Laurent Sorber

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The canonical polyadic and rank-(Lr, Lr, 1) block term decomposition (CPD and BTD, respectively) are two closely related tensor decompositions. The CPD and, recently, BTD are important tools in psychometrics, chemometrics, neuroscience, and signal processing. We present a decomposition that generalizes these two and develop algorithms for its computation.(More)
We present structured data fusion (SDF) as a framework for the rapid prototyping of knowledge discovery in one or more possibly incomplete data sets. In SDF, each data set-stored as a dense, sparse, or incomplete tensor-is factorized with a matrix or tensor decomposition. Factorizations can be coupled, or fused, with each other by indicating which factors(More)
Nonlinear optimization problems in complex variables are frequently encountered in applied mathematics and engineering applications such as control theory, signal processing and electrical engineering. Optimization of these problems often requires a first-or second-order approximation of the objective function to generate a new step or descent direction.(More)
Higher-order tensors and their decompositions are abundantly present in domains such as signal processing (e.g., higher-order statistics [1] and sensor array processing [2]), scientific computing (e.g., discretized multivariate functions [3]?[6]), and quantum information theory (e.g., representation of quantum many-body states [7]). In many applications,(More)
In this paper, we conjecture a formula for the value of the Pythago-ras number for real multivariate sum of squares polynomials as a function of the (total or coordinate) degree and the number of variables. The conjecture is based on the comparison between the number of parameters and the number of conditions for a corresponding low-rank representation.(More)
Efficient and effective algorithms are designed to compute the coordinates of nearly optimal points for multivariate polynomial interpolation on a general geometry. " Nearly optimal " refers to the property that the set of points has a Lebesgue constant near to the minimal Lebesgue constant with respect to multivariate polynomial interpolation on a finite(More)
Decompositions of higher-order tensors are becoming more and more important in signal processing, data analysis, machine learning, scientific computing, optimization and many other fields. A new trend is the study of coupled matrix/tensor decompositions (i.e., decompo-sitions of multiple matrices and/or tensors that are linked in one or several ways).(More)