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 Matematika
In 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.
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
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.

Galar Idoate, Mikel

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