Giovanni Barbarino

Identifiability of Nonnegative Tucker Decompositions—Part I: Theory

Subhayan Saha, Giovanni Barbarino, Nicolas Gillis

Abstract. Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic decomposition, is identifiability: the factors are …

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Computing the Least Cone-Constrained Singular Value of Matrices

Giovanni Barbarino, Nicolas Gillis, David Sossa

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Computing the Least Cone-Constrained Singular Value of Matrices

Giovanni Barbarino, Nicolas Gillis, David Sossa

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A short note on $A_α$-eigenvalues for simple graphs

Giovanni Barbarino

Given a simple graph $G$, its $A_α$ matrix is a convex combination with parameter $α\in [0,1]$ of its adjacency matrix and its degree diagonal matrices. Here we compare two lower bounds presented in [J. D. G. Silva Jr., C. S. Oliveira and …

A short note on $A_α$-eigenvalues for simple graphs

Giovanni Barbarino

Given a simple graph $G$, its $A_α$ matrix is a convex combination with parameter $α\in [0,1]$ of its adjacency matrix and its degree diagonal matrices. Here we compare two lower bounds presented in [J. D. G. Silva Jr., C. S. Oliveira and …

Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition

Giovanni Barbarino, Nicolas Gillis, Subhayan Saha

Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove …

On the Robustness of the Successive Projection Algorithm

Giovanni Barbarino, Nicolas Gillis

Abstract. The successive projection algorithm (SPA) is a workhorse algorithm to learn the [Formula: see text] vertices of the convex hull of a set of [Formula: see text]-dimensional data points, a.k.a. a latent simplex, which has numerous applications in data science. In …

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Relations Between Analytic Spectral and Singular Value Decompositions

Stephan Weiss, Giovanni Barbarino

We compare the existence and uniqueness of the analytic singular value decomposition (SVD) of a matrix$\boldsymbol{A}(z)$to that of the analytic spectral or eigenvalue decomposition (EVD) of$\boldsymbol{R}(z)=\boldsymbol{A}(z) \boldsymbol{A}^{\mathrm{P}}(z)$. Both cases require oversampling if the matrices are connected to multiplexing operations. Additionally, the analytic …

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From asymptotic distribution and vague convergence to uniform convergence, with numerical applications

Giovanni Barbarino, Sven‐Erik Ekström, Carlo Garoni, David Meadon et autres

Abstract Let { Λ n = { λ 1 , n , … , λ d n , n } } n ${\left\{{{\Lambda}}_{n}=\left\{{\lambda }_{1,n},\dots ,{\lambda }_{{d}_{n},n}\right\}\right\}}_{n}$ be a sequence of finite multisets of real numbers such that d n → ∞ as …

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Spectral properties of flipped Toeplitz matrices and computational applications

Giovanni Barbarino, Sven‐Erik Ekström, Carlo Garoni, David Meadon et autres

We study the spectral properties of flipped Toeplitz matrices of the form 𝐻𝑛 (𝑓 ) = 𝑌𝑛 𝑇𝑛 (𝑓), where 𝑇𝑛 (𝑓) is the 𝑛 × 𝑛 Toeplitz generated by the function 𝑓 and 𝑌𝑛 is the 𝑛 × 𝑛 exchange (or …

GLT sequences and normal matrices

Giovanni Barbarino, Carlo Garoni

The theory of generalized locally Toeplitz (GLT) sequences is an apparatus for computing the asymptotic spectral distribution of matrices $A_n$ arising from numerical discretizations of differential equations. Indeed, when the mesh fineness parameter $n$ tends to infinity, these matrices $A_n$ give rise …

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Matrix-less spectral approximation for large structured matrices

Giovanni Barbarino, Melker Claesson, Sven‐Erik Ekström, Carlo Garoni et autres

Abstract Sequences of structured matrices of increasing size, such as generalized locally Toeplitz sequences, arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume that the eigenvalues of a matrix $$X_n$$ X n , belonging …

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