Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Ferri, Massimo"'
The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of
Externí odkaz:
http://arxiv.org/abs/2406.08045
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware o
Externí odkaz:
http://arxiv.org/abs/2212.13985
In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges.
Externí odkaz:
http://arxiv.org/abs/2206.14798
Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and \textit{ranging} sets:
Externí odkaz:
http://arxiv.org/abs/2009.06897
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to significan
Externí odkaz:
http://arxiv.org/abs/1901.08051
Autor:
Bergomi, Mattia G.1 (AUTHOR) mattiagbergomi@gmail.com, Ferri, Massimo2 (AUTHOR) massimo.ferri@unibo.it
Publikováno v:
Algorithms. Oct2023, Vol. 16 Issue 10, p465. 14p.
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function. Comparing the pers
Externí odkaz:
http://arxiv.org/abs/1805.03266
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can
Externí odkaz:
http://arxiv.org/abs/1707.09670
Autor:
Ferri, Massimo
Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classificati
Externí odkaz:
http://arxiv.org/abs/1706.00411
Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through "Betti Numbers" the presence of holes and t
Externí odkaz:
http://arxiv.org/abs/1605.09781