http://www.cnr.it/ontology/cnr/individuo/prodotto/ID250390
Multi-Resolutive Sparse Approximations of d-Dimensional Data (Articolo in rivista)
- Type
- Label
- Multi-Resolutive Sparse Approximations of d-Dimensional Data (Articolo in rivista) (literal)
- Anno
- 2013-01-01T00:00:00+01:00 (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
- 10.1016/j.cviu.2012.10.012 (literal)
- Alternative label
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
- Giuseppe Patanè (literal)
- Pagina inizio
- Pagina fine
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
- Rivista
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
- Note
- ISI Web of Science (WOS) (literal)
- Scopu (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- Consiglio Nazionale delle Ricerche, Istituto di Matematica Applicata e Tecnologie Informatiche, Genova, Italy (literal)
- Titolo
- Multi-Resolutive Sparse Approximations of d-Dimensional Data (literal)
- Abstract
- This paper proposes an iterative computation of sparse representations of functions defined on Rd, which
exploits a formulation of the sparsification problem equivalent to Support Vector Machine and based on
Tikhonov regularization. Through this equivalent formulation, the sparsification reduces to an approximation
problem with a Tikhonov regularizer, which selects the null coefficients of the resulting approximation.
The proposed multi-resolutive sparsification achieves a different resolution in the
approximation of the input data through a hierarchy of nested approximation spaces. The idea behind
our approach is to combine a smooth and strictly convex approximation of the l1-norm with Tikhonov
regularization and iterative solvers of linear/non-linear equations. Firstly, the iterative sparsification
scheme is introduced in a Reproducing Kernel Hilbert Space with respect to its native norm. Then, the
sparsification is generalized to arbitrary function spaces using the least-squares norm and radial basis
functions. Finally, the discrete sparsification is derived using the eigendecomposition and the spectral
properties of sparse matrices; in this case, the computational cost is O(nlogn), with n number of input
points. Assuming that the data is supported on a (d ? 1)-dimensional manifold, we derive a variant of
the sparsification scheme that guarantees the smoothness of the solution in the ambient and intrinsic
space by using spectral graph theory and manifold learning techniques. Finally, we discuss the multiresolutive
approximation of d-dimensional data such as signals, images, and 3D shapes. (literal)
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