Open Access
Enhancing LSTM for sequential image classification by modifying data aggregation
(IEEE, 2021) Takáč, Zdenko; Ferrero Jaurrieta, Mikel; Horanská, Lubomíra; Krivonakova, Nada; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Recurrent Neural Networks (RNN) model sequential information and are commonly used for the analysis of time series. The most usual operation to fuse information in RNNs is the sum. In this work, we use a RNN extended type, Long Short-Term Memory (LSTM) and we use it for image classification, to which we give a sequential interpretation. Since the data used may not be independent to each other, we modify the sum operator of an LSTM unit using the n-dimensional Choquet integral, which considers possible data coalitions. We compare our methods to those based on usual aggregation functions, using the datasets Fashion-MNIST and MNIST.
Open Access
Entropía en conjuntos difusos intervalo-valorados y aplicación a umbralización de imágenes con órdenes admisibles
(2020) Ferrero Jaurrieta, Mikel; Fernández Fernández, Francisco Javier; Escuela Técnica Superior de Ingeniería Industrial, Informática y de Telecomunicación; Industria, Informatika eta Telekomunikazio Ingeniaritzako Goi Mailako Eskola Teknikoa
El problema clásico de umbralización tiene como finalidad principal la separación de objetos de una imagen respecto del fondo. En el presente trabajo, trataremos el tema desde la lógica difusa, puesto que proporciona una herramienta adecuada para manejar la incertidumbre inherente a las imágenes. A la hora de trabajar con conjuntos difusos, puede resultar difícil dar un valor de pertenencia exacto. Por ello, trabajaremos con conjuntos difusos intervalo-valorados, entendiendo que la amplitud de los intervalos de pertenencia es una medida de la incertidumbre. Dado que la comparación entre dos valores intervalares cualesquiera es un problema complejo a la hora de trabajar con intervalos, utilizaremos órdenes admisibles para su tratamiento. El método de umbralización planteado se basa en el uso de funciones de equivalencia restringidas, medidas de inclusión para conjuntos difusos intervalo-valorados y funciones de entropía intervalo-valoradas.
Open Access
From restricted equivalence functions on Ln to similarity measures between fuzzy multisets
(IEEE, 2023) Ferrero Jaurrieta, Mikel; Takáč, Zdenko; Rodríguez Martínez, Iosu; Marco Detchart, Cedric; Bernardini, Ángela; Fernández Fernández, Francisco Javier; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from L to L n and present a new similarity construction on L n . Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.
Open Access
Applying d-XChoquet integrals in classification problems
(IEEE, 2022) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Emmendorfer, Leonardo R.; Ferrero Jaurrieta, Mikel; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS's) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.
Open Access
Reduction of complexity using generators of pseudo-overlap and pseudo-grouping functions
(2024) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Zhang, Xiaohong; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Overlap and grouping functions can be used to measure events in which we must consider either the maximum or the minimum lack of knowledge. The commutativity of overlap and grouping functions can be dropped out to introduce the notions of pseudo-overlap and pseudo-grouping functions, respectively. These functions can be applied in problems where distinct orders of their arguments yield different values, i.e., in non-symmetric contexts. Intending to reduce the complexity of pseudo-overlap and pseudo-grouping functions, we propose new construction methods for these functions from generalized concepts of additive and multiplicative generators. We investigate the isomorphism between these families of functions. Finally, we apply these functions in an illustrative problem using them in a time series prediction combined model using the IOWA operator to evidence that using these generators and functions implies better performance.
Open Access
Extensión multidimensional de la integral de Choquet discreta y su aplicación en redes neuronales recurrentes
(Universidad de Málaga, 2021) Ferrero Jaurrieta, Mikel; Rodríguez Martínez, Iosu; Pereira Dimuro, Graçaliz; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este trabajo presentamos una definición de la integral de Choquet discreta n-dimensional, para fusionar datos vectoriales. Como aplicación, utilizamos estas nuevas integrales de Choquet discretas multidimensionales en la fusión de información secuencial en las redes neuronales recurrentes, mejorando los resultados obtenidos mediante el método de agregación tradicional.
Embargo
Non-symmetric over-time pooling using pseudo-grouping functions for convolutional neural networks
(Elsevier, 2024) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Miguel Turullols, Laura de; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Convolutional Neural Networks (CNNs) are a family of networks that have become state-of-the-art in several fields of artificial intelligence due to their ability to extract spatial features. In the context of natural language processing, they can be used to build text classification models based on textual features between words. These networks fuse local features to generate global features in their over-time pooling layers. These layers have been traditionally built using the maximum function or other symmetric functions such as the arithmetic mean. It is important to note that the order of input local features is significant (i.e. the symmetry is not an inherent characteristic of the model). While this characteristic is appropriate for image-oriented CNNs, where symmetry might make the network robust to image rigid transformations, it seems counter-productive for text processing, where the order of the words is certainly important. Our proposal is, hence, to use non-symmetric pooling operators to replace the maximum or average functions. Specifically, we propose to perform over-time pooling using pseudo-grouping functions, a family of non-symmetric aggregation operators that generalize the maximum function. We present a construction method for pseudo-grouping functions and apply different examples of this family to over-time pooling layers in text-oriented CNNs. Our proposal is tested on seven different models and six different datasets in the context of engineering applications, e.g. text classification. The results show an overall improvement of the models when using non-symmetric pseudo-grouping functions over the traditional pooling function.
Open Access
Fuzzy sets complement-based gated recurrent unit
(CEUR Workshop Proceedings (CEUR-WS.org), 2021) Ferrero Jaurrieta, Mikel; Pereira Dimuro, Graçaliz; Takáč, Zdenko; Santiago, Regivan; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Gobierno de Navarra / Nafarroako Gobernua
Gated Recurrent Units (GRU) are neural network gated architectures that simplify other ones (suchas, LSTM) by joining gates mainly. For this, instead of using two gates, if𝑥is the first gate, standardoperation1−𝑥is used to generate the second one, optimizing the number of parameters. In this work, we interpret this information as a fuzzy set, and we generalize the standard operation using fuzzy negations, and improving the accuracy obtained with the standard one.
Embargo
Multivalued and non-symmetric operators for sequential information processing
(2024) Ferrero Jaurrieta, Mikel; López Molina, Carlos; Takáč, Zdenko; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Las estructuras de datos multivaluadas son un tipo de organización de datos que permiten representar información compuesta por varios atributos, variables, dimensiones o coordenadas. Para su funcionamiento básico se dotan de operaciones básicas como la igualdad, comparación y orden. A partir de estas se definen operaciones como, por ejemplo, la agregación de información. Un tipo de dato multivaluado de especial interés es la información secuencial, en el cual existe una dependencia temporal, espacial o de orden entre sus elementos. Ejemplos relevantes de información secuencial son el texto (lenguaje natural) o las series temporales. En esta tesis presentamos un nuevo framework para información multivaluada. De esta manera, presentamos nuevos métodos de agregación de información multivaluada. Para ello, se extienden funciones que tienen en cuenta la posible relación entre los datos internos a la estructura multivaluada. Dado que estas funciones necesitan una ordenación de sus argumentos, se presentan distintos enfoques: por componentes individuales y proponiendo un nuevo método de ordenación. Estas funciones se aplican en la fusión de información secuencial en redes neuronales recurrentes. En el contexto multivaluado también se presenta un nuevo método para la comparación de estructuras multivaluadas. De forma complementaria, se considera un problema adicional en el procesamiento de información secuencial: la simetría. Se considera que, en la agregación de información secuencial, el orden de los argumentos es una cuestión de gran relevancia. Por lo tanto, el uso de funciones simétricas no tiene sentido, dado que puede que estemos rompiendo la correlación temporal. Por ello, se presentan nuevos métodos de construcción de funciones de agregación no-simétricas. Estas serán aplicadas en tareas de agregación de información con dependencia secuencial, como puede ser el procesamiento de texto en redes neuronales convolucionales y la combinación de modelos de predicción de series temporales.
Embargo
Degree of totalness: how to choose the best admissible permutation for vector fuzzy integration
(Elsevier, 2023) Ferrero Jaurrieta, Mikel; Horanská, Lubomíra; Lafuente López, Julio; Mesiar, Radko; Pereira Dimuro, Graçaliz; Takáč, Zdenko; Gómez Fernández, Marisol; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The use of aggregation operators that require ordering of the data brings a problem when the structures to be aggregated are multi-valued, since there may be several admissible orders. To addressing this problem, the concept of admissible permutation was introduced for intervals. In this paper we extend this concept to vector domain. However, the problem of selecting the best possible permutation is still an open problem. In this paper we present a novel concept in order to choose the best admissible permutation for vectors: the degree of totalness. This concept allows us to represent to which degree the admissible permutation reorder given vectors as a chain with respect to the partial order. Finally, from the best admissible permutation we construct the Choquet integral.