packages. Results also revealed the following: the SAT is a more widely accepted tool for determining NMSC status as opposed to the ACT; the majority of National Merit Finalists have a GPA between 3.600 and 3.999 at the University of Central Florida; the University of Central Florida is succeeding in making its National Merit Finalists feel special during the recruitment process; the most influential reason that National Merit Finalists are choosing UCF is based upon the financial scholarship packages they are offered; and the majority of National Merit Finalists at the University of Central Florida do not feel that there are disadvantages toward being labeled as such. This data provides a basis for further research on National Merit Finalists trends, attrition, and retention. Practical considerations are revealed in the data that will influence future recruitment methods and lead to higher retention rates and increased student satisfaction. Several other recommendations are made to conduct further research studies on the trends, attrition, and retention rates of National Merit Finalists.

Ces travaux de thèse concernent le développement de nouvelles méthodes de séparation aveugle de mélanges linéaires instantanés pour des applications à des données hyperspectrales en astrophysique. Nous avons proposé trois approches pour effectuer la séparation des données. Une première contribution est fondée sur l'hybridation de deux méthodes existantes de séparation aveugle de source (SAS) : la méthode SpaceCORR nécessitant une hypothèse de parcimonie et une méthode de factorisation en matrices non négatives (NMF). Nous montrons que l'utilisation des résultats de SpaceCORR pour initialiser la NMF permet d'améliorer les performances des méthodes utilisées seules. Nous avons ensuite proposé une première méthode originale permettant de relâcher la contrainte de parcimonie de SpaceCORR. La méthode MASS (pour \textit{Maximum Angle Source Separation}) est une méthode géométrique basée sur l'extraction de pixels mono-sources pour réaliser la séparation des données. Nous avons également étudié l'hybridation de MASS avec la NMF. Enfin, nous avons proposé une seconde approche permettant de relâcher la contrainte de parcimonie de SpaceCORR. La méthode originale SIBIS (pour \textit{Subspace-Intersection Blind Identification and Separation}) est une méthode géométrique basée sur l'identification de l'intersection de sous-espaces engendrés par des régions de l'image hyperspectrale. Ces intersections permettent, sous une hypothèse faible de parcimonie, de réaliser la séparation des données. L'ensemble des approches proposées dans ces travaux ont été validées par des tests sur données simulées puis appliquées sur données réelles. Les résultats obtenus sur ces données sont très encourageants et sont comparés à ceux obtenus par des méthodes de la littérature. / This thesis deals with the development of new blind separation methods for linear instantaneous mixtures applicable to astrophysical hyperspectral data sets. We propose three approaches to perform data separation. A first contribution is based on hybridization of two existing blind source separation (BSS) methods: the SpaceCORR method, requiring a sparsity assumption, and a non-negative matrix factorization (NMF) method. We show that using SpaceCORR results to initialize the NMF improves the performance of the methods used alone. We then proposed a first original method to relax the sparsity constraint of SpaceCORR. The method called MASS (Maximum Angle Source Separation) is a geometric method based on the extraction of single-source pixels to achieve the separation of data. We also studied the hybridization of MASS with the NMF. Finally, we proposed an approach to relax the sparsity constraint of SpaceCORR. The original method called SIBIS (Subspace-Intersection Blind Identification and Separation) is a geometric method based on the identification of intersections of subspaces generated by regions of the hyperspectral image. Under a sparsity assumption, these intersections allow one to achieve the separation of the data. The approaches proposed in this manuscript have been validated by experimentations on simulated data and then applied to real data. The results obtained on our data are very encouraging and are compared with those obtained by methods from the literature.

In this thesis, improving the performance of the automatic recognition of the Doppler radar targets is studied. The radar used in this study is a ground-surveillance doppler radar. Target types are car, truck, bus, tank, helicopter, moving man and running man. The input of this thesis is the output of the real doppler radar signals which are normalized and preprocessed (TRP vectors: Target Recognition Pattern vectors) in the doctorate thesis by Erdogan (2002). TRP vectors are normalized and homogenized doppler radar target signals with respect to target speed, target aspect angle and target range. Some target classes have repetitions in time in their TRPs. By the use of these repetitions, improvement of the target type classification performance is studied. K-Nearest Neighbor (KNN) and Support Vector Machine (SVM) algorithms are used for doppler radar target classification and the results are evaluated. Before classification PCA (Principal Component Analysis), LDA (Linear Discriminant Analysis), NMF (Nonnegative Matrix Factorization) and ICA (Independent Component Analysis) are implemented and applied to normalized doppler radar signals for feature extraction and dimension reduction in an efficient way. These techniques transform the input vectors, which are the normalized doppler radar signals, to another space. The effects of the implementation of these feature extraction algoritms and the use of the repetitions in doppler radar target signals on the doppler radar target classification performance are studied.

Basés sur les outils théoriques et algorithmiques de la programmation DC et DCA, les travaux de recherche dans cette thèse portent sur les approches locales et globales pour l'optimisation non convexe et l'optimisation globale en variables mixtes entières. La thèse comporte 5 chapitres. Le premier chapitre présente les fondements de la programmation DC et DCA, et techniques de Séparation et Evaluation (B&B) (utilisant la technique de relaxation DC pour le calcul des bornes inférieures de la valeur optimale) pour l'optimisation globale. Y figure aussi des résultats concernant la pénalisation exacte pour la programmation en variables mixtes entières. Le deuxième chapitre est consacré au développement d'une méthode DCA pour la résolution d'une classe NP-difficile des programmes non convexes non linéaires en variables mixtes entières. Ces problèmes d'optimisation non convexe sont tout d'abord reformulées comme des programmes DC via les techniques de pénalisation en programmation DC de manière que les programmes DC résultants soient efficacement résolus par DCA et B&B bien adaptés. Comme première application en optimisation financière, nous avons modélisé le problème de gestion de portefeuille sous le coût de transaction concave et appliqué DCA et B&B à sa résolution. Dans le chapitre suivant nous étudions la modélisation du problème de minimisation du coût de transaction non convexe discontinu en gestion de portefeuille sous deux formes : la première est un programme DC obtenu en approximant la fonction objectif du problème original par une fonction DC polyèdrale et la deuxième est un programme DC mixte 0-1 équivalent. Et nous présentons DCA, B&B, et l'algorithme combiné DCA-B&B pour leur résolution. Le chapitre 4 étudie la résolution exacte du problème multi-objectif en variables mixtes binaires et présente deux applications concrètes de la méthode proposée. Nous nous intéressons dans le dernier chapitre à ces deux problématiques challenging : le problème de moindres carrés linéaires en variables entières bornées et celui de factorisation en matrices non négatives (Nonnegative Matrix Factorization (NMF)). La méthode NMF est particulièrement importante de par ses nombreuses et diverses applications tandis que les applications importantes du premier se trouvent en télécommunication. Les simulations numériques montrent la robustesse, rapidité (donc scalabilité), performance et la globalité de DCA par rapport aux méthodes existantes.