Person: Paternain Dallo, Daniel
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Paternain Dallo
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Daniel
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Estadística, Informática y Matemáticas
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ISC. Institute of Smart Cities
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0000-0002-5845-887X
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810056
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Publication Open Access On the influence of interval normalization in IVOVO fuzzy multi-class classifier(Springer, 2019) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13IVOVO stands for Inverval-Valued One-Vs-One and is the combination of IVTURS fuzzy classifier and the One-Vs-One strategy. This method is designed to improve the performance of IVTURS in multi-class problems, by dividing the original problem into simpler binary ones. The key issue with IVTURS is that interval-valued confidence degrees for each class are returned and, consequently, they have to be normalized for applying a One-Vs-One strategy. However, there is no consensus on which normalization method should be used with intervals. In IVOVO, the normalization method based on the upper bounds was considered as it maintains the admissible order between intervals and also the proportion of ignorance, but no further study was developed. In this work, we aim to extend this analysis considering several normalizations in the literature. We will study both their main theoretical properties and empirical performance in the final results of IVOVO.Publication Open Access On the influence of admissible orders in IVOVO(Springer, 2019) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13It is known that when dealing with interval-valued data, there exist problems associated with the non-existence of a total order. In this work we investigate a reformulation of an interval-valued decomposition strategy for multi-class problems called IVOVO, and we analyze the effectiveness of considering different admissible orders in the aggregation phase of IVOVO. We demonstrate that the choice of an appropriate admissible order allows the method to obtain significant differences in terms of accuracy.Publication Embargo A supervised fuzzy measure learning algorithm for combining classifiers(Elsevier, 2023) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaFuzzy measure-based aggregations allow taking interactions among coalitions of the input sources into account. Their main drawback when applying them in real-world problems, such as combining classifier ensembles, is how to define the fuzzy measure that governs the aggregation and specifies the interactions. However, their usage for combining classifiers has shown its advantage. The learning of the fuzzy measure can be done either in a supervised or unsupervised manner. This paper focuses on supervised approaches. Existing supervised approaches are designed to minimize the mean squared error cost function, even for classification problems. We propose a new fuzzy measure learning algorithm for combining classifiers that can optimize any cost function. To do so, advancements from deep learning frameworks are considered such as automatic gradient computation. Therefore, a gradient-based method is presented together with three new update policies that are required to preserve the monotonicity constraints of the fuzzy measures. The usefulness of the proposal and the optimization of cross-entropy cost are shown in an extensive experimental study with 58 datasets corresponding to both binary and multi-class classification problems. In this framework, the proposed method is compared with other state-of-the-art methods for fuzzy measure learning.Publication Open Access A study of different families of fusion functions for combining classifiers in the one-vs-one strategy(Springer, 2018) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Jurío Munárriz, Aránzazu; Bustince Sola, Humberto; Galar Idoate, Mikel; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaIn this work we study the usage of different families of fusion functions for combining classifiers in a multiple classifier system of One-vs-One (OVO) classifiers. OVO is a decomposition strategy used to deal with multi-class classification problems, where the original multi-class problem is divided into as many problems as pair of classes. In a multiple classifier system, classifiers coming from different paradigms such as support vector machines, rule induction algorithms or decision trees are combined. In the literature, several works have addressed the usage of classifier selection methods for these kinds of systems, where the best classifier for each pair of classes is selected. In this work, we look at the problem from a different perspective aiming at analyzing the behavior of different families of fusion functions to combine the classifiers. In fact, a multiple classifier system of OVO classifiers can be seen as a multi-expert decision making problem. In this context, for the fusion functions depending on weights or fuzzy measures, we propose to obtain these parameters from data. Backed-up by a thorough experimental analysis we show that the fusion function to be considered is a key factor in the system. Moreover, those based on weights or fuzzy measures can allow one to better model the aggregation problem.Publication Open Access An empirical study on supervised and unsupervised fuzzy measure construction methods in highly imbalanced classification(IEEE, 2020) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaThe design of an ensemble of classifiers involves the definition of an aggregation mechanism that produces a single response obtained from the information provided by the classifiers. A specific aggregation methodology that has been studied in the literature is the use of fuzzy integrals, such as the Choquet or the Sugeno integral, where the associated fuzzy measure tries to represent the interaction existing between the classifiers of the ensemble. However, defining the big number of coefficients of a fuzzy measure is not a trivial task and therefore, many different algorithms have been proposed. These can be split into supervised and unsupervised, each class having different learning mechanisms and particularities. Since there is no clear knowledge about the correct method to be used, in this work we propose an experimental study for comparing the performance of eight different learning algorithms under the same framework of imbalanced dataset. Moreover, we also compare the specific fuzzy integral (Choquet or Sugeno) and their synergies with the different fuzzy measure construction methods.Publication Open Access Discrete IV dG-Choquet integrals with respect to admissible orders(Elsevier, 2021) Takáč, Zdenko; Uriz Martín, Mikel Xabier; Galar Idoate, Mikel; Paternain Dallo, Daniel; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio Ingeniaritzaren; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería Eléctrica, Electrónica y de Comunicación; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of dG-Choquet integral are both the discrete Choquet integral and the d-Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with dG-Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. © 2021Publication Open Access Unsupervised fuzzy measure learning for classifier ensembles from coalitions performance(IEEE, 2020) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Domínguez Catena, Iris; Bustince Sola, Humberto; Galar Idoate, Mikel; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13In Machine Learning an ensemble refers to the combination of several classifiers with the objective of improving the performance of every one of its counterparts. To design an ensemble two main aspects must be considered: how to create a diverse set of classifiers and how to combine their outputs. This work focuses on the latter task. More specifically, we focus on the usage of aggregation functions based on fuzzy measures, such as the Sugeno and Choquet integrals, since they allow to model the coalitions and interactions among the members of the ensemble. In this scenario the challenge is how to construct a fuzzy measure that models the relations among the members of the ensemble. We focus on unsupervised methods for fuzzy measure construction, review existing alternatives and categorize them depending on their features. Furthermore, we intend to address the weaknesses of previous alternatives by proposing a new construction method that obtains the fuzzy measure directly evaluating the performance of each possible subset of classifiers, which can be efficiently computed. To test the usefulness of the proposed fuzzy measure, we focus on the application of ensembles for imbalanced datasets. We consider a set of 66 imbalanced datasets and develop a complete experimental study comparing the reviewed methods and our proposal.