Classification is a data mining technique used to predict group membership for data instances whose classes are unknown . Pattern classification involves building a function that maps the input feature space to an output space of two or more than two classes. Decision trees, Bayesian models, and artificial neural networks (ANNs) are examples of effective classifiers in the field of pattern classification . However, by the No Free Lunch theorem, there is no single classifier that can be considered optimal for all tasks. In an attempt to improve recognition performance of a single classifier, a common approach is to combine various classifiers forming what is called a multi-classifier systems (MCS) .
There are several reasons for combining multiple classifiers to solve a given learning task . First, MCS, also known as ensembles or committees, exploits the idea that a pool of different classifiers, referred as experts, can offer complementary information about the patterns to be classified, improving the effectiveness of the overall recognition process. Second, in some cases, ensembles might not be better than the single best classifier but can diminish or eliminate the risk of picking an inadequate single classifier. Another reason for ensembles arises from limited representational capability of learning algorithms. It is possible that the classifier space considered for the task does not contain the optimal classifier.
Successful applications of MCS have been reported in various works in the literature, such as handwritten digit recognition , signature verification , image labeling , just to name a few. Basically, most of these systems may take two approaches: selection and fusion (SF) . In the classifier fusion, every classifier in the ensemble is used. Bagging , boosting , and the random subspace method (RSM)  are frequently used for the generation of members, while arithmetic rule (e.g., maximum, mean, median, minimum, product), majority vote or the use of another classifier are examples of strategies used to combine their decisions . In classifier selection, each ensemble member is supposed to know well a part of the feature space and be responsible for objects in this part .
Most of the discussions and design methodologies of ensembles are devoted to fusion version and are concerned with how to achieve good performance by creating diversity measure and combination schema. Research is less common in selection methodology. Basically, for the selection scheme, a means of partitioning the feature space and estimating the performance of each classifier are required. In Woods’ DCS-LA approach , for example, the classification accuracy is estimated in small regions of feature space surrounding an unknown test sample, and then the most locally accurate classifier is nominated to make the final decision. On the other hand, Kuncheva  presents an algorithm where the training data are clustered to form the decision regions, and a confidence interval is used to determine whether one or multiple classifiers should be used to make a final decision.
Non-automatic design of ensembles often involves a tedious trial-and-error process which might be appropriate where prior knowledge and an experienced expert are available, which might not be the case for many real-world tasks and are hard to find in practice . The goal of ensembles design is to determine ensemble architectures automatically. In this paper, we report the performance of a novel automatic method, named SFJADE, to combine selection and fusion (SF) via adaptive differential evolution (JADE). JADE is a powerful stochastic real-parameter optimization algorithm in current use . For the clustering phase, self-organizing maps (SOM) was chosen since it is a simple technique that has good performance . For the classification phase, the attractiveness of ANNs stems from their many inherent characteristics, including nonlinearity, high parallelism, robustness, fault tolerance, learning, and their capability to generalize .
This paper is organized as follows. Section 2 gives the theoretical justification of selection and fusion, by means of clustering algorithms; Sect. 3 presents some related works, that show strengths and weaknesses in the development of ensembles; Sect. 4 presents the evolutionary algorithm used in the current work; Sect. 5 describes the basic idea of proposed methodology; Sect. 6 presents the experimental results; Finally, Sect. 7 presents some final considerations about the main topics covered in this work, including contributions reached and directions for future works.
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