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08/25/2023
A topological model for partial equivariance in deep learning and data analysis
In this article, we propose a topological model to encode partial equiva...
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06/13/2023
Low-Resource White-Box Semantic Segmentation of Supporting Towers on 3D Point Clouds via Signature Shape Identification
Research in 3D semantic segmentation has been increasing performance met...
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06/29/2022
Generalized Permutants and Graph GENEOs
In this paper we establish a bridge between Topological Data Analysis an...
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02/28/2022
A probabilistic result on impulsive noise reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
In recent years, group equivariant non-expansive operators (GENEOs) have...
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01/31/2022
GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection
Nowadays there is a big spotlight cast on the development of techniques ...
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03/03/2021
On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators
Group equivariant non-expansive operators have been recently proposed as...
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07/06/2020
Parametric machines: a fresh approach to architecture search
Using tools from category theory, we provide a framework where artificia...
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12/31/2018
Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning
The aim of this paper is to provide a general mathematical framework for...
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01/20/2018
On the geometrical properties of the coherent matching distance in 2D persistent homology
In this paper we study a new metric for comparing Betti numbers function...
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03/07/2016
Position paper: Towards an observer-oriented theory of shape comparison
In this position paper we suggest a possible metric approach to shape co...
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12/27/2013
Combining persistent homology and invariance groups for shape comparison
In many applications concerning the comparison of data expressed by R^m-...
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12/04/2012
G-invariant Persistent Homology
Classical persistent homology is a powerful mathematical tool for shape ...
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11/12/2008
Necessary Conditions for Discontinuities of Multidimensional Size Functions
Some new results about multidimensional Topological Persistence are pres...
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08/02/2006