Os P-splines de Eilers e Marx (1996) são métodos de suavização que é uma combinação de bases B-splines e uma penalização discreta sobre os coeficientes das bases utilizados para suavizar dados normais e não normais em uma ou mais dimensões, no caso de várias dimensões utiliza-se como suavização o produto tensor dos P-splines. Também os P-splines são utilizados como representação de modelos mistos Currie et al. (2006) pela presença de características tais como: efeitos fixos, efeitos aleatórios, correlação espacial ou temporal e utilizados em modelos mais generalizados tais como os modelos mistos lineares generalizados e modelos mistos aditivos generalizados. Neste trabalho apresentou-se toda a abordagem, metodologia e descrição dos P-splines como modelos mistos e como componentes das estruturas suavizadoras de variáveis unidimensionais e bidimensionais dos modelos mistos aditivos generalizados, mostrando essa abordagem e propondo seu uso em uma aplicação no comportamento dos níveis médios da produção de cana-de-açúcar sob a influência das alterações das variáveis climáticas como temperatura e precipitação, que foram medidos ao longo de 10 anos em cada mesorregião do Estado de São Paulo. O motivo de usar essa abordagem como método de suavização é que muitas vezes não é conhecido a tendência dessas covariáveis climáticas mas sabe-se que elas influenciam diretamente sobre a variável resposta. Além de permitir essa abordagem inclusão de efeitos fixos e aleatórios nos modelos a serem propostos, permitirá a inclusão do processo autoregressivo AR(1) como estrutura de correlação nos resíduos. / P-splines of Eilers e Marx (1996) are methods of smoothing that is a combination of B-splines bases and penalty the coefficients of the bases used to smooth normal and non-normal data in one or more dimensions; in the case of several dimensions it is used as smoothing the tensor product of the P-splines. Also the P-splines are used as representation of mixed models Currie et al. (2006) by the presence of characteristics such as: fixed effects, random effects, spatial or temporal correlation and used in more generalized models such as generalized linear mixed models and generalized additive mixed models. In this work the whole approach, methodology and description of the P-splines as mixed models and as components of the smoothing structures of one-dimensional and two-dimensional variables of generalized additive mixed models were presented, showing this approach and proposing its application in the behavior of the average levels of sugarcane production, which is influenced by changes in climatic variables such as temperature and precipitation , which were measured over 10 years in each mesoregion of the state of São Paulo. The reason for using this approach as a smoothing method is that the tendency of these climate covariables is not know for the most part, but is known that they influence directly the response variable, besides allowing this approach to include fixed and random effects in the models to be proposed, will allow the inclusion of the autoregressive process AR(1) as a correlation structure in the residuos.

Orientador: Elizabeth Maria Aparecida Barasnevicius Quagliato / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Ciências Médicas / Made available in DSpace on 2018-08-25T22:29:43Z (GMT). No. of bitstreams: 1 Martins_SergilainePereira_D.pdf: 2688714 bytes, checksum: 50e69a64ddbe919094b642d6fcc2f77a (MD5) Previous issue date: 2014 / Resumo: A ressonância magnética por tensor de difusão (DTI) proporciona aumento da sensibilidade para estudar a alterações na microestrutura da substância branca aparentemente normal (SBAN) in vivo e é especialmente indicada para estudar doenças que apresentam lesão axonal e desmielinização. No presente estudo, sugerimos a hipótese de que a neurodegeneração produz alterações microestruturais na SBAN de indivíduos com DA e CCL, especialmente em regiões específicas do cérebro. Foram estudados 71 participantes (21 com DA leve, 25 com CCL e 25 controles normais-CN) que foram recrutados de serviço médico neurológico em Campinas. Os indivíduos foram avaliados por um protocolo de avaliação clínica padronizada que incluiu: escala de depressão geriátrica (GDS), questionário de atividades funcionais (FAQ - Pfeffer), mini exame do estado mental (MEEM), teste de aprendizado auditivo-verbal de REY (RAVLT), testes de memória prospectiva (MP) (consulta e pertence) (subtestes do Teste de Memória Comportamental Rivermead), teste de fluência verbal (FV) (animais e FAS), teste desenho do relógio (TDR) e teste de nomeação de Boston (TNB). As imagens de RNM foram adquiridas usando um scanner MRT 1.5. A anisotropia fracionada (FA) e as difusividades axial (DAx) e radial (DRa) foram analisadas em regiões de interesse (ROI) alocados nos lobos frontal, parietal, temporal e occipital. FA, DAx e DRa foram calculadas para cada ROI. Em seguida, calculamos as médias de todas as seções para FA, DAx, e DRa para cada região da SBAN bilateralmente. Resultados: Nossos resultados mostraram que: (1) Comparado com CN, o grupo CCL demonstrou diminuição da FA no lobo frontal (parte do fórceps menor e do fascículo uncinado e coroa radiada), região importante para a memória episódica. (2) Na avaliação por análise de regressão múltipla, FA e DAx frontal, DAx temporal e parietal e FA occipital formaram um padrão de parâmetros associados ao maior risco para CCL e DA. (3) O estudo da acurácia revelou que a DTI da região frontal é a que apresenta maior sensibilidade e especificidade para identificar CCL. Em relação à DA, as variáveis FA frontal e temporal e DAx parietal apresentaram maior especificidade para identificar DA. (4) Não encontramos correlação robusta entre variáveis neuropsicológicas e de neuroimagem / Abstract: MRI technique, diffusion tensor imaging (DTI), provides increased sensitivity to alterations in the microstructure of white matter in vivo and is especially indicative for diseases causing axonal damage and demyelination. In the present study, we hypothesized that neurodegeneration produces microstructural changes in the cerebral white matter of subjects with AD and MCI, especially in specific regions in the brain. We studied 71 participants (21 mild AD, 25 MCI, and 25 normal controls-NC) that were recruited from neurological medical service in Campinas. Subjects were evaluated by using a standardized clinical evaluation protocol, which included: Geriatric depression Scal (GDS), the functional activities questionnaire (FAQ-Pfeffer), mini-mental status examination (MMSE), Rey auditory verbal learning test (RAVLT), prospective memory (Rivermead Behavioral Memory Test), verbal fluency test (animal and FAS), clock drawing test and Boston naming test. MR images were acquired using a 1.5 T MR scanner. Fractional anisotropy (FA) and axial and radial diffusivities (DA and DR) were analyzed in regions of interest (ROIs) in frontal, parietal, temporal and occipital lobes. FA, DA, and DR were calculated for each ROI. Then the measures of FA, DA, and DR were averaged across all the sections of each white matter region bilaterally. Our results showed that: (1) Compared to NC, MCI group showed decreased FA in the frontal lobe (the minor forceps and the uncinate fasciculus, and corona radiata), important region to episodic memory. (2) The evaluation by multiple regression analysis, frontal FA and DA, temporal and parietal DA and occipital FA formed a pattern of parameters associated with increased risk for MCI and AD. (3) The accuracy revealed that the frontal area has the greatest sensitivity and specificity to identify MCI. Regarding the AD, the frontal FA and temporal and parietal DA have the greatest specificity for identifying AD. (4) We did not find correlation between neuropsychological and neuroimaging variables / Doutorado / Neurologia / Doutora em Ciências Médicas

Orientador: Diego Sebastian Ledesma / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T22:36:25Z (GMT). No. of bitstreams: 1 Paula_PedroManfrimMagalhaesde_M.pdf: 1130226 bytes, checksum: bbd8d375ddf7846ed2eafe024103e682 (MD5) Previous issue date: 2015 / Resumo: Este trabalho apresenta um estudo sobre variedades Riemannianas que possuem um tensor de Bakry-Émery-Ricci com limitações. Inicialmente abordamos tanto aspectos da geometria Riemanniana tradicional como métricas e geodésicas, quanto aspectos mais avançados como as fórmulas de Bochner, Weitzenböck e o teorema de Hodge. Em seguida discutimos a convergência de Gromov-Hausdorff e suas propriedades, além de serem apresentados alguns teoremas como os de Kasue e Fukaya. Por fim estudamos as propriedades topológicas e geométricas de variedades com limitação no tensor de Bakry-Émery-Ricci e o comportamento de tais limitações com respeito à submersões e à convergência de Gromov-Hausdorff / Abstract: This work presents a study about Riemannian manifolds having a Bakry-Émery-Ricci tensor with bounds. Initially we approached both the traditional aspects of Riemannian geometry like metrics and geodesics, as more advanced aspects like the Bochner, Weitzenböck formulas and the Hodge's theorem. Then we discussed the Gromov-Hausdorff convergence and its properties, in addition to showing some theorems as those from Kasue and Fukaya. Lastly we studied the topological and geometric properties of manifolds with bounds on the Bakry-Émery-Ricci tensor and the behavior of these bounds with respect to submersions and the Gromov-Hausdorff convergence / Mestrado / Matematica / Mestre em Matemática

In der vorliegenden Arbeit wird der Hypothalamus, eine kleine, aber bedeutsame Struktur des Zwischenhirns untersucht. Er spielt unter anderem eine Rolle bei der Regulation des Schlaf-Wach-Rhythmus, des Sexualverhaltens, der Stimmungslage, autonomer und Stoffwechsel-Funktionen. Veränderungen einzelner oder mehrerer spezifischer Kerngruppen sind bei neuropsychiatrischen bzw. -endokrinologischen Erkrankungen, wie Narkolepsie, Schizophrenie, affektiver Störung, Demenz, Borderline-Persönlichkeitsstörung, Pädophilie oder Adipositas zu beobachten. Die Substrukturierung und Darstellung der einzelnen Kerngruppen gelang bisher nur in Postmortem-Studien. Im Rahmen dieser Studie konnte mit Hilfe der Diffusions-Tensor-Bildgebung erstmals eine in-vivo Substrukturierung des Hypothalamus konsistent bei zehn gesunden Probanden vorgenommen werden. Dabei wurden nach einem Algorithmus zunächst die Segmentierung und anschließend die Parzellierung durchgeführt, woraus sich drei konsistente Cluster ergaben. Der topografische Vergleich der erhaltenen Cluster mit Postmortem-Studien der Literatur ergab vergleichbare und anatomisch plausible Korrelate. Mit der von uns entwickelten Methode könnten anhand einer größeren Patientengruppe pathophysiologische Zusammenhänge neuropsychiatrischer und –endokrinologischer Störungen genauer eruiert werden und zu einem besseren Verständnis des Krankheitsverlaufs und der Therapie beitragen.:1 Einleitung 1.1 Topographie und Funktion des Hypothalamus 1.2 MRT- Kartierung des Hypothalamus 1.3 Diffusions-Tensor- Bildgebung 1.3.1 Diffusionsellipsoid 1.3.2 Fraktionelle Anisotropie 1.3.3 Clusteranalyse 1.3.4 k-means- Clusteralgorithmus 1.4 Pathomorphologische Veränderungen des Hypothalamus bei neuropsychiatrischen Erkrankungen 1.4.1 Narkolepsie 1.4.2 Schizophrenie 1.4.3 Affektive Störung 1.4.4 Demenz 1.4.5 Borderline- Persönlichkeitsstörung 1.4.6 Pädophilie 1.4.7 Adipositas 1.4.8 Zusammenfassung 2 Fragestellung: Ist eine Subpartialisierung des Hypothalamus in-vivo mit struktureller Bildgebung möglich? 3 Material und Methoden 3.1 Probanden 3.2 Bilderfassung und -bearbeitung 3.3 Segementierung des Hypothalamus - Definition der ROI`s („region of interest“) 3.3.1 Präoptischer Hypothalamus 3.3.2 Anteriorer Hypothalamus 3.3.3 Tuberaler Hypothalamus 3.3.4 Posteriorer Hypothalamus, Mamillarkörperchen 3.4 Parzellierung und Clusteranalyse 4 Ergebnisse: Mit qualitativen Analysen konnte gezeigt werden, dass eine Subpartialisierung des Hypothalamus möglich ist. 4.1 Segmentierung des Hypothalamus 4.2 Substrukturen/Cluster 5 Diskussion der Ergebnisse 5.1 Neuroanatomie des Hypothalamus 5.1.1 Kerngruppen des Hypothalamus 5.1.2 Faserverbindungen des Hypothalamus 5.1.3 Zusammenfassung der Faserverbindungen der Kerngruppen 5.2 Interpretation der einzelnen Cluster 5.2.1 Anteriore Substruktur 5.2.2 Posteromediale Substruktur 5.2.3 Laterale Substruktur 5.3 Topografische Beziehung der drei Cluster untereinander 5.3.1 Ähnlichkeiten der Cluster der zehn Probanden 5.3.2 Unterschiede der Cluster der zehn Probanden 5.4 Verbesserung der Hypothalamusmaske 6 Zusammenfassung 7 Literaturverzeichnis

Die vorliegende Arbeit beschäftigt sich mit der zweidimensionalen Simulation der Rissausbreitung mit Hilfe der adaptiven Finite-Elemente-Methode. Das Ziel war die Entwicklung von Algorithmen zur effizienten und automatisierten Modellierung des Risswachstums. Das zugrunde liegende Konzept besteht in der vollständigen Integration aller Teilschritte der Risswachstumssimulation in ein einziges FE-Programm. Während der gesamten Simulation erfolgt durch den Einsatz eines fehlergesteuerten h-adaptiven Verfahrens die automatische Anpassung der FE-Diskretisierung an das gestellte Rissproblem. Die Simulation der spröden Rissausbreitung erfolgt auf Basis der linear-elastischen Bruchmechanik. Die dafür benötigten Spannungsintensitätsfaktoren werden mit Hilfe des J-Integrals in Form der Interaction-Integral-Technik ermittelt. Die Simulation des duktilen Versagens in der Prozesszone an der Rissspitze wird mit Hilfe des Schädigungsmodells von Rousselier beschrieben. Das Kriterium für duktiles Risswachstum basiert auf der Auswertung des akustischen Tensors an der Rissspitze und legt den Beginn der makroskopischen Rissausbreitung mit dem Einsetzen der Lokalisierung fest.

Les réseaux tensoriels offrent un cadre puissant pour représenter efficacement des objets de très haute dimension. Les réseaux tensoriels ont récemment montré leur potentiel pour les applications d’apprentissage automatique et offrent une vue unifiée des modèles de décomposition tensorielle courants tels que Tucker, tensor train (TT) et tensor ring (TR). Cependant, l’identification de la meilleure structure de réseau tensoriel à partir de données pour une tâche donnée est un défi. Dans cette thèse, nous nous appuyons sur le formalisme des réseaux tensoriels pour développer un algorithme adaptatif générique et efficace pour apprendre conjointement la structure et les paramètres d’un réseau de tenseurs à partir de données. Notre méthode est basée sur une approche simple de type gloutonne, partant d’un tenseur de rang un et identifiant successivement les bords du réseau tensoriel les plus prometteurs pour de petits incréments de rang. Notre algorithme peut identifier de manière adaptative des structures avec un petit nombre de paramètres qui optimisent efficacement toute fonction objective différentiable. Des expériences sur des tâches de décomposition de tenseurs, de complétion de tenseurs et de compression de modèles démontrent l’efficacité de l’algorithme proposé. En particulier, notre méthode surpasse l’état de l’art basée sur des algorithmes évolutionnaires introduit dans [26] pour la décomposition tensorielle d’images (tout en étant plusieurs ordres de grandeur plus rapide) et trouve des structures efficaces pour compresser les réseaux neuronaux en surpassant les approches populaires basées sur le format TT [30]. / Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models such as Tucker, tensor train (TT) and tensor ring (TR). However, identifying the best tensor network structure from data for a given task is challenging. In this thesis, we leverage the TN formalism to develop a generic and efficient adaptive algorithm to jointly learn the structure and the parameters of a TN from data. Our method is based on a simple greedy approach starting from a rank one tensor and successively identifying the most promising tensor network edges for small rank increments. Our algorithm can adaptively identify TN structures with small number of parameters that effectively optimize any differentiable objective function. Experiments on tensor decomposition, tensor completion and model compression tasks demonstrate the effectiveness of the proposed algorithm. In particular, our method outperforms the state-of-the- art evolutionary topology search introduced in [26] for tensor decomposition of images (while being orders of magnitude faster) and finds efficient structures to compress neural networks outperforming popular TT based approaches [30].

Starting with the work of Volker Strassen, algorithms for matrix multiplication have been developed which are time complexity-wise more efficient than the standard algorithm from the definition of multiplication. The general method of the developments has been viewing the bilinear mapping that matrix multiplication is as a three-dimensional tensor, where there is an exact correspondence between time complexity of the multiplication algorithm and tensor rank. The latter can be seen as a generalisation of matrix rank, being the minimum number of terms a tensor can be decomposed as. However, in contrast to matrix rank there is no general method of computing tensor ranks, with many values being unknown for important three-dimensional tensors. To further improve the theoretical bounds of the time complexity of matrix multiplication, support rank of tensors has been introduced, which is the lowest rank of tensors with the same support in some basis. The goal of this master's thesis has been to go through the history of faster matrix multiplication, as well as specifically examining the properties of support rank for general tensors. In regards to the latter, a complete classification of rank structures of support classes is made for the smallest non-degenerate tensor product space in three dimensions. From this, the size of a support can be seen affecting the pool of possible ranks within a support class. At the same time, there is in general no symmetry with regards to support size occurring in the rank structures of the support classes, despite there existing a symmetry and bijection between mirrored supports. Discussions about how to classify support rank structures for larger tensor product spaces are also included. / Från och med forskning gjord av Volker Strassen har flera algoritmer för matrismultiplikation utvecklats som är effektivare visavi tidskomplexitet än standardalgoritmen som utgår från defintionen av multiplikation. Generellt sett har metoden varit att se den bilinjära avbildningen som matrismultiplikation är som en tredimensionell tensor. Där används att det finns en exakt korrespondens mellan multiplikationsalgoritmens tidskomplexitet och tensorrang. Det sistnämnda är ett slags generalisering av matrisrang, och är minsta antalet termer en tensor kan skrivas som. Till skillnad frpn matrisrang finns ingen allmän metod för att beräkna tensorrang, och många värden är okända även för välstuderade och viktiga tensorer. För att hitta fler övre begränsningar på matrismultiplikations tidskomplexitet har stödrang av tensorer införts, som är den lägsta rangen bland tensor med samma stöd i en viss bas. Målet med detta examensarbete har varit att göra en genomgång av historien om snabbare matrismultiplikation, samt att specifikt undersöka egenskaper av stödrang för allmänna tredimensionella tensorer. För det sistnämnda görs en fullständig klassificering av rangstrukturer bland stödklasser för den minsta icke-degenererade tensorprodukten av tre vektorrum. Slutsatser är bl.a. att storleken av ett stöd kan ses påverka antalet möjliga ranger inom en stödklass. Samtidigt finns i allmänhet ingen symmetri med avseende på stödstorlek i stödklassernas rangstrukturer. Detta trots att det finns en symmetri och bijektion mellan speglade stöd. I arbetet ingår även en diskussion om hur stödrangstrukturer skulle kunna klassificeras för större tensorprodukter.

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In dieser Arbeit werden verschiedene Ansätze untersucht, um Tensorzerlegungsmethoden auf die Full-Configuration-Interaction-Methode (FCI) anzuwenden. Das Ziel dieser Ansätze ist es, zuverlässig konvergierende Algorithmen zu erstellen, welche es erlauben, die Wellenfunktion effizient im Canonical-Product-Tensorformat (CP) zu approximieren. Hierzu werden drei Ansätze vorgestellt, um die FCI-Wellenfunktion zu repräsentieren und darauf basierend die benötigten Koeffizienten zu bestimmen. Der erste Ansatz beruht auf einer Entwicklung der Wellenfunktion als Linearkombination von Slaterdeterminanten, bei welcher in einer Hierarchie ausgehend von der Hartree-Fock-Slaterdeterminante sukzessive besetzte Orbitale durch virtuelle Orbitale ersetzt werden. Unter Nutzung von Tensorrepräsentationen im CP wird ein lineares Gleichungssystem gelöst, um die FCI-Koeffizienten zu bestimmen. Im darauf folgenden Ansatz, welcher an Direct-CI angelehnt ist, werden Tensorrepräsentationen der Hamiltonmatrix und des Koeffizientenvektors aufgestellt, welche zur Lösung des FCI-Eigenwertproblems erforderlich sind. Hier wird ein Algorithmus vorgestellt, mit welchem das Eigenwertproblem im CP gelöst wird. In einem weiteren Ansatz wird die Repräsentation der Hamiltonmatrix und des Koeffizientenvektors im Fockraum formuliert. Dieser Ansatz erlaubt die Lösung des FCI-Eigenwertproblems mit Hilfe verschiedener Algorithmen. Diese orientieren sich an den Rayleighquotienteniterationen oder dem Davidsonalgorithmus, wobei für den ersten Algorithmus eine zweite Version entwickelt wurde, wo die Rangreduktion teilweise durch Projektionen ersetzt wurde. Für den Davidsonalgorithmus ist ein breiteres Spektrum von Molekülen behandelbar und somit können erste Untersuchungen zur Skalierung und zu den zu erwartenden Fehlern vorgestellt werden. Schließlich wird ein Ausblick auf mögliche Weiterentwicklungen gegeben, welche eine effizientere Berechnung ermöglichen und somit FCI im CP auch für größere Moleküle zugänglich macht. / In this thesis, various approaches are investigated to apply tensor decomposition methods to the Full Configuration Interaction method (FCI). The aim of these approaches is the development of algorithms, which converge reliably and which permit to approximate the wave function efficiently in the Canonical Product format (CP). Three approaches are introduced to represent the FCI wave function and to obtain the corresponding coefficients. The first approach ist based on an expansion of the wave function as a linear combination of slater determinants. In this hierarchical expansion, starting from the Hartree Fock slater determinant, the occupied orbitals are substituted by virtual orbitals. Using tensor representations in the CP, a linear system of equations is solved to obtain the FCI coefficients. In a further approach, tensor representations of the Hamiltonian matrix and the coefficient vectors are set up, which are required to solve the FCI eigenvalue problem. The tensor contractions and an algorithm to solve the eigenvalue problem in the CP are explained her in detail. In the next approach, tensor representations of the Hamiltonian matrix and the coefficient vector are constructed in the Fock space. This approach allows the application of various algorithms. They are based on the Rayleight Quotient Algorithm and the Davidson algorithm and for the first one, there exists a second version, where the rank reduction algorithm is replaced by projections. The Davidson algorithm allows to treat a broader spectrum of molecules. First investigations regarding the scaling behaviour and the expectable errors can be shown for this approach. Finally, an outlook on the further development is given, that allows for more efficient calculations and makes FCI in the CP accessible for larger molecules.

Le traitement des données massives, communément connu sous l’appellation “Big Data”, constitue l’un des principaux défis scientifiques de la communauté STIC.Plusieurs domaines, à savoir économique, industriel ou scientifique, produisent des données hétérogènes acquises selon des protocoles technologiques multi-modales. Traiter indépendamment chaque ensemble de données mesurées est clairement une approche réductrice et insatisfaisante. En faisant cela, des “relations cachées” ou des inter-corrélations entre les données peuvent être totalement ignorées.Les représentations tensorielles ont reçu une attention particulière dans ce sens en raison de leur capacité à extraire de données hétérogènes et volumineuses une information physiquement interprétable confinée à un sous-espace de dimension réduite. Dans ce cas, les données peuvent être organisées selon un tableau à D dimensions, aussi appelé tenseur d’ordre D.Dans ce contexte, le but de ce travail et que certaines propriétés soient présentes : (i) avoir des algorithmes de factorisation stables (ne souffrant pas de probème de convergence), (ii) avoir un faible coût de stockage (c’est-à-dire que le nombre de paramètres libres doit être linéaire en D), et (iii) avoir un formalisme sous forme de graphe permettant une visualisation mentale simple mais rigoureuse des décompositions tensorielles de tenseurs d’ordre élevé, soit pour D > 3.Par conséquent, nous nous appuyons sur la décomposition en train de tenseurs (TT) pour élaborer de nouveaux algorithmes de factorisation TT, et des nouvelles équivalences en termes de modélisation tensorielle, permettant une nouvelle stratégie de réduction de dimensionnalité et d'optimisation de critère des moindres carrés couplés pour l'estimation des paramètres d'intérêts nommé JIRAFE.Ces travaux d'ordre méthodologique ont eu des applications dans le contexte de l'analyse spectrale multidimensionelle et des systèmes de télécommunications à relais. / Massive and heterogeneous data processing and analysis have been clearly identified by the scientific community as key problems in several application areas. It was popularized under the generic terms of "data science" or "big data". Processing large volumes of data, extracting their hidden patterns, while preforming prediction and inference tasks has become crucial in economy, industry and science.Treating independently each set of measured data is clearly a reductiveapproach. By doing that, "hidden relationships" or inter-correlations between thedatasets may be totally missed. Tensor decompositions have received a particular attention recently due to their capability to handle a variety of mining tasks applied to massive datasets, being a pertinent framework taking into account the heterogeneity and multi-modality of the data. In this case, data can be arranged as a D-dimensional array, also referred to as a D-order tensor.In this context, the purpose of this work is that the following properties are present: (i) having a stable factorization algorithms (not suffering from convergence problems), (ii) having a low storage cost (i.e., the number of free parameters must be linear in D), and (iii) having a formalism in the form of a graph allowing a simple but rigorous mental visualization of tensor decompositions of tensors of high order, i.e., for D> 3.Therefore, we rely on the tensor train decomposition (TT) to develop new TT factorization algorithms, and new equivalences in terms of tensor modeling, allowing a new strategy of dimensionality reduction and criterion optimization of coupled least squares for the estimation of parameters named JIRAFE.This methodological work has had applications in the context of multidimensional spectral analysis and relay telecommunications systems.