Heterogeneous tensor decomposition for clustering via manifold optimization

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.

Joint multiple dictionary learning for tensor sparse coding

Traditional dictionary learning algorithms are used for finding a sparse representation on high dimensional data by transforming samples into a one-dimensional (1D) vector. This 1D model loses the inherent spatial structure property of data. An alternative solution is to employ Tensor Decomposition for dictionary learning on their original structural form —a tensor— by learning multiple dictionaries along each mode and the corresponding sparse representation in respect to the Kronecker product of these dictionaries. To learn tensor dictionaries along each mode, all the existing methods update each dictionary iteratively in an alternating manner. Because atoms from each mode dictionary jointly make contributions to the sparsity of tensor, existing works ignore atoms correlations between different mode dictionaries by treating each mode dictionary independently. In this paper, we propose a joint multiple dictionary learning method for tensor sparse coding, which explores atom correlations for sparse representation and updates multiple atoms from each mode dictionary simultaneously. In this algorithm, the Frequent-Pattern Tree (FP-tree) mining algorithm is employed to exploit frequent atom patterns in the sparse representation. Inspired by the idea of K-SVD, we develop a new dictionary update method that jointly updates elements in each pattern. Experimental results demonstrate our method outperforms other tensor based dictionary learning algorithms.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

An algorithmic approach for collaborative-based prediction of user contexts in ubiquitous environments under consideration of legal implications

Mit Hilfe der Vorhersage von Kontexten können z. B. Dienste innerhalb einer ubiquitären Umgebung proaktiv an die Bedürfnisse der Nutzer angepasst werden. Aus diesem Grund hat die Kontextvorhersage einen signifikanten Stellenwert innerhalb des ’ubiquitous computing’. Nach unserem besten Wissen, verwenden gängige Ansätze in der Kontextvorhersage ausschließlich die Kontexthistorie des Nutzers als Datenbasis, dessen Kontexte vorhersagt werden sollen. Im Falle, dass ein Nutzer unerwartet seine gewohnte Verhaltensweise ändert, enthält die Kontexthistorie des Nutzers keine geeigneten Informationen, um eine zuverlässige Kontextvorhersage zu gewährleisten. Daraus folgt, dass Vorhersageansätze, die ausschließlich die Kontexthistorie des Nutzers verwenden, dessen Kontexte vorhergesagt werden sollen, fehlschlagen könnten. Um die Lücke der fehlenden Kontextinformationen in der Kontexthistorie des Nutzers zu schließen, führen wir den Ansatz zur kollaborativen Kontextvorhersage (CCP) ein. Dabei nutzt CCP bestehende direkte und indirekte Relationen, die zwischen den Kontexthistorien der verschiedenen Nutzer existieren können, aus. CCP basiert auf der Singulärwertzerlegung höherer Ordnung, die bereits erfolgreich in bestehenden Empfehlungssystemen eingesetzt wurde. Um Aussagen über die Vorhersagegenauigkeit des CCP Ansatzes treffen zu können, wird dieser in drei verschiedenen Experimenten evaluiert. Die erzielten Vorhersagegenauigkeiten werden mit denen von drei bekannten Kontextvorhersageansätzen, dem ’Alignment’ Ansatz, dem ’StatePredictor’ und dem ’ActiveLeZi’ Vorhersageansatz, verglichen. In allen drei Experimenten werden als Evaluationsbasis kollaborative Datensätze verwendet. Anschließend wird der CCP Ansatz auf einen realen kollaborativen Anwendungsfall, den proaktiven Schutz von Fußgängern, angewendet. Dabei werden durch die Verwendung der kollaborativen Kontextvorhersage Fußgänger frühzeitig erkannt, die potentiell Gefahr laufen, mit einem sich nähernden Auto zu kollidieren. Als kollaborative Datenbasis werden reale Bewegungskontexte der Fußgänger verwendet. Die Bewegungskontexte werden mittels Smartphones, welche die Fußgänger in ihrer Hosentasche tragen, gesammelt. Aus dem Grund, dass Kontextvorhersageansätze in erster Linie personenbezogene Kontexte wie z.B. Standortdaten oder Verhaltensmuster der Nutzer als Datenbasis zur Vorhersage verwenden, werden rechtliche Evaluationskriterien aus dem Recht des Nutzers auf informationelle Selbstbestimmung abgeleitet. Basierend auf den abgeleiteten Evaluationskriterien, werden der CCP Ansatz und weitere bekannte kontextvorhersagende Ansätze bezüglich ihrer Rechtsverträglichkeit untersucht. Die Evaluationsergebnisse zeigen die rechtliche Kompatibilität der untersuchten Vorhersageansätze bezüglich des Rechtes des Nutzers auf informationelle Selbstbestimmung auf. Zum Schluss wird in der Dissertation ein Ansatz für die verteilte und kollaborative Vorhersage von Kontexten vorgestellt. Mit Hilfe des Ansatzes wird eine Möglichkeit aufgezeigt, um den identifizierten rechtlichen Probleme, die bei der Vorhersage von Kontexten und besonders bei der kollaborativen Vorhersage von Kontexten, entgegenzuwirken.

Dispersion relation for hadronic light-by-light scattering: theoretical foundations

In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to (g − 2) μ . We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam double-dispersive representation; and the explicit relation for the HLbL contribution to (g − 2) μ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

Machine learning and data decompositions for complex networked dynamical systems

Thesis (Ph.D.)--University of Washington, 2016-08

Invariant decomposition of the retarded electromagnetic field.

The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor J. These field equations are an algebraic differential first-order system of oneforms, which verifies automatically the integrability conditions.

Dimensionality reduction assisted tensor clustering

This paper is concerned with tensor clustering with the assistance of dimensionality reduction approaches. A class of formulation for tensor clustering is introduced based on tensor Tucker decomposition models. In this formulation, an extra tensor mode is formed by a collection of tensors of the same dimensions and then used to assist a Tucker decomposition in order to achieve data dimensionality reduction. We design two types of clustering models for the tensors: PCA Tensor Clustering model and Non-negative Tensor Clustering model, by utilizing different regularizations. The tensor clustering can thus be solved by the optimization method based on the alternative coordinate scheme. Interestingly, our experiments show that the proposed models yield comparable or even better performance compared to most recent clustering algorithms based on matrix factorization.

Tensor coupling and pseudospin symmetry in nuclei

In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy. decomposition of the pseudospin energy splittings, we show that the changes in these splittings come mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners and through changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.

Multi-Mode Tensor Representation of Motion Data

In this paper, we investigate how a multilinear model can be used to represent human motion data. Based on technical modes (referring to degrees of freedom and number of frames) and natural modes that typically appear in the context of a motion capture session (referring to actor, style, and repetition), the motion data is encoded in form of a high-order tensor. This tensor is then reduced by using N-mode singular value decomposition. Our experiments show that the reduced model approximates the original motion better then previously introduced PCA-based approaches. Furthermore, we discuss how the tensor representation may be used as a valuable tool for the synthesis of new motions.

Compact Ag@fe3o4 Core-shell Nanoparticles By Means Of Single-step Thermal Decomposition Reaction.

A temperature pause introduced in a simple single-step thermal decomposition of iron, with the presence of silver seeds formed in the same reaction mixture, gives rise to novel compact heterostructures: brick-like Ag@Fe3O4 core-shell nanoparticles. This novel method is relatively easy to implement, and could contribute to overcome the challenge of obtaining a multifunctional heteroparticle in which a noble metal is surrounded by magnetite. Structural analyses of the samples show 4 nm silver nanoparticles wrapped within compact cubic external structures of Fe oxide, with curious rectangular shape. The magnetic properties indicate a near superparamagnetic like behavior with a weak hysteresis at room temperature. The value of the anisotropy involved makes these particles candidates to potential applications in nanomedicine.

Thermal decomposition of mercerized linter cellulose and its acetates obtained from a homogeneous reaction

Cellulose acetates with different degrees of substitution (DS, from 0.6 to 1.9) were prepared from previously mercerized linter cellulose, in a homogeneous medium, using N,N-dimethylacetamide/lithium chloride as a solvent system. The influence of different degrees of substitution on the properties of cellulose acetates was investigated using thermogravimetric analyses (TGA). Quantitative methods were applied to the thermogravimetric curves in order to determine the apparent activation energy (Ea) related to the thermal decomposition of untreated and mercerized celluloses and cellulose acetates. Ea values were calculated using Broido's method and considering dynamic conditions. Ea values of 158 and 187 kJ mol-1 were obtained for untreated and mercerized cellulose, respectively. A previous study showed that C6OH is the most reactive site for acetylation, probably due to the steric hindrance of C2 and C3. The C6OH takes part in the first step of cellulose decomposition, leading to the formation of levoglucosan and, when it is changed to C6OCOCH3, the results indicate that the mechanism of thermal decomposition changes to one with a lower Ea. A linear correlation between Ea and the DS of the acetates prepared in the present work was identified.

Thermal behavior and decomposition kinetics of rifampicin polymorphs under isothermal and non-isothermal conditions

The thermal behavior of two polymorphic forms of rifampicin was studied by DSC and TG/DTG. The thermoanalytical results clearly showed the differences between the two crystalline forms. Polymorph I was the most thermally stable form, the DSC curve showed no fusion for this species and the thermal decomposition process occurred around 245 ºC. The DSC curve of polymorph II showed two consecutive events, an endothermic event (Tpeak = 193.9 ºC) and one exothermic event (Tpeak = 209.4 ºC), due to a melting process followed by recrystallization, which was attributed to the conversion of form II to form I. Isothermal and non-isothermal thermogravimetric methods were used to determine the kinetic parameters of the thermal decomposition process. For non-isothermal experiments, the activation energy (Ea) was derived from the plot of Log β vs 1/T, yielding values for polymorph form I and II of 154 and 123 kJ mol-1, respectively. In the isothermal experiments, the Ea was obtained from the plot of lnt vs 1/T at a constant conversion level. The mean values found for form I and form II were 137 and 144 kJ mol-1, respectively.

Aspects of a noncommutative scalar/tensor duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in theta. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order theta is also derived.