Abstract
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 behavior of fuzzy association rule-based classification model for high-dimensional problems (FARC-HD) fuzzy classifier in multiclass classification problems using decomposition strategies, and more specifically One-versus-One (OVO) and One-versus-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 20 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.
Highlights
F UZZY Rule-Based Classification Systems (FRBCSs) are well-known and widely used tools in the field of pattern recognition and classification problems
We present the results of OVA and OVO models considering the previously mentioned overlap functions for those aggregation strategies that are not affected by the confidences of FARC-HD in the case of OVO (ND and Voting strategy (VOTE)), whereas those being affected (LVPC, Weighted Voting (WV)) are shown in Table IV, together with our proposed solution (WinWV)
We have shown that the confidences returned by FARC-HD may adversely affect the aggregation phase in these decomposition strategies and the final prediction
Summary
F UZZY Rule-Based Classification Systems (FRBCSs) are well-known and widely used tools in the field of pattern recognition and classification problems. In the case of FARC-HD, due to the usage of additive combination [17] as fuzzy reasoning method, we consider as confidence the sum of the association degrees obtained for each class, which are computed by multiplying the matching degrees (of the example with the antecedents of the rules using the product t-norm to model the conjunction) and the rule weight For this reason, when combining FARC-HD and decomposition strategies the confidences obtained when carrying out the inference process of FARC-HD are not suitable for the subsequent aggregation. In order to address the former problem, we propose to adapt the inference process of FARC-HD in such a way that the confidences obtained allow decomposition strategies to produce more accurate aggregations and can lead to improve the classification in OVO and OVA models.
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