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37 results on '"FAVATI, PAOLA"'

2. Construction of the similarity matrix for the spectral clustering method: numerical experiments

Author

Favati, Paola, Lotti, Grazia, Menchi, Ornella, and Romani, Francesco

Subjects
Mathematics - Numerical Analysis, Computer Science - Machine Learning
Abstract

Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual clusters is highly non-convex. Its accuracy depends on how the similarity between pairs of data points is defined. Two important items contribute to the construction of the similarity matrix: the sparsity of the underlying weighted graph, which depends mainly on the distances among data points, and the similarity function. When a Gaussian similarity function is used, the choice of the scale parameter $\sigma$ can be critical. In this paper we examine both items, the sparsity and the selection of suitable $\sigma$'s, based either directly on the graph associated to the dataset or on the minimal spanning tree (MST) of the graph. An extensive numerical experimentation on artificial and real-world datasets has been carried out to compare the performances of the methods., Comment: Submitted to Journal of Computational and Applied Mathematics

Published
2019

3. Adaptive computation of the Symmetric Nonnegative Matrix Factorization (NMF)

Author

Favati, Paola, Lotti, Grazia, Menchi, Ornella, and Romani, Francesco

Subjects
Mathematics - Numerical Analysis
Abstract

Nonnegative Matrix Factorization (NMF), first proposed in 1994 for data analysis, has received successively much attention in a great variety of contexts such as data mining, text clustering, computer vision, bioinformatics, etc. In this paper the case of a symmetric matrix is considered and the symmetric nonnegative matrix factorization (SymNMF) is obtained by using a penalized nonsymmetric minimization problem. Instead of letting the penalizing parameter increase according to an a priori fixed rule, as suggested in literature, we propose a heuristic approach based on an adaptive technique. Extensive experimentation shows that the proposed algorithm is effective., Comment: Submitted to SeMA Journal

Published
2019

14. Local error estimates and regularity tests for the implementation of double adaptive quadrature

Author

Favati, Paola, Fiorentino, Giuseppe, Lotti, Grazia, and Romani, Francesco

Subjects
Error analysis (Mathematics) -- Research, Numerical integration -- Research, Computers, Mathematics, Research
Abstract

1. INTRODUCTION We consider the problem of computing an approximation of the definite integral [integral of] f(x)dx between limits b and a by using an automatic integration routine. In a [...]

Published
1997

20. CALCOLO - A Quaterly on Numerical Analysis and Theory of Computation

Author

Favati Paola and Codenotti Bruno

Subjects
Numerical Solution of Differential and Integral Equations
Abstract

Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation. The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory.Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews

Published
2012

21. Superfast solution of Toeplitz-like systems

Author

Favati, Paola, Lotti, Grazia, and Menchi, Ornella

Subjects
Toeplitz systems, linear algebra
Abstract

In this paper a new O(N log3 N) solver for N £ N Toeplitz-like sys- tems, based on a divide and conquer technique, is presented. Similarly to the superfast algorithm MBA for the inversion of a Toeplitz-like matrix [2, 16], it exploits the displacement properties. In order to avoid the well known numerical instability of the explicit inversion, the new algorithm relies on the triangular factorization and back-substitution formula for the system seen as a 2£2 block system with blocks of half size. The same idea has been used in [19] to improve the numerical stability of superfast meth- ods based on the generalized Schur algorithm for positive de¯nite Toeplitz matrices, but the algorithm we propose can be applied also to nonsym- metric Toeplitz-like systems. The stability of the algorithm is examined through numerical experiments.

Published
2011

22. Stopping rules for iterative methods in nonnegatively constrained deconvolution

Author

Favati, Paola, Lotti, Grazia, Menchi, Ornella, and Romani, Francesco

Subjects
regularization, Iterative methods, statistical methods, image reconstruction
Abstract

We consider the two-dimensional discrete nonnegatively constrained deconvolution problem, whose goal is to reconstruct an object x¤ from its image b obtained through an optical system and a®ected by noise. When the large size of the problem prevents regularization by ¯l- tering, iterative methods enjoying semiconvergence property, coupled with suitable strategies for enforcing nonnegativity, are suggested. For these methods an accurate detection of the stopping index is essential. In this paper we analyze various stopping rules and test their e®ect on three di®erent iterative regularizing methods, by a large experimenta- tion.

Published
2011

27. AN INNER-OUTER REGULARIZING METHOD FOR ILL-POSED PROBLEMS.

Author

FAVATI, PAOLA, LOTTI, GRAZIA, MENCHI, ORNELLA, and ROMANI, FRANCESCO

Subjects
LINEAR systems, MATRICES (Mathematics), INTEGRAL equations, DUAL integral equations, CONJUGATE gradient methods, ALGORITHMS
Abstract

Conjugate Gradient is widely used as a regularizing technique for solving linear systems with ill-conditioned coefficient matrix and right-hand side vector perturbed by noise. It enjoys a good convergence rate and computes quickly an iterate, say xkopt, which minimizes the error with respect to the exact solution. This behavior can be a disadvantage in the regularization context, because also the high-frequency components of the noise enter quickly the computed solution, leading to a difficult detection of kopt and to a sharp increase of the error after the koptth iteration. In this paper we propose an inner-outer algorithm based on a sequence of restarted Conjugate Gradients, with the aim of overcoming this drawback. A numerical experimentation validates the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Published
2014
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36. On the robustness of Gaussian elimination with partial pivoting

Author

Favati, Paola, Leoncini, Mauro, angeles martinez, Favati, P, Leoncini, M, and Martinez, A

Subjects
Applied Mathematic, Computational Mathematics, algorithm, Pivoting, gaussian elimination, robustness, Applied Mathematics, Gaussian elimination, Stability, Computer Graphics and Computer-Aided Design, Software

37. On functional iteration methods for solving nonlinear matrix equations arising in queueing problems.

Author

Favati, P, Favati, Paola, Meini, B, and Meini, Beatrice

Subjects
*ITERATIVE methods (Mathematics), *NONLINEAR theories, *APPROXIMATION theory, *QUEUING theory
Abstract

Discusses functional iteration methods for solving nonlinear matrix equations arising in queueing problems. Convergence rate and the starting approximation; Selection of the starting approximation; Numerical results.

Published
1999
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