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75
A multiobjective evolutionary approach to concurrently learn rule and data bases of Linguistic . . .
, 2009
"... In this paper, we propose the use of a multiobjective evolutionary approach to generate a set of linguistic fuzzyrulebased systems with different tradeoffs between accuracy and interpretability in regression problems. Accuracy and interpretability are measured in terms of approximation error and r ..."
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Cited by 16 (2 self)
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In this paper, we propose the use of a multiobjective evolutionary approach to generate a set of linguistic fuzzyrulebased systems with different tradeoffs between accuracy and interpretability in regression problems. Accuracy and interpretability are measured in terms of approximation error and rule base (RB) complexity, respectively. The proposed approach is based on concurrently learning RBs and parameters of the membership functions of the associated linguistic labels. To manage the size of the search space, we have integrated the linguistic twotuple representation model, which allows the symbolic translation of a label by only considering one parameter, with an efficient modification of the wellknown (2 + 2) Pareto Archived Evolution Strategy (PAES). We tested our approach on nine realworld datasets of different sizes and with different numbers of variables. Besides the (2 + 2)PAES, we have also used the wellknown nondominated sorting genetic algorithm (NSGAII) and an accuracydriven singleobjective evolutionary algorithm (EA). We employed these optimization techniques both to concurrently learn rules and parameters and to learn only rules. We compared the different approaches by applying a nonparametric statistical test for pairwise comparisons, thus taking into consideration three representative points from the obtained Pareto fronts in the case of the multiobjective EAs. Finally, a datacomplexity measure, which is typically used in pattern recognition to evaluate the data density in terms of average number of patterns per variable, has been introduced to characterize regression problems. Results confirm the effectiveness of our approach, particularly for (possibly highdimensional) datasets with high values of the complexity metric.
Multilabel Classification with Metalevel Features
"... Effective learning in multilabel classification (MLC) requires an appropriate level of abstraction for representing the relationship between each instance and multiple categories. Current MLC methods have been focused on learningtomap from instances to ranked lists of categories in a relatively h ..."
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Cited by 9 (2 self)
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Effective learning in multilabel classification (MLC) requires an appropriate level of abstraction for representing the relationship between each instance and multiple categories. Current MLC methods have been focused on learningtomap from instances to ranked lists of categories in a relatively highdimensional space. The finegrained features in such a space may not be sufficiently expressive for characterizing discriminative patterns, and worse, make the model complexity unnecessarily high. This paper proposes an alternative approach by transforming conventional representations of instances and categories into a relatively small set of linkbased metalevel features, and leveraging successful learningtorank retrieval algorithms (e.g., SVMMAP) over this reduced feature space. Controlled experiments on multiple benchmark datasets show strong empirical evidence for the strength of the proposed approach, as it significantly outperformed several stateoftheart methods, including RankSVM, MLkNN and
A fast and scalable multiobjective genetic fuzzy system for linguistic fuzzy modeling in highdimensional regression problems
 IEEE Trans. Fuzzy Syst
, 2011
"... Abstract—Linguistic fuzzy modeling in highdimensional regression problems poses the challenge of exponentialrule explosion when the number of variables and/or instances becomes high. One way to address this problem is by determining the used variables, the linguistic partitioning and the rule set ..."
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Cited by 6 (1 self)
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Abstract—Linguistic fuzzy modeling in highdimensional regression problems poses the challenge of exponentialrule explosion when the number of variables and/or instances becomes high. One way to address this problem is by determining the used variables, the linguistic partitioning and the rule set together, in order to only evolve very simple, but still accurate models. However, evolving these components together is a difficult task, which involves a complex search space. In this study, we propose an effective multiobjective evolutionary algorithm that, based on embedded genetic database (DB) learning (involved variables, granularities, and slight fuzzypartition displacements), allows the fast learning of simple and quiteaccurate linguistic models. Some efficient mechanisms have been designed to ensure a very fast, but not premature, convergence in problems with a high number of variables. Further, since additional problems could arise for datasets with a large number of instances, we also propose a general mechanism for the estimation of the model error when using evolutionary algorithms, by only considering a reduced subset of the examples. By doing so, we can also apply a fast postprocessing stage for further refining the learned solutions. We tested our approach on 17 realworld datasets with different numbers of variables and instances. Three wellknown methods based on embedded genetic DB learning have been executed as references. We compared the different approaches by applying nonparametric statistical tests for multiple comparisons. The results confirm the effectiveness of the proposed method not only in terms of scalability but in terms of the simplicity and generalizability of the obtained models as well. Index Terms—Embedded genetic database learning, highdimensional regression problems, linguistic fuzzy modeling, multiobjective genetic fuzzy systems, scalability. I.
A New Sequential Covering Strategy for Inducing Classification Rules With Ant Colony Algorithms
 IEEE Transactions on Evolutionary Computation
"... Ant colony optimization (ACO) algorithms have been successfully applied to discover a list of classification rules. In general, these algorithms follow a sequential covering strategy, where a single rule is discovered at each iteration of the algorithm in order to build a list of rules. The sequenti ..."
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Cited by 5 (3 self)
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Ant colony optimization (ACO) algorithms have been successfully applied to discover a list of classification rules. In general, these algorithms follow a sequential covering strategy, where a single rule is discovered at each iteration of the algorithm in order to build a list of rules. The sequential covering strategy has the drawback of not coping with the problem of rule interaction—i.e., the outcome of a rule affects the rules that can be discovered subsequently since the search space is modified due to the removal of examples covered by previous rules. This paper proposes a new sequential covering strategy for ACO classification algorithms to mitigate the problem of rule interaction, where the order of the rules is implicitly encoded as pheromone values and the search is guided by the quality of a candidate list of rules. Our experiments using eighteen publicly available data sets show that the predictive accuracy obtained by a new ACO classification algorithm implementing the proposed sequential covering strategy is statistically significantly higher than the predictive accuracy of stateoftheart rule induction classification algorithms.
q²Index: Quantitative and qualitative evaluation based on the number and impact of papers in the Hirsch core
 JOURNAL OF INFORMETRICS
, 2010
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Improved Step Size Adaptation for the MOCMAES
 N/P
, 2010
"... The multiobjective covariance matrix adaptation evolution strategy (MOCMAES) is an evolutionary algorithm for continuous vectorvalued optimization. It combines indicatorbased selection based on the contributing hypervolume with the efficient strategy parameter adaptation of the elitist covarian ..."
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Cited by 3 (1 self)
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The multiobjective covariance matrix adaptation evolution strategy (MOCMAES) is an evolutionary algorithm for continuous vectorvalued optimization. It combines indicatorbased selection based on the contributing hypervolume with the efficient strategy parameter adaptation of the elitist covariance matrix adaptation evolution strategy (CMAES). Step sizes (i.e., mutation strengths) are adapted on individuallevel using an improved implementation of the 1/5th success rule. In the original MOCMAES, a mutation is regarded as successful if the offspring ranks better than its parent in the elitist, rankbased selection procedure. In contrast, we propose to regard a mutation as successful if the offspring is selected into the next parental population. This criterion is easier to implement and reduces the computational complexity of the MOCMAES, in particular of its steadystate variant. The new step size adaptation improves the performance of the MOCMAES as shown empirically using a large set of benchmark functions. The new update scheme in general leads to larger step sizes and thereby counteracts premature convergence. The experiments comprise the first evaluation of the MOCMAES for problems with more than two objectives.
GAODE and HAODE: Two Proposals based on AODE to Deal with Continuous Variables
"... AODE (Aggregating OneDependence Estimators) is considered one of the most interesting representatives of the Bayesian classifiers, taking into account not only the low error rate it provides but also its efficiency. Until now, all the attributes in a dataset have had to be nominal to build an AODE ..."
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Cited by 3 (2 self)
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AODE (Aggregating OneDependence Estimators) is considered one of the most interesting representatives of the Bayesian classifiers, taking into account not only the low error rate it provides but also its efficiency. Until now, all the attributes in a dataset have had to be nominal to build an AODE classifier or they have had to be previously discretized. In this paper, we propose two different approaches in order to deal directly with numeric attributes. One of them uses conditional Gaussian networks to model a dataset exclusively with numeric attributes; and the other one keeps the superparent on each model discrete and uses univariate Gaussians to estimate the probabilities for the numeric attributes and multinomial distributions for the categorical ones, it also being able to model hybrid datasets. Both of them obtain competitive results compared to AODE, the latter in particular being a very attractive alternative to AODE in numeric datasets. 1.
Enhancing IPADE algorithm with a different individual codification
 in: Proceedings of the Sixth International Conference on Hybrid Artificial Intelligence Systems (HAIS'11), 2011
"... Abstract. Nearest neighbor is one of the most used techniques for performing classification tasks. However, its simplest version has several drawbacks, such as low efficiency, storage requirements and sensitivity to noise. Prototype generation is an appropriate process to alleviate these drawbacks t ..."
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Cited by 3 (1 self)
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Abstract. Nearest neighbor is one of the most used techniques for performing classification tasks. However, its simplest version has several drawbacks, such as low efficiency, storage requirements and sensitivity to noise. Prototype generation is an appropriate process to alleviate these drawbacks that allows the fitting of a data set for nearest neighbor classification. In this work, we present an extension of our previous proposal called IPADE, a methodology to learn iteratively the positioning of prototypes using a differential evolution algorithm. In this extension, which we have called IPADECS, a complete solution is codified in each individual. The results are contrasted with nonparametrical statistical tests and show that our proposal outperforms previously proposed methods. 1
A Fuzzy Association RuleBased Classification Model for HighDimensional Problems with Genetic Rule Selection and Lateral Tuning
 IEEE TRANSACTIONS ON FUZZY SYSTEMS
, 2011
"... The inductive learning of fuzzy rule based classification systems suffers from exponential growth of the fuzzy rule search space when the number of patterns and/or variables becomes high. This growth makes the learning process more difficult and, in most cases, it leads to problems of scalability (i ..."
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Cited by 3 (1 self)
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The inductive learning of fuzzy rule based classification systems suffers from exponential growth of the fuzzy rule search space when the number of patterns and/or variables becomes high. This growth makes the learning process more difficult and, in most cases, it leads to problems of scalability (in terms of the time and memory consumed) and/or complexity (with respect to the number of rules obtained and the number of variables included in each rule). In this work, we propose a fuzzy association rulebased classification method for highdimensional problems based on three stages to obtain an accurate and compact fuzzy rule based classifier with a low computational cost. This method limits the order of the associations in the association rule extraction and considers the use of subgroup discovery based on an Improved Weighted Relative Accuracy measure to preselect the most interesting rules before a genetic postprocessing process for rule selection and parameter tuning. The results obtained over twentysix realworld datasets of different sizes and with different numbers of variables demonstrate the effectiveness of the proposed approach.
Differential evolution for optimizing the positioning of prototypes in nearest neighbor classification
 PATTERN RECOGNITION
, 2011
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