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Artículo
Topology-based representative datasets to reduce neural network training resources
(Springer, 2022)
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. ...
Artículo
Emotion recognition in talking-face videos using persistent entropy and neural networks
(American Institute of Mathematical Sciences (AIMS), 2022)
The automatic recognition of a person’s emotional state has become a very active research field that involves scientists specialized in different areas such as artificial intelligence, computer vi sion, or psychology, ...
Artículo
Persistent entropy for separating topological features from noise in vietoris-rips complexes
(Springer, 2019)
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional ...
Artículo
Computing Adem Cohomology Operations
(Cornell University, 2006)
We deal with the problem of obtaining explicit simplicial formu- lae defining the classical Adem cohomology operations at the cochain level. Having these formulae at hand, we design an algorithm for com- puting these ...
Artículo
Approximating lower-star persistence via 2D combinatorial map simplification
(Elsevier, 2020)
Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in the associated persistence diagrams. In this paper, we propose a filtration simplification algorithm ...
Artículo
A combinatorial method for computing Steenrod squares
(Elsevier, 1999)
We present here a combinatorial method for computing Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal ...
Artículo
Characterizing Configurations of critical points through LBP Extended Abstract
(Universidad de Sevilla, 2015)
In this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) is given using combinatorial maps and a method for obtaining a representative LBP image is developed ...
Artículo
Cubical cohomology ring of 3D photographs
(2011)
Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. ...
Artículo
Persistent-homology-based gait recognition
(Cornell University, 2017)
Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. In this paper, we present a persistent homology-based method to extract topological features ...
Artículo
On the stability of persistent entropy and new summary functions for Topological Data Analysis
(Cornell University, 2018)
Persistent entropy of persistence barcodes, which is based on the Shannon entropy, has been recently defined and successfully applied to different scenarios: characterization of the idiotypic immune network, detection ...