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008			220601s2018 sz | s |||| 0|eng d
020			_a9783031018206
024	7		_a10.1007/978-3-031-01820-6 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aTA1634 _b2018 EB
100			_aMinh, Hà Quang. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9100006
245	1	0	_aCovariances in Computer Vision and Machine Learning _cby Hà Quang Minh, Vittorio Murino
250			_a1st edition 2018
264		1	_aCham _bSpringer International Publishing _c2018
300			_a1 recurso en línea (XIII, 156 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Computer Vision _x2153-1064
505	0		_aAcknowledgments -- Introduction -- Data Representation by Covariance Matrices -- Geometry of SPD Matrices -- Kernel Methods on Covariance Matrices -- Data Representation by Covariance Operators -- Geometry of Covariance Operators -- Kernel Methods on Covariance Operators -- Conclusion and Future Outlook -- Bibliography -- Authors' Biographies.
520			_aCovariance matrices play important roles in many areas of mathematics, statistics, and machine learning, as well as their applications. In computer vision and image processing, they give rise to a powerful data representation, namely the covariance descriptor, with numerous practical applications. In this book, we begin by presenting an overview of the {\it finite-dimensional covariance matrix} representation approach of images, along with its statistical interpretation. In particular, we discuss the various distances and divergences that arise from the intrinsic geometrical structures of the set of Symmetric Positive Definite (SPD) matrices, namely Riemannian manifold and convex cone structures. Computationally, we focus on kernel methods on covariance matrices, especially using the Log-Euclidean distance. We then show some of the latest developments in the generalization of the finite-dimensional covariance matrix representation to the {\it infinite-dimensional covariance operator} representation via positive definite kernels. We present the generalization of the affine-invariant Riemannian metric and the Log-Hilbert-Schmidt metric, which generalizes the Log-Euclidean distance. Computationally, we focus on kernel methods on covariance operators, especially using the Log-Hilbert-Schmidt distance. Specifically, we present a two-layer kernel machine, using the Log-Hilbert-Schmidt distance and its finite-dimensional approximation, which reduces the computational complexity of the exact formulation while largely preserving its capability. Theoretical analysis shows that, mathematically, the approximate Log-Hilbert-Schmidt distance should be preferred over the approximate Log-Hilbert-Schmidt inner product and, computationally, it should be preferred over the approximate affine-invariant Riemannian distance. Numerical experiments on image classification demonstrate significant improvements of the infinite-dimensional formulation over the finite-dimensional counterpart. Given the numerous applications of covariance matrices in many areas of mathematics, statistics, and machine learning, just to name a few, we expect that the infinite-dimensional covariance operator formulation presented here will have many more applications beyond those in computer vision.
988			_aSynthesis Collection of Technology_2018
650		7	_2embne _9166090 _aAprendizaje automático _xModelos matemáticos
650		7	_2embne _9159793 _aVisión por ordenador _xModelos matemáticos
700			_aMurino, Vittorio _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9100007
776	0	8	_iPrinted edition: _z9783031000775
776	0	8	_iPrinted edition: _z9783031006920
776	0	8	_iPrinted edition: _z9783031029486
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-01820-6 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b03/2023 _dz _esc _zSI