Open Access
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 Publikoa
Fuzzy 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.
Open Access
Extensions of fuzzy sets in image processing: an overview
(EUSFLAT, 2011) Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Galar Idoate, Mikel; Jurío Munárriz, Aránzazu; López Molina, Carlos; Paternain Dallo, Daniel; Sanz Delgado, José Antonio; Couto, Pedro; Melo-Pinto, Pedro; Automática y Computación; Automatika eta Konputazioa
This work presents a valuable review for the interested reader of the recent Works using extensions of fuzzy sets in image processing. The chapter is divided as follows: first we recall the basics of the extensions of fuzzy sets, i.e. Type 2 fuzzy sets, interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets. In sequent sections we review the methods proposed for noise removal (sections 3), image enhancement (section 4), edge detection (section 5) and segmentation (section 6). There exist other image segmentation tasks such as video de-interlacing, stereo matching or object representation that are not described in this work.
Open Access
A survey of fingerprint classification Part I: taxonomies on feature extraction methods and learning models
(Elsevier, 2015) Galar Idoate, Mikel; Derrac, Joaquín; Peralta, Daniel; Triguero, Isaac; Paternain Dallo, Daniel; López Molina, Carlos; García, Salvador; Benítez, José Manuel; Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
This paper reviews the fingerprint classification literature looking at the problem from a double perspective. We first deal with feature extraction methods, including the different models considered for singular point detection and for orientation map extraction. Then, we focus on the different learning models considered to build the classifiers used to label new fingerprints. Taxonomies and classifications for the feature extraction, singular point detection, orientation extraction and learning methods are presented. A critical view of the existing literature have led us to present a discussion on the existing methods and their drawbacks such as difficulty in their reimplementation, lack of details or major differences in their evaluations procedures. On this account, an experimental analysis of the most relevant methods is carried out in the second part of this paper, and a new method based on their combination is presented.
Open Access
CFM-BD: a distributed rule induction algorithm for building compact fuzzy models in Big Data classification problems
(IEEE, 2020) Elkano Ilintxeta, Mikel; Sanz Delgado, José Antonio; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Galar Idoate, Mikel; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Interpretability has always been a major concern for fuzzy rule-based classifiers. The usage of human-readable models allows them to explain the reasoning behind their predictions and decisions. However, when it comes to Big Data classification problems, fuzzy rule based classifiers have not been able to maintain the good tradeoff between accuracy and interpretability that has characterized these techniques in non-Big-Data environments. The most accurate methods build models composed of a large number of rules and fuzzy sets that are too complex, while those approaches focusing on interpretability do not provide state-of-the-art discrimination capabilities. In this paper, we propose a new distributed learning algorithm named CFM-BD to construct accurate and compact fuzzy rule-based classification systems for Big Data. This method has been specifically designed from scratch for Big Data problems and does not adapt or extend any existing algorithm. The proposed learning process consists of three stages: Preprocessing based on the probability integral transform theorem; rule induction inspired by CHI-BD and Apriori algorithms; and rule selection by means of a global evolutionary optimization. We conducted a complete empirical study to test the performance of our approach in terms of accuracy, complexity, and runtime. The results obtained were compared and contrasted with four state-of-the-art fuzzy classifiers for Big Data (FBDT, FMDT, Chi-Spark-RS, and CHI-BD). According to this study, CFM-BD is able to provide competitive discrimination capabilities using significantly simpler models composed of a few rules of less than three antecedents, employing five linguistic labels for all variables.
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 Publikoa
In 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. © 2021
Open Access
FUZZ-EQ: a data equalizer for boosting the discrimination power of fuzzy classifiers
(Elsevier, 2020) Uriz Martín, Mikel Xabier; Elkano Ilintxeta, Mikel; 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, PJUPNA13
The definition of linguistic terms is a critical part of the construction of any fuzzy classifier. Fuzzy partitioning methods (FPMs) range from simple uniform partitioning to sophisticated optimization algorithms. In this paper we present FUZZ-EQ, a preprocessing algorithm that facilitates the construc-tion of meaningful fuzzy partitions regardless of the FPM used. The proposed approach is radically different from any existing FPM: instead of adjusting the fuzzy sets to the training data, FUZZ-EQ adjusts the training data to a hypothetical uniform partition before applying any FPM. To do so, the original data distribution is transformed into a uniform distribution by applying the probability integral transform. FUZZ-EQ allows FPMs to provide classifiers with more granularity on high density regions, increasing the overall discrimination capability. Additionally, we describe the procedure to reverse this transformation and recover the interpretability of linguistic terms. To assess the effectiveness of our proposal, we conducted an extensive empirical study consisting of 41 classification tasks and 9 fuzzy classifiers with different FPMs, rule induction algorithms, and rule structures. We also tested the scalability of FUZZ-EQ in Big Data classification problems such as HIGGS, with 11 million examples. Experimental results reveal that FUZZ-EQ significantly boosted the classification performance of those classifiers using the same linguistic terms for all rules, including state-of-the-art classifiers such as FARC-HD or IVTURS.
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 Publikoa
The 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.
Open Access
A framework for radial data comparison and its application to fingerprint analysis
(Elsevier, 2016) Marco Detchart, Cedric; Cerrón González, Juan; Miguel Turullols, Laura de; López Molina, Carlos; Bustince Sola, Humberto; Galar Idoate, Mikel; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
This work tackles the comparison of radial data, and proposes comparison measures that are further applied to fingerprint analysis. First, we study the similarity of scalar and non-scalar radial data, elaborated on previous works in fuzzy set theory. This study leads to the concepts of restricted radial equivalence function and Radial Similarity Measure, which model the perceived similarity between scalar and vectorial pieces of radial data, respectively. Second, the utility of these functions is tested in the context of fingerprint analysis, and more specifically, in the singular point detection. With this aim, a novel Template-based Singular Point Detection method is proposed, which takes advantage of these functions. Finally, their suitability is tested in different fingerprint databases. Different Similarity Measures are considered to show the flexibility offered by these measures and the behaviour of the new method is compared with well-known singular point detection methods.
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, PJUPNA13
IVOVO 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.
Open Access
A survey on fingerprint minutiae-based local matching for verification and identification: taxonomy and experimental evaluation
(Elsevier, 2015) Peralta, Daniel; Galar Idoate, Mikel; Triguero, Isaac; Paternain Dallo, Daniel; García, Salvador; Barrenechea Tartas, Edurne; Benítez, José Manuel; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
Fingerprint recognition has found a reliable application for verification or identification of people in biometrics. Globally, fingerprints can be viewed as valuable traits due to several perceptions observed by the experts; such as the distinctiveness and the permanence on humans and the performance in real applications. Among the main stages of fingerprint recognition, the automated matching phase has received much attention from the early years up to nowadays. This paper is devoted to review and categorize the vast number of fingerprint matching methods proposed in the specialized literature. In particular, we focus on local minutiae-based matching algorithms, which provide good performance with an excellent trade-off between efficacy and efficiency. We identify the main properties and differences of existing methods. Then, we include an experimental evaluation involving the most representative local minutiae-based matching models in both verification and evaluation tasks. The results obtained will be discussed in detail, supporting the description of future directions.