Approximating high order tensors by low Tucker-rank tensors have applications in psychometrics, chemometrics, computer vision, biomedical informatics, among others. Traditionally, solution methods for finding a low Tu...
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Approximating high order tensors by low Tucker-rank tensors have applications in psychometrics, chemometrics, computer vision, biomedical informatics, among others. Traditionally, solution methods for finding a low Tucker-rank approximation presume that the size of the core tensor is specified in advance, which may not be a realistic assumption in many applications. In this paper we propose a new computational model where the configuration and the size of the core become a part of the decisions to be optimized. Our approach is based on the so-called maximum block improvement method for non-convex block optimization. Numerical tests on various real data sets from gene expression analysis and image compression are reported, which show promising performances of the proposed algorithms.
The estimation of directions of arrival is formulated as the decomposition of a 3-way array into a sum of rank-one terms, which is possible when the receive array enjoys some geometrical structure. The main advantage ...
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The estimation of directions of arrival is formulated as the decomposition of a 3-way array into a sum of rank-one terms, which is possible when the receive array enjoys some geometrical structure. The main advantage is that this decomposition is essentially unique under mild assumptions, if computed exactly. The drawback is that a low-rank approximation does not always exist. Therefore, a coherence constraint is introduced that ensures the existence of the latter best approximate, which allows to localize and estimate closely located or highly correlated sources. Then Cramer-Rao bounds are derived for localization parameters and source signals, assuming the others are nuisance parameters;some inaccuracies found in the literature are pointed out. Performances are eventually compared with unconstrained reference algorithms such as ESPRIT, in the presence of additive complex Gaussian noise, with possibly noncircular distribution.
In chemometrics, two-way singular value decomposition (SVD), CANDECOMP-PARAFAC decomposition (PARAFAC), and Tucker decomposition (TUKER) are three main array decomposition methods. There are disadvantages with the thr...
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In chemometrics, two-way singular value decomposition (SVD), CANDECOMP-PARAFAC decomposition (PARAFAC), and Tucker decomposition (TUKER) are three main array decomposition methods. There are disadvantages with the three methods. If multiway data are indeed multilinear, PARAFAC and TUCKER can provide more robust and interpretable models compared to two-way SVD. However, PARAFAC is sometimes numerically unstable, and TUCKER cannot guarantee the uniqueness of an approximate solution. This paper proposes a new array decomposition model with multiple bilinear structure. Then, utilizing this model, a new method, called multiple bilinear decomposition (MBD), is proposed as a generalization of two-way SVD. An algorithm is established to successively decompose an array without a full decomposition, which is not based on alternating least squares. Theoretically, the proposed method has an advantage over PARAFAC and TUCKER in its three important properties, including orthonormality of loading vectors, closed-form decomposition, and successive decomposition of variation. The simulation results based on orthogonal PARAFAC models show that the proposed method outperforms PARAFAC with respect to accuracy and robustness of loading estimate and data-fitting of model, even though the former does not use the priori information of multilinear structure. And. especially in the simulation under no noise, the equivalence of loading estimates indicates that as a successive decomposition, MBD is a superior alternative to PARAFAC. (C) 2010 Elsevier B.V. All rights reserved.
Recently, there has been a growing interest in multiway probabilistic clustering. Some efficient algorithms have been developed for this problem. However, not much attention has been paid on how to detect the number o...
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Recently, there has been a growing interest in multiway probabilistic clustering. Some efficient algorithms have been developed for this problem. However, not much attention has been paid on how to detect the number of clusters for the general n-way clustering (n >= 2). To fill this gap, this problem is investigated based on n-way algebraic theory in this paper. A simple, yet efficient, detection method is proposed by eigenvalue decomposition (EVD), which is easy to implement. We justify this method. In addition, its effectiveness is demonstrated by the experiments on both simulated and real-world data sets.
The purpose of this paper is to develop new component-wise component and regression multiblock methods that overcome some of the difficulties traditionally associated with multiblocks, such as the step-by-step optimiz...
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The purpose of this paper is to develop new component-wise component and regression multiblock methods that overcome some of the difficulties traditionally associated with multiblocks, such as the step-by-step optimization and component orthogonalities. Generalized orthogonal multiple co-inertia analysis (GOMCIA) and generalized orthogonal multiple co-inertia analysis-partial least squares (GOMCIA-PLS) are proposed for modelling two sets of blocks measured on the same observations. We especially emphasize GOMCIA-PLS methods in which we consider one of the sets as predictive. All these methods are based on the step-by-step maximization of the same criterion under normalization constraints and produce orthogonal components or super-components. The solutions of the problem have to be computed with an iterative algorithm (which we prove to be convergent). We also give some interesting special cases and discuss the differences compared with a few other multiblock and/or multiway methods. Finally, short examples of real data are processed to show how GOMCIA-PLS can be used and its properties. Copyright (C) 2003 John Wiley Sons, Ltd.
It is often admitted that a static system with more inputs (sources) than outputs (sensors, or channels) cannot be blindly identified, that is, identified only from the observation of its outputs, and without any a pr...
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ISBN:
(纸本)0819429163
It is often admitted that a static system with more inputs (sources) than outputs (sensors, or channels) cannot be blindly identified, that is, identified only from the observation of its outputs, and without any a priori knowledge on the source statistics but their independence. By resorting to High-Order Statistics, it turns out that static MIMO systems with fewer outputs than inputs can be identified, as demonstrated in the present paper. The principle, already described in a recent rather theoretical paper, had not yet been applied to a concrete blind identification problem. Here, in order to demonstrate its feasiblity, the procedure is detailed in the case of a 2-sensor 3-source mixture;a numerical algorithm is devised, that blindly identifies a 5-input 2-output mixture. Computer results show its behavior as a function of the data length when sources are QPSK-modulated signals, widely used in digital communications. Then another algorithm is proposed to extract the 3 sources from the 2 observations, once the mixture has been identified. Contrary to the first algorithm, this one assumes that the sources have a known discrete distribution. Computer experiments are run in the case of three BPSK sources in presence of Gaussian noise. Keywords: High-Order Statistics (HOS), Source Separation, Downlink Communications, User Extraction, Cumulant Tensor, Binary Quantics, multiway array, Independent Component Analysis (ICA), Multiple Inputs Multiple Outputs (MIMO) static linear systems.
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