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Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As…

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…

We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm…

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…

Tensor decompositions are powerful tools for large data analytics as they jointly model multiple aspects of data into one framework and enable the discovery of the latent structures and higher-order correlations within the data. One of the…

Generalized Eigenvalue Problems (GEPs) encompass a range of interesting dimensionality reduction methods. Development of efficient stochastic approaches to these problems would allow them to scale to larger datasets. Canonical Correlation…

Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…

We present a machine-learning method for the nonparametric extraction of generalized parton distributions (GPDs) from Compton form factors (CFFs) constrained by experimental data. The method addresses the longstanding inverse problem posed…

In this work, we propose a decoupled support vector regression (SVR) approach for direct canonical polyadic decomposition (CPD) of a potential energy surface (PES) through a set of discrete training energy data. This approach, denoted by…

Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and…

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

Completely positive (CP) tensors, which correspond to a generalization of CP matrices, allow to reformulate or approximate a general polynomial optimization problem (POP) with a conic optimization problem over the cone of CP tensors.…

We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials. We introduce algebraic techniques which reduce this task to linear, second order cone, and semidefinite programming. This allows…

Tensor decomposition, a collection of factorization techniques for multidimensional arrays, are among the most general and powerful tools for scientific analysis. However, because of their increasing size, today's data sets require more…

We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) \citep{ghosh2022supervised}. SLCE works by mapping the samples of a…

The CANDECOMP/PARAFAC (or Canonical polyadic, CP) decomposition of tensors has numerous applications in various fields, such as chemometrics, signal processing, machine learning, etc. Tensor CP decomposition assumes the knowledge of the…

This paper presents a canonical polyadic (CP) tensor decomposition that addresses unaligned observations. The mode with unaligned observations is represented using functions in a reproducing kernel Hilbert space (RKHS). We introduce a…