Open Access
Generalizando el pooling maximo por funciones (a, b)-grouping en redes neuronales convolucionales
(CAEPIA, 2024) Rodríguez Martínez, Iosu; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Herrera, Francisco; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Gobierno de Navarra / Nafarroako Gobernua
Este artículo es un resumen del trabajo publicado en la revista Information Fusion [1]. En este artículo explorábamos el reemplazo del operador de pooling máximo comunmente empleado en redes neuronales convolucionales (CNNs) por funciones (a, b)-grouping. Estas funciones extienden el concepto de función de grouping clásica [2] a un intervalo cerrado [a, b], siguiendo la filosofía de [3]. En el contexto del operador de pooling, estas nuevas funciones ayudan a la optimización de los modelos suavizando los gradientes en el proceso de retropropagación y obteniendo resultados competitivos con métodos más complejos
Open Access
VCI-LSTM: Vector choquet integral-based long short-term memory
(IEEE, 2022) Ferrero Jaurrieta, Mikel; Takáč, Zdenko; Fernández Fernández, Francisco Javier; Horanská, Lubomíra; Pereira Dimuro, Graçaliz; Montes Rodríguez, Susana; Díaz, Irene; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Choquet integral is a widely used aggregation operator on one-dimensional and interval-valued information, since it is able to take into account the possible interaction among data. However, there are many cases where the information taken into account is vectorial, such as Long Short-Term Memories (LSTM). LSTM units are a kind of Recurrent Neural Networks that have become one of the most powerful tools to deal with sequential information since they have the power of controlling the information flow. In this paper, we first generalize the standard Choquet integral to admit an input composed by $n$-dimensional vectors, which produces an $n$-dimensional vector output. We study several properties and construction methods of vector Choquet integrals. Then, we use this integral in the place of the summation operator, introducing in this way the new VCI-LSTM architecture. Finally, we use the proposed VCI-LSTM to deal with two problems: sequential image classification and text classification.
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
Type-(2, k) overlap indices
(IEEE, 2022) Roldán López de Hierro, Antonio Francisco; Roldán, Concepción; Tíscar, Miguel Ángel; Takáč, Zdenko; Santiago, Regivan; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Automatic image detection is one of the most im- portant areas in computing due to its potential application in numerous real-world scenarios. One important tool to deal with that is called overlap indices. They were introduced as a procedure to provide the maximum lack of knowledge when comparing two fuzzy objects. They have been successfully applied in the following fields: image processing, fuzzy rule-based systems, decision making and computational brain interfaces. This notion of overlap indices is also necessary for applications in which type-2 fuzzy sets are required. In this paper we introduce the notion of type-(2, k) overlap index (k 0, 1, 2) in the setting of type-2 fuzzy sets. We describe both the reasons that have led to this notion and the relationships that naturally arise among the algebraic underlying structures. Finally, we illustrate how type- (2, k) overlap indices can be employed in the setting of fuzzy rule-based systems when the involved objects are type-2 fuzzy sets.
Embargo
Non-symmetric over-time pooling using pseudo-grouping functions for convolutional neural networks
(Elsevier, 2024-07-01) 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
A study on the suitability of different pooling operators for convolutional neural networks in the prediction of COVID-19 through chest x-ray image analysis
(Elsevier, 2024) Rodríguez Martínez, Iosu; Ursúa Medrano, Pablo; Fernández Fernández, Francisco Javier; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
The 2019 coronavirus disease outbreak, caused by the severe acute respiratory syndrome type-2 virus (SARS-CoV-2), was declared a pandemic in March 2020. Since its emergence to the present day, this disease has brought multiple countries to the brink of health care collapse during several waves of the disease. One of the most common tests performed on patients is chest x-ray imaging. These images show the severity of the patient's illness and whether it is indeed covid or another type of pneumonia. Automated assessment of this type of imaging could alleviate the time required for physicians to treat and diagnose each patient. To this end, in this paper we propose the use of Convolutional Neural Networks (CNNs) to carry out this process. The aim of this paper is twofold. Firstly, we present a pipeline adapted to this problem, covering all steps from the preprocessing of the datasets to the generation of classification models based on CNNs. Secondly, we have focused our study on the modification of the information fusion processes of this type of architectures, in the pooling layers. We propose a number of aggregation theory functions that are suitable to replace classical processes and have shown their benefits in past applications, and study their performance in the context of the x-ray classification problem. We find that replacing the feature reduction processes of CNNs leads to drastically different behaviours of the final model, which can be beneficial when prioritizing certain metrics such as precision or recall.
Open Access
A generalization of the Sugeno integral to aggregate interval-valued data: an application to brain computer interface and social network analysis
(Elsevier, 2022) Fumanal Idocin, Javier; Takáč, Zdenko; Horanská, Lubomíra; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Vidaurre Arbizu, Carmen; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Institute of Smart Cities - ISC
Intervals are a popular way to represent the uncertainty related to data, in which we express the vagueness of each observation as the width of the interval. However, when using intervals for this purpose, we need to use the appropriate set of mathematical tools to work with. This can be problematic due to the scarcity and complexity of interval-valued functions in comparison with the numerical ones. In this work, we propose to extend a generalization of the Sugeno integral to work with interval-valued data. Then, we use this integral to aggregate interval-valued data in two different settings: first, we study the use of intervals in a brain-computer interface; secondly, we study how to construct interval-valued relationships in a social network, and how to aggregate their information. Our results show that interval-valued data can effectively model some of the uncertainty and coalitions of the data in both cases. For the case of brain-computer interface, we found that our results surpassed the results of other interval-valued functions.
Open Access
Generalizing max pooling via (a, b)-grouping functions for convolutional neural networks
(Elsevier, 2023) Rodríguez Martínez, Iosu; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Herrera, Francisco; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Due to their high adaptability to varied settings and effective optimization algorithm, Convolutional Neural Networks (CNNs) have set the state-of-the-art on image processing jobs for the previous decade. CNNs work in a sequential fashion, alternating between extracting significant features from an input image and aggregating these features locally through ‘‘pooling" functions, in order to produce a more compact representation. Functions like the arithmetic mean or, more typically, the maximum are commonly used to perform this downsampling operation. Despite the fact that many studies have been devoted to the development of alternative pooling algorithms, in practice, ‘‘max-pooling" still equals or exceeds most of these possibilities, and has become the standard for CNN construction. In this paper we focus on the properties that make the maximum such an efficient solution in the context of CNN feature downsampling and propose its replacement by grouping functions, a family of functions that share those desirable properties. In order to adapt these functions to the context of CNNs, we present (𝑎, 𝑏)- grouping functions, an extension of grouping functions to work with real valued data. We present different construction methods for (𝑎, 𝑏)-grouping functions, and demonstrate their empirical applicability for replacing max-pooling by using them to replace the pooling function of many well-known CNN architectures, finding promising results.
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
Fuzzy clustering to encode contextual information in artistic image classification
(Springer, 2022) Fumanal Idocin, Javier; Takáč, Zdenko; Horanská, Lubomíra; Bustince Sola, Humberto; Cordón, Óscar; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Automatic art analysis comprises of utilizing diverse processing methods to classify and categorize works of art. When working with this kind of pictures, we have to take under consideration different considerations compared to classical picture handling, since works of art alter definitely depending on the creator, the scene delineated or their aesthetic fashion. This extra data improves the visual signals gotten from the images and can lead to better performance. However, this information needs to be modeled and embed alongside the visual features of the image. This is often performed utilizing deep learning models, but they are expensive to train. In this paper we utilize the Fuzzy C-Means algorithm to create a embedding strategy based on fuzzy memberships to extract relevant information from the clusters present in the contextual information. We extend an existing state-of-the-art art classification system utilizing this strategy to get a new version that presents similar results without training additional deep learning models.