Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Patrizio Frosini"'
Publikováno v:
Machine Learning and Knowledge Extraction, Vol 5, Iss 4, Pp 1905-1920 (2023)
This paper is part of a line of research devoted to developing a compositional and geometric theory of Group Equivariant Non-Expansive Operators (GENEOs) for Geometric Deep Learning. It has two objectives. The first objective is to generalize the not
Externí odkaz:
https://doaj.org/article/55c31ce5fab94e558e2bf0a94cfcfa68
Publikováno v:
Frontiers in Artificial Intelligence, Vol 6 (2023)
In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain sets of t
Externí odkaz:
https://doaj.org/article/c787d04fefac4fa5a0ca7ddbbf761cf3
Publikováno v:
Entropy, Vol 25, Iss 8, p 1150 (2023)
In recent years, group equivariant non-expansive operators (GENEOs) have started to find applications in the fields of Topological Data Analysis and Machine Learning. In this paper we show how these operators can be of use also for the removal of imp
Externí odkaz:
https://doaj.org/article/7bf9fbaa36af408db62d0da541815fbf
Publikováno v:
Frontiers in Artificial Intelligence, Vol 5 (2022)
Group Equivariant Operators (GEOs) are a fundamental tool in the research on neural networks, since they make available a new kind of geometric knowledge engineering for deep learning, which can exploit symmetries in artificial intelligence and reduc
Externí odkaz:
https://doaj.org/article/d3bc5935b9564b8e80711770a9b92c10
Autor:
Andrea Cerri, Patrizio Frosini
Publikováno v:
Image Analysis and Stereology, Vol 29, Iss 1, Pp 19-26 (2011)
Size Theory was proposed in the early 90's as a geometrical/topological approach to the problem of Shape Comparison, a very lively research topic in the fields of Computer Vision and Pattern Recognition. The basic idea is to discriminate shapes by co
Externí odkaz:
https://doaj.org/article/a8cae01ad20f4efea0754bbf4f1f3e44
Publikováno v:
Annals of Mathematics and Artificial Intelligence.
Recent advances in machine learning have highlighted the importance of using group equivariant non-expansive operators for building neural networks in a more transparent and interpretable way. An operator is called equivariant with respect to a group
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dfc14e3bf65597954597a544f835da46
https://doi.org/10.1007/s10472-022-09830-1
https://doi.org/10.1007/s10472-022-09830-1
Publikováno v:
Frontiers in artificial intelligence. 5
Group Equivariant Operators (GEOs) are a fundamental tool in the research on neural networks, since they make available a new kind of geometric knowledge engineering for deep learning, which can exploit symmetries in artificial intelligence and reduc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=pmid________::d42f1c1461da855c4119c500f050e8fb
https://pubmed.ncbi.nlm.nih.gov/35243336
https://pubmed.ncbi.nlm.nih.gov/35243336
Publikováno v:
Homology, Homotopy and Applications. 21:231-259
We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in the definition of dHT is to measure the minimal shift that is necessa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85e5385c2715a6f5d87200c4441f1217
https://doi.org/10.4310/hha.2019.v21.n2.a13
https://doi.org/10.4310/hha.2019.v21.n2.a13
Autor:
Patrizio Frosini
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9789811601736
The natural pseudo-distance \(d_G\) associated with a group G of self-homeomorphisms of a topological space X is a pseudo-metric developed to compare real-valued functions defined on X, when the equivalence between functions is expressed by the group
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::678b78fac2574b894186ae022b67012e
https://doi.org/10.1007/978-981-16-0174-3_17
https://doi.org/10.1007/978-981-16-0174-3_17
Autor:
Andrea Cerri, Patrizio Frosini
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9789811601736
In this paper, we propose a brief overview about multidimensional persistent Betti numbers (PBNs) and the metric that is usually used to compare them, i.e., the multidimensional matching distance. We recall the main definitions and results, mainly fo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6dc52565910c9e867292ed783b309a7b
https://doi.org/10.1007/978-981-16-0174-3_18
https://doi.org/10.1007/978-981-16-0174-3_18