Cette thèse porte sur le problème de Séparation Aveugle de Sources (SAS) en présence de données aberrantes. La plupart des méthodes de SAS sont faussées par la présence de déviations structurées par rapport au modèle de mélange linéaire classique: des évènements physiques inattendus ou des dysfonctionnements de capteurs en sont des exemples fréquents.Nous proposons un nouveau modèle prenant en compte explicitement les données aberrantes. Le problème de séparation en résultant, mal posé, est adressé grâce à la parcimonie. L'utilisation de cette dernière est particulièrement intéressante en SAS robuste car elle permet simultanément de démélanger les sources et de séparer les différentes contributions. Ces travaux sont étendus pour l'estimation de variabilité spectrale pour l'imagerie hyperspectrale terrestre.Des comparaisons avec des méthodes de l'état-de-l'art montrent la robustesse et la fiabilité des algorithmes associés pour un large éventail de configurations, incluant le cas déterminé. / This manuscript addresses the Blind Source Separation (BSS) problem in the presence of outliers. Most BSS techniques are hampered by the presence of structured deviations from the standard linear mixing model, such as unexpected physical events or malfunctions of sensors. We propose a new data model taking explicitly into account the deviations. The resulting joint estimation of the components is an ill-posed problem, tackled using sparse modeling. The latter is particularly efficient for solving robust BSS since it allows for a robust unmixing of the sources jointly with a precise separation of the components. These works are then extended for the estimation of spectral variability in the framework of terrestrial hyperspectral imaging. Numerical experiments highlight the robustness and reliability of the proposed algorithms in a wide range of settings, including the full-rank regime.

In our daily life, time is of the essence. People do not have time to browse through hundreds of thousands of digital items every day to find the right item for them. This is where a recommendation system shines. Tigerhall is a company that distributes podcasts, ebooks and events to subscribers. They are expanding their digital content warehouse which leads to more data for the users to filter. To make it easier for users to find the right podcast or the most exciting e-book or event, a recommendation system has been implemented. A recommender system can be implemented in many different ways. There are content-based filtering methods that can be used that focus on information about the items and try to find relevant items based on that. Another alternative is to use collaboration filtering methods that use information about what the consumer has previously consumed in correlation with what other users have consumed to find relevant items. In this project, a hybrid recommender system that uses a k-nearest neighbors algorithm alongside a matrix factorization algorithm has been implemented. The k-nearest neighbors algorithm performed well despite the sparse data while the matrix factorization algorithm performs worse. The matrix factorization algorithm performed well when the user has consumed plenty of items.

Recommender systems are helpful tools employed abundantly in online applications to help users find what they want. This thesis re-purposes a collaborative filtering recommender built for incorporating social media (hash)tags to be used as a context-aware recommender, using time of day and activity as contextual factors. The recommender uses a matrix factorization approach for implicit feedback, in a music streaming setting. Contextual data is collected from users' mobile phones while they are listening to music. It is shown in an offline test that this approach improves recall when compared to a recommender that does not account for the context the user was in. Future work should explore the qualities of this model further, as well as investigate how this model's recommendations can be surfaced in an application.

Social networks are a popular form of communication. They are also used by universities in order to simplify information providing and addressing candidates for study. Foreign study stays are also a popular form of education. Students, however, encounter a number of obstacles. The results of this work can help universities make their social network communication more efficient and better support foreign studies. In this work, the data from Facebook related to Czech universities and the Erasmus program questionnaire data were analyzed in order to find useful knowledge. The main emphasis was on textual content of communication. The statistical and machine learning methods, including mostly feature selection, topic modeling and clustering were used. The results reveal interesting and popular topics discussed on Czech universities social networks. The main problems of students related to their foreign studies were identified too and some of them were compared for countries and universities.

Abstract in English / The research will analyze and compare the current research on the spectral factorization of non-singular and singular matrices. We show that a nonsingular non-scalar matrix A can be written as a product A = BC where the eigenvalues of B and C are arbitrarily prescribed subject to the condition that the product of the eigenvalues of B and C must be equal to the determinant of A. Further, B and C can be simultaneously triangularised as a lower and upper triangular matrix respectively. Singular matrices will be factorized in terms of nilpotent matrices and otherwise over an arbitrary or complex field in order to present an integrated and detailed report on the current state of research in this area. Applications related to unipotent, positive-definite, commutator, involutory and Hermitian factorization are studied for non-singular matrices, while applications related to positive-semidefinite matrices are investigated for singular matrices. We will consider the theorems found in Sourour [24] and Laffey [17] to show that a non-singular non-scalar matrix can be factorized spectrally. The same two articles will be used to show applications to unipotent, positive-definite and commutator factorization. Applications related to Hermitian factorization will be considered in [26]. Laffey [18] shows that a non-singular matrix A with det A = ±1 is a product of four involutions with certain conditions on the arbitrary field. To aid with this conclusion a thorough study is made of Hoffman [13], who shows that an invertible linear transformation T of a finite dimensional vector space over a field is a product of two involutions if and only if T is similar to T−1. Sourour shows in [24] that if A is an n × n matrix over an arbitrary field containing at least n + 2 elements and if det A = ±1, then A is the product of at most four involutions. We will review the work of Wu [29] and show that a singular matrix A of order n ≥ 2 over the complex field can be expressed as a product of two nilpotent matrices, where the rank of each of the factors is the same as A, except when A is a 2 × 2 nilpotent matrix of rank one. Nilpotent factorization of singular matrices over an arbitrary field will also be investigated. Laffey [17] shows that the result of Wu, which he established over the complex field, is also valid over an arbitrary field by making use of a special matrix factorization involving similarity to an LU factorization. His proof is based on an application of Fitting's Lemma to express, up to similarity, a singular matrix as a direct sum of a non-singular and nilpotent matrix, and then to write the non-singular component as a product of a lower and upper triangular matrix using a matrix factorization theorem of Sourour [24]. The main theorem by Sourour and Tang [26] will be investigated to highlight the necessary and sufficient conditions for a singular matrix to be written as a product of two matrices with prescribed eigenvalues. This result is used to prove applications related to positive-semidefinite matrices for singular matrices. / National Research Foundation of South Africa / Mathematical Sciences / M Sc. (Mathematics)

La région Nord-Pas-de-Calais figure parmi les régions françaises les plus concernées par les dépassements de valeurs limites journalières de concentrations de PM₁₀ (50 µg m-³). Sur le littoral, le niveau de fond atmosphérique particulaire demeure parfois élevé, bien que relativement éloigné des sources principales de particules que sont le trafic routier et l'industrie. Alors que de nombreuses études ont été réalisées sur les émissions en milieu industrialo-portuaire, il ressort un manque de connaissances concernant l'impact des émissions issues du secteur maritime, qu'il s'agisse d'apports naturels (sels marins) ou anthropiques (trafic maritime). Dans ce travail, deux campagnes de mesures ont été menées : en 2013 au Cap Gris-Nez et au premier trimestre 2014, simultanément au Cap Gris-Nez et dans le port de Calais. La concentration en PM₁₀ a été suivie et la composition chimique (métaux, ions hydrosolubles, EC, OC, traceurs organiques) en a été déterminée. Sur le site du Cap Gris-Nez en 2013, l'évolution des niveaux de PM₁₀ est similaire à celle observée en région, reflétant la fluctuation du fond atmosphérique. Les espèces majoritairement sont NO₃-, OC, SO₄²-, CI-, Na⁺ et NH₄⁺ et représentent 69% de la masse de PM₁₀. La proportion de ces espèces varie selon la saison et les conditions météorologiques (température, vitesse et direction du vent). Les situations de fortes teneurs de PM₁₀ sont caractérisées par une plus grande proportion de nitrate d'ammonium. Les données recueillies sur le site de Calais ont permis de montrer que les émissions du trafic maritime ont pour effet d'augmenter le nombre de particules ultrafines dans l'atmosphère. Sous cette influence, les concentrations en NOx et SO₂ apparaissent plus élevées, ainsi que celles des espèces V, Ni et Co qui peuvent être proposées comme traceurs du trafic maritime. L'utilisation de la factorisation matricielle nous a permis d'identifier 10 sources de particules et d'en estimer les contributions. Ainsi, en moyenne en 2013 au Cap Gris-Nez, 41% des PM₁₀ sont issus des aérosols inorganiques secondaires, 37% des sels marins et 10% de la combustion de biomasse. Pour cette dernière, la contribution peut atteindre 17% en hiver. Enfin, le trafic maritime (5%) contribue davantage à la concentration de PM₁₀ que le trafic routier (2%). / The Nord-Pas-de-Calais region is one of the most concerned areas in France by exceedance of the PM₁₀ mean daily limit value (50 µg m-³). The particulate atmospheric background level can also be high on the coastal zone, despite the absence of any urban and industrial sources at its vicinity. Numerous studies have been performed regarding those sources, but there is still a lack of knowledge about the impact of emissions resulting from the marine compartment, including natural emissions (sea salts) and anthropogenic emissions (maritime traffic). Two measurement campaigns have been achieved, in 2013 at Cape Gris-Nez and in the first trimester 2014, simultaneously at Cape Gris-Nez and in the harbour of Calais. Concentrations of PM₁₀ were recorded and chemical composition was determined (metals, water soluble ions, Ec, OC, organic tracers). In 2013, the evolutions of PM₁₀ levels at Cape Gris-Nez and in the region similar, reflecting the atmospheric background fluctuation. NO₃-, OC, SO₄²-, CI-, Na⁺ and NH₄⁺ were found as the major species and correspond to 69% of PM₁₀ mass. The proportion of these species evolves depending on the season and the meteorological conditions (temperature, wind speed and direction). High PM₁₀ concentration situations are characterized by high proportion of ammonium nitrate. Data collected in Calais show that maritime traffic emissions increase the number of ultrafine particles in the atmosphere. Under this influence, NOx and SO₂ concentrations are higher, as those of V, Ni and Co, species that could be used as maritime traffic tracers. 10 sources were identified and apportioned by matrix factorization. In average, in 2013 at Cape Gris-Nez, 41% of PM₁₀ come from secondary inorganic aerosols, 37% from sea salts and 10% from biomass combustion. This last contribution can reach 17% in winter. Maritime traffic represents a higher contribution to PM₁₀ than road traffic, 5% against 2%.

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In this dissertation, some new algorithms are developed for hyperspectral imaging analysis enhancement. Tensor data format is applied in hyperspectral dataset sparse and low-rank decomposition, which could enhance the classification and detection performance. And multi-view learning technique is applied in hyperspectral imaging clustering. Furthermore, kernel version of multi-view learning technique has been proposed, which could improve clustering performance. Most of low-rank and sparse decomposition algorithms are based on matrix data format for HSI analysis. As HSI contains high spectral dimensions, tensor based extended low-rank and sparse decomposition (TELRSD) is proposed in this dissertation for better performance of HSI classification with low-rank tensor part, and HSI detection with sparse tensor part. With this tensor based method, HSI is processed in 3D data format, and information between spectral bands and pixels maintain integrated during decomposition process. This proposed algorithm is compared with other state-of-art methods. And the experiment results show that TELRSD has the best performance among all those comparison algorithms. HSI clustering is an unsupervised task, which aims to group pixels into different groups without labeled information. Low-rank sparse subspace clustering (LRSSC) is the most popular algorithms for this clustering task. The spatial-spectral based multi-view low-rank sparse subspace clustering (SSMLC) algorithms is proposed in this dissertation, which extended LRSSC with multi-view learning technique. In this algorithm, spectral and spatial views are created to generate multi-view dataset of HSI, where spectral partition, morphological component analysis (MCA) and principle component analysis (PCA) are applied to create others views. Furthermore, kernel version of SSMLC (k-SSMLC) also has been investigated. The performance of SSMLC and k-SSMLC are compared with sparse subspace clustering (SSC), low-rank sparse subspace clustering (LRSSC), and spectral-spatial sparse subspace clustering (S4C). It has shown that SSMLC could improve the performance of LRSSC, and k-SSMLC has the best performance. The spectral clustering has been proved that it equivalent to non-negative matrix factorization (NMF) problem. In this case, NMF could be applied to the clustering problem. In order to include local and nonlinear features in data source, orthogonal NMF (ONMF), graph-regularized NMF (GNMF) and kernel NMF (k-NMF) has been proposed for better clustering performance. The non-linear orthogonal graph NMF combine both kernel, orthogonal and graph constraints in NMF (k-OGNMF), which push up the clustering performance further. In the HSI domain, kernel multi-view based orthogonal graph NMF (k-MOGNMF) is applied for subspace clustering, where k-OGNMF is extended with multi-view algorithm, and it has better performance and computation efficiency.

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Recommender systems provide new opportunities for retrieving personalized information on the Internet. Due to the availability of big data, the fitness industries are now focusing on building an efficient recommender system for their end-users. This thesis investigates the possibilities of building an efficient recommender system for gym users. BRP Systems AB has provided the gym data for evaluation and it consists of approximately 896,000 customer interactions with 8 features. Four different matrix factorization methods, Latent semantic analysis using Singular value decomposition, Alternating least square, Bayesian personalized ranking, and Logistic matrix factorization that are based on implicit feedback are applied for the given data. These methods decompose the implicit data matrix of user-gym group activity interactions into the product of two lower-dimensional matrices. They are used to calculate the similarities between the user and activity interactions and based on the score, the top-k recommendations are provided. These methods are evaluated by the ranking metrics such as Precision@k, Mean average precision (MAP) @k, Area under the curve (AUC) score, and Normalized discounted cumulative gain (NDCG) @k. The qualitative analysis is also performed to evaluate the results of the recommendations. For this specific dataset, it is found that the optimal method is the Alternating least square method which achieved around 90\% AUC for the overall system and managed to give personalized recommendations to the users.