In many situations, a researcher is interested in the analysis of the scores of a set of observation units on a set of variables. However, in medicine, it is very frequent that the information is replicated at differe...
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In many situations, a researcher is interested in the analysis of the scores of a set of observation units on a set of variables. However, in medicine, it is very frequent that the information is replicated at different occasions. The occasions can be time-varying or refer to different conditions. In such cases, the data can be stored in a 3-way array or tensor. The Candecomp/Parafac and Tucker3 methods represent the most common methods for analyzing 3-way tensors. In this work, a review of these methods is provided, and then this class of methods is applied to a 3-way data set concerning hospital care data for a hospital in Rome (Italy) during 15years distinguished in 3 groups of consecutive years (1892-1896, 1940-1944, 1968-1972). The analysis reveals some peculiar aspects about the use of health services and its evolution along the time.
Over the last two decades, tensor-based methods have received growing attention in the signal processing community. In this work, the authors proposed a comprehensive overview of tensor-based models and methods for mu...
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Over the last two decades, tensor-based methods have received growing attention in the signal processing community. In this work, the authors proposed a comprehensive overview of tensor-based models and methods for multisensor signal processing. They presented for instance the Tucker decomposition, the canonical polyadic decomposition, the tensor-train decomposition (TTD), the structured TTD, including nested Tucker train, as well as the associated optimisation strategies. More precisely, they gave synthetic descriptions of state-of-the-art estimators as the alternating least square (ALS) algorithm, the high-order singular value decomposition (HOSVD), and of more advanced algorithms as the rectified ALS, the TT-SVD/TT-HSVD and the Joint dImensionally Reduction and Factor retrieval Estimator scheme. They illustrated the efficiency of the introduced methodological and algorithmic concepts in the context of three important and timely signal processing-based applications: the direction-of-arrival estimation based on sensor arrays, multidimensional harmonic retrieval and multiple-input-multiple-output wireless communication systems.
This study introduces a modified tensor-based power flow method designed using complex voltages represented in their rectangular form. tensor-based methods employ the second-order Taylor series expansion of the power ...
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This study introduces a modified tensor-based power flow method designed using complex voltages represented in their rectangular form. tensor-based methods employ the second-order Taylor series expansion of the power flow equations to estimate a correction vector to be added to the iterative increments of the Newton-Raphson method. In the proposed approach, the estimation of the correction vector is improved by taking advantage of a relation between the Jacobian and tensor arrays and symmetries between matrix-vector products involving Jacobian matrices. Result analysis highlights the efficiency and robustness of the proposed method in comparison with the original tensor-based approach using test systems and an actual system.
This paper introduces an idea of generating a kernel from an arbitrary function by embedding the training samples into the *** on this idea,we present two nonlinear feature extraction methods:generating kernel princip...
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This paper introduces an idea of generating a kernel from an arbitrary function by embedding the training samples into the *** on this idea,we present two nonlinear feature extraction methods:generating kernel principal component analysis(GKPCA)and generating kernel Fisher discriminant(GKFD).These two methods are shown to be equivalent to the function-mapping-space PCA(FMS-PCA)and the function-mapping-space linear discriminant analysis(FMS-LDA)methods,*** equivalence reveals that the generating kernel is actually determined by the corresponding function *** the generating kernel point of view,we can classify the current kernel Fisher discriminant(KFD)algorithms into two categories:KPCA+LDA based algorithms and straightforward KFD(SKFD)*** KPCA+LDA based algorithms directly work on the given kernel and are not suitable for non-kernel functions,while the SKFD algorithms essentially work on the generating kernel from a given symmetric function and are therefore suitable for non-kernels as well as ***,we outline the tensor-based feature extraction methods and discuss ways of extending tensor-based methods to their generating kernel versions.
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