Open Access
Do we still need fuzzy classifiers for small data in the era of big data?
(IEEE, 2019) Elkano Ilintxeta, Mikel; Bustince Sola, Humberto; Galar Idoate, Mikel; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13
The Era of Big Data has forced researchers to explore new distributed solutions for building fuzzy classifiers, which often introduce approximation errors or make strong assumptions to reduce computational and memory requirements. As a result, Big Data classifiers might be expected to be inferior to those designed for standard classification tasks (Small Data) in terms of accuracy and model complexity. To our knowledge, however, there is no empirical evidence to confirm such a conjecture yet. Here, we investigate the extent to which state-of-the-art fuzzy classifiers for Big Data sacrifice performance in favor of scalability. To this end, we carry out an empirical study that compares these classifiers with some of the best performing algorithms for Small Data. Assuming the latter were generally designed for maximizing performance without considering scalability issues, the results of this study provide some intuition around the tradeoff between performance and scalability achieved by current Big Data solutions. Our findings show that, although slightly inferior, Big Data classifiers are gradually catching up with state-of-the-art classifiers for Small data, suggesting that a unified learning algorithm for Big and Small Data might be possible.
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
Fuzzy rule-based classification systems for multi-class problems using binary decomposition strategies: on the influence of n-dimensional overlap functions in the fuzzy reasoning method
(Elsevier, 2016) Elkano Ilintxeta, Mikel; Galar Idoate, Mikel; Sanz Delgado, José Antonio; Bustince Sola, Humberto; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación
Multi-class classification problems appear in a broad variety of real-world problems, e.g., medicine, genomics, bioinformatics, or computer vision. In this context, decomposition strategies are useful to increase the classification performance of classifiers. For this reason, in a previous work we proposed to improve the performance of FARC-HD (Fuzzy Association Rule-based Classification model for High-Dimensional problems) fuzzy classifier using One-vs-One (OVO) and One-vs-All (OVA) decomposition strategies. As a result of an exhaustive experimental analysis, we concluded that even though the usage of decomposition strategies was worth to be considered, further improvements could be achieved by introducing n-dimensional overlap functions instead of the product t-norm in the Fuzzy Reasoning Method (FRM). In this way, we can improve confidences for the subsequent processing performed in both OVO and OVA. In this paper, we want to conduct a broader study of the influence of the usage of n-dimensional overlap functions to model the conjunction in several Fuzzy Rule-Based Classification Systems (FRBCSs) in order to enhance their performance in multi-class classification problems applying decomposition techniques. To do so, we adapt the FRM of four well-known FRBCSs (CHI, SLAVE, FURIA, and FARC-HD itself). We will show that the benefits of the usage of n-dimensional overlap functions strongly depend on both the learning algorithm and the rule structure of each classifier, which explains why FARC-HD is the most suitable one for the usage of these functions.
Open Access
Novel methodologies for improving fuzzy classifiers: dealing with multi-class and Big Data classification problems
(2018) Elkano Ilintxeta, Mikel; Galar Idoate, Mikel; Barrenechea Tartas, Edurne; Automática y Computación; Automatika eta Konputazioa
Los Sistemas de Clasificación Basados en Reglas Difusas (SCBRDs) son métodos de aprendizaje automático que permiten construir modelos predictivos capaces de predecir la clase a la que pertenecen los datos de entrada. La ventaja de estos sistemas es que proporcionan un modelo formado por una serie de reglas que contienen etiquetas lingüísticas interpretables por el ser humano (por ejemplo, “bajo”, “medio”, “alto”), lo que les permite explicar el razonamiento llevado a cabo al realizar una predicción. Estas etiquetas lingüísticas permiten a los SCBRDs no solamente explicar el porqué de las predicciones, sino también manejar la incertidumbre proveniente de información imprecisa. Los problemas de clasificación pueden dividirse en dos grupos dependiendo del número de clases que los componen: binarios (dos clases) y multi-clase (más de dos clases). En general, los problemas multi-clase implican fronteras de decisión más complejas que son más difíciles de aprender que en problemas binarios, debido al mayor número de clases. Una forma eficaz de lidiar con esta situación es descomponer el problema multi-clase original en problemas binarios más sencillos que son afrontados por clasificadores independientes, cuyas predicciones son agregadas cuando se clasifican los datos de entrada. Esta metodología ha mostrado ser eficaz a la hora de mejorar el rendimiento de una gran variedad de clasificadores, incluidos los SCBRDs. Sin embargo, el uso de estrategias de descomposición en SCBRDs plantea una nueva problemática: lidiar con diferentes estructuras de reglas y métodos de razonamiento difuso (FRM). Las diferencias estructurales en las reglas vienen dadas por la variedad de métodos de construcción de reglas existentes en la literatura. Estos métodos pueden diferir, por ejemplo, en el tipo de etiquetas lingüísticas generadas, en el operador de conjunción/disyunción empleado en reglas con más de un antecedente, o en la longitud media de las reglas. Por otro lado, el FRM encargado de inferir la salida adecuada a partir de las reglas construidas puede variar notablemente de un SCBRD a otro. Estos factores hacen que el comportamiento de las técnicas de descomposición sea dependiente del SCBRD empleado. Por consiguiente, algunos de los métodos de agregación más populares no son capaces de aprovechar el potencial mostrado en otro tipo de clasificadores. Además de la dificultad añadida de los problemas multi-clase, en los últimos años las técnicas de aprendizaje automático se han topado con un nuevo reto: en ocasiones la cantidad de información a procesar excede la capacidad de cómputo o almacenamiento de un ordenador convencional moderno, lo que denominamos problemas Big Data. Para solventar este problema se hace uso de la computación distribuida, la cual consiste en distribuir los datos a través de múltiples nodos (ordenadores) con el objetivo de procesarlos en paralelo. A pesar de que esta metodología soluciona los problemas asociados con las exigencias de cómputo y almacenamiento, el procesamiento distribuido de la información implica diseñar métodos que soporten dicha funcionalidad. En el caso de los SCBRDs diseñados para Big Data, la dificultad añadida de la computación distribuida ha impedido explotar el potencial que han mostrado estos sistemas cuando se han aplicado de forma local y secuencial. Además de la computación distribuida, otra metodología (complementaria) para poder manejar grandes volúmenes de datos son las técnicas de reducción de prototipos (PR). Los métodos de PR permiten que algoritmos de aprendizaje automático que no están diseñados para Big Data puedan ejecutarse en estos entornos empleando una versión reducida de los datos. Sin embargo, gran parte de las aproximaciones de PR propuestas hasta la fecha presentan serias limitaciones de escalabilidad que afectan a su eficiencia, debido en gran parte a la complejidad computacional cuadrática que generalmente caracteriza a este tipo de técnicas. El objetivo de esta tesis es mejorar el rendimiento de los SCBRDs en problemas multi-clase y Big Data. En el caso de los problemas multi-clase, hemos estudiado y analizado el efecto de diferentes métodos de aprendizaje y razonamiento difuso de varios SCBRDs en el rendimiento de las estrategias de descomposición. Una vez identificados algunos de los problemas que presenta esta sinergia, hemos propuesto una modificación del FRM que permite mejorar su rendimiento. En cuanto a las metodologías planteadas para Big Data, hemos presentado dos nuevos algoritmos de aprendizaje distribuido para SCBRDs que solucionan algunas de las limitaciones presentes en los métodos existentes. De forma transversal, hemos aprovechado uno de estos algoritmos para desarrollar un nuevo método de PR de complejidad lineal.
Open Access
Enhancing multi-class classification in FARC-HD fuzzy classifier: on the synergy between n-dimensional overlap functions and decomposition strategies
(IEEE, 2014) Elkano Ilintxeta, Mikel; Galar Idoate, Mikel; Sanz Delgado, José Antonio; Fernández, Alberto; Barrenechea Tartas, Edurne; Herrera, Francisco; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision or medicine. These problems are generally more difficult than their binary counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper we aim to improve the behaviour of FARC-HD fuzzy classifier in multi-class classification problems using decomposition strategies, and more specifically One-vs-One (OVO) and One-vs-All (OVA) strategies. However, when these strategies are applied on FARC-HD a problem emerges due to the low confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t-norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t-norm with overlap functions. To do so, we define n-dimensional overlap functions. The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using twenty datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.
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 algorithm for group decision making using n -dimensional fuzzy sets, admissible orders and OWA operators
(Elsevier, 2017) Miguel Turullols, Laura de; Sesma Sara, Mikel; Elkano Ilintxeta, Mikel; Asiain Ollo, María José; Bustince Sola, Humberto; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an in- creasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these condi- tions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.