Eduardo Paluzo Hidalgo
Assistant Professor
Sevilla, Andalucía, España
85 contactos
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Especialmente interesado en Inteligencia artificial, lógica, álgebra y topología. Desarrollándome en el ámbito de la investigación.
Actividad
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Una cultura laboral positiva no es: - Cesta de frutas gratis - Mesas de ping pong - 2 porciones de pizza cada dos viernes - Trabaja duro/juega duro…
Una cultura laboral positiva no es: - Cesta de frutas gratis - Mesas de ping pong - 2 porciones de pizza cada dos viernes - Trabaja duro/juega duro…
Recomendado por Eduardo Paluzo Hidalgo
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📣 INFORME Ya se han publicado los datos del paro de octubre de 2023 y las previsiones de cara al mes de noviembre, por nuestro The Adecco Group…
📣 INFORME Ya se han publicado los datos del paro de octubre de 2023 y las previsiones de cara al mes de noviembre, por nuestro The Adecco Group…
Recomendado por Eduardo Paluzo Hidalgo
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¡Feliz martes, escutoides! 😁 La investigadora Clara Grima nos presenta al escutoide, la forma geométrica que te da forma Vía ABC de Sevilla S. L.
¡Feliz martes, escutoides! 😁 La investigadora Clara Grima nos presenta al escutoide, la forma geométrica que te da forma Vía ABC de Sevilla S. L.
Recomendado por Eduardo Paluzo Hidalgo
Experiencia
Educación
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Universidad Internacional Menéndez Pelayo
Curso Algebraic and Combinatorial Methods in Stochastic Calculus
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Publicaciones
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Simplicial-Map Neural Networks Robust to Adversarial Examples
Mathematics
Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data point produces a change on the output label assigned by the model. Such adversarial examples represent a weakness for the safety of neural network applications, and many different solutions have been proposed for minimizing their effects. In this paper, we propose a new approach by means of a family of neural networks called simplicial-map neural networks constructed from an…
Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data point produces a change on the output label assigned by the model. Such adversarial examples represent a weakness for the safety of neural network applications, and many different solutions have been proposed for minimizing their effects. In this paper, we propose a new approach by means of a family of neural networks called simplicial-map neural networks constructed from an Algebraic Topology perspective. Our proposal is based on three main ideas. Firstly, given a classification problem, both the input dataset and its set of one-hot labels will be endowed with simplicial complex structures, and a simplicial map between such complexes will be defined. Secondly, a neural network characterizing the classification problem will be built from such a simplicial map. Finally, by considering barycentric subdivisions of the simplicial complexes, a decision boundary will be computed to make the neural network robust to adversarial attacks of a given size.
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Approximating lower-star persistence via 2D combinatorial map simplification
Pattern Recognition letters
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 for orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented by 2D combinatorial maps. Given a lower-star filtration of the mesh, faces are added into contiguous clusters according to a “height” function and a parameter ϵ. Faces in the same…
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 for orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented by 2D combinatorial maps. Given a lower-star filtration of the mesh, faces are added into contiguous clusters according to a “height” function and a parameter ϵ. Faces in the same cluster are merged into a single face, resulting in a lower resolution mesh and a simpler filtration. We prove that the parameter ϵ bounds the perturbation in the original persistence diagrams, and we provide experiments demonstrating the computational advantages of the simplification process.
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Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
Neural Networks
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This…
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This approach is based on an approximation of continuous functions by simplicial maps. Once a triangulation of the space is given, a concrete architecture and set of weights can be obtained. The quality of the approximation depends on the refinement of the covering of the space by simplicial complexes.
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Towards Emotion Recognition: A Persistent Entropy Application
Computational Topology in Image Context. CTIC 2019. Lecture Notes in Computer Science, vol 11382. Springer, Cham
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Representative Datasets for Neural Networks
Electronic Notes in Discrete Mathematics 68C (2018) pp. 89-94
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Towards a Philological Metric through a Topological Data Analysis Approach
ArXiV
The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives of the poetry of this epoch are Francisco de Quevedo and Luis de Góngora y Argote. They are commonly classified by the literary experts in two different streams: Quevedo belongs to the Conceptismo and Góngora to the Culteranismo. Besides, traditionally, even if Quevedo is considered the most representative of the Conceptismo, Lope de Vega is also considered to be, at…
The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives of the poetry of this epoch are Francisco de Quevedo and Luis de Góngora y Argote. They are commonly classified by the literary experts in two different streams: Quevedo belongs to the Conceptismo and Góngora to the Culteranismo. Besides, traditionally, even if Quevedo is considered the most representative of the Conceptismo, Lope de Vega is also considered to be, at least, closely related to this literary trend. In this paper, we use Topological Data Analysis techniques to provide a first approach to a metric distance between the literary style of these poets. As a consequence, we reach results that are under the literary experts' criteria, locating the literary style of Lope de Vega, closer to the one of Quevedo than to the one of Góngora.
Cursos
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Algebraic and Combinatorial Methods in Stochastic Calculus, 18th Santaló Summer School
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Idiomas
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Inglés C1
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Francés B2
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Español
Competencia bilingüe o nativa