Open Access
Interval subsethood measures with respect to uncertainty for the interval-valued fuzzy setting
(Atlantis Press, 2020) Pekala, Barbara; Bentkowska, Urszula; Sesma Sara, Mikel; Fernández Fernández, Francisco Javier; Lafuente López, Julio; Altalhi, A. H.; Knap, Maksymilian; Bustince Sola, Humberto; Pintor Borobia, Jesús María; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería
In this paper, the problem of measuring the degree of subsethood in the interval-valued fuzzy setting is addressed. Taking into account the widths of the intervals, two types of interval subsethood measures are proposed. Additionally, their relation and main properties are studied. These developments are made both with respect to the regular partial order of intervals and with respect to admissible orders. Finally, some construction methods of the introduced interval subsethood measures with the use interval-valued aggregation functions are examined.
Open Access
A fuzzy association rule-based classifier for imbalanced classification problems
(Elsevier, 2021) Sanz Delgado, José Antonio; Sesma Sara, Mikel; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Imbalanced classification problems are attracting the attention of the research community because they are prevalent in real-world problems and they impose extra difficulties for learning methods. Fuzzy rule-based classification systems have been applied to cope with these problems, mostly together with sampling techniques. In this paper, we define a new fuzzy association rule-based classifier, named FARCI, to tackle directly imbalanced classification problems. Our new proposal belongs to the algorithm modification category, since it is constructed on the basis of the state-of-the-art fuzzy classifier FARC–HD. Specifically, we modify its three learning stages, aiming at boosting the number of fuzzy rules of the minority class as well as simplifying them and, for the sake of handling unequal fuzzy rule lengths, we also change the matching degree computation, which is a key step of the inference process and it is also involved in the learning process. In the experimental study, we analyze the effectiveness of each one of the new components in terms of performance, F-score, and rule base size. Moreover, we also show the superiority of the new method when compared versus FARC–HD alongside sampling techniques, another algorithm modification approach, two cost-sensitive methods and an ensemble.
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
Learning ordered pooling weights in image classification
(Elsevier, 2020) Forcén Carvalho, Juan Ignacio; Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Spatial pooling is an important step in computer vision systems like Convolutional Neural Networks or the Bag-of-Words method. The spatial pooling purpose is to combine neighbouring descriptors to obtain a single descriptor for a given region (local or global). The resultant combined vector must be as discriminant as possible, in other words, must contain relevant information, while removing irrelevant and confusing details. Maximum and average are the most common aggregation functions used in the pooling step. To improve the aggregation of relevant information without degrading their discriminative power for image classification, we introduce a simple but effective scheme based on Ordered Weighted Average (OWA) aggregation operators. We present a method to learn the weights of the OWA aggregation operator in a Bag-of-Words framework and in Convolutional Neural Networks, and provide an extensive evaluation showing that OWA based pooling outperforms classical aggregation operators.
Open Access
New classes of the moderate deviation functions
(Springer Nature, 2021) Špirková, Jana; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
At present, in the field of aggregation of various input values, attention is focused on the construction of aggregation functions using other functions that can affect the resulting aggregated value. This resulting value should characterize the properties of the individual input values as accurately as possible. Attention is also paid to aggregation using the so-called moderate deviation function. Using this function in aggregation ensures that all properties of aggregation functions are preserved. This work offers constructions of the moderate deviation functions using negations and automorphisms on the symmetric interval [−1, 1] and a general closed interval [a, b] ⊂ [−∞, ∞].
Open Access
Reemplazo de la función de pooling de redes neuronales convolucionales por combinaciones lineales de funciones crecientes
(Universidad de Málaga, 2021) Rodríguez Martínez, Iosu; Lafuente López, Julio; Sesma Sara, Mikel; Herrera, Francisco; Ursúa Medrano, Pablo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Las redes convolucionales llevan a cabo un proceso automatico de extracción y fusión de características mediante el cual obtienen la información más relevante de una imagen dada. El proceso de submuestreo mediante el cual se fusionan características localmente próximas, conocido como ‘pooling’, se lleva a cabo tradicionalmente con funciones sencillas como el máximo o la media aritmética, ignorando otras opciones muy populares en el campo de la teoría de agregaciones. En este trabajo proponemos reemplazar dichas funciones por otra serie de ordenes estadísticos, así como por la integral de Sugeno y una nueva generalización de la misma. Además, basándonos en trabajos que emplean la combinación convexa del máximo y la media, presentamos una nueva capa que permite combinar varias de las nuevas agregaciones, mejorando sus resultados individuales.
Open Access
Clusterig cosmológico: un enfoque del clustering gravitacional clásico inspirado en la estructura y dinámica del cosmos a gran escala
(Universidad de Málaga, 2021) Castillo López, Aitor; Fumanal Idocin, Javier; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este trabajo proponemos un nuevo enfoque del algoritmo de clustering gravitacional basado en lo que Einstein considero su 'mayor error': la constante cosmológica. De manera similar al algoritmo de clustering gravitacional, nuestro enfoque está inspirado en principios y leyes del cosmos, y al igual que ocurre con la teoría de la relatividad de Einstein y la teoría de la gravedad de Newton, nuestro enfoque puede considerarse una generalización del agrupamiento gravitacional, donde, el algoritmo de clustering gravitacional se recupera como caso límite. Además, se desarrollan e implementan algunas mejoras que tienen como objetivo optimizar la cantidad de iteraciones finales, y de esta forma, se reduce el tiempo de ejecución tanto para el algoritmo original como para nuestra versión.
Open Access
Generalized decomposition integral
(Elsevier, 2020) Horanská, Lubomíra; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Mesiar, Radko; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this paper we propose two different generalizations of the decomposition integral introduced by Even and Lehrer. We modify the product operator merging a given capacity and the decomposition coefficients by some more general functions F and G and compare properties of the obtained functionals with properties of the original decomposition integral. Generalized decomposition integrals corresponding to the particular decomposition systems, being generalizations of Shilkret, Choquet and concave integrals, are studied and exemplified.
Open Access
General grouping functions
(Springer, 2020) Santos, Helida; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Sanz Delgado, José Antonio; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Some aggregation functions that are not necessarily associative, namely overlap and grouping functions, have called the attention of many researchers in the recent past. This is probably due to the fact that they are a richer class of operators whenever one compares with other classes of aggregation functions, such as t-norms and t-conorms, respectively. In the present work we introduce a more general proposal for disjunctive n-ary aggregation functions entitled general grouping functions, in order to be used in problems that admit n dimensional inputs in a more flexible manner, allowing their application in different contexts. We present some new interesting results, like the characterization of that operator and also provide different construction methods.
Open Access
Neuro-inspired edge feature fusion using Choquet integrals
(Elsevier, 2021) Marco Detchart, Cedric; Lucca, Giancarlo; López Molina, Carlos; Miguel Turullols, Laura de; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
It is known that the human visual system performs a hierarchical information process in which early vision cues (or primitives) are fused in the visual cortex to compose complex shapes and descriptors. While different aspects of the process have been extensively studied, such as lens adaptation or feature detection, some other aspects, such as feature fusion, have been mostly left aside. In this work, we elaborate on the fusion of early vision primitives using generalizations of the Choquet integral, and novel aggregation operators that have been extensively studied in recent years. We propose to use generalizations of the Choquet integral to sensibly fuse elementary edge cues, in an attempt to model the behaviour of neurons in the early visual cortex. Our proposal leads to a fully-framed edge detection algorithm whose performance is put to the test in state-of-the-art edge detection datasets.