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Combining Predictions in Pairwise Classification: An Optimal Adaptive Voting Strategy and Its Relation to Weighted Voting
 TO APPEAR IN PATTERN RECOGNITION
, 2009
"... Weighted voting is the commonly used strategy for combining predictions in pairwise classification. Even though it shows good classification performance in practice, it is often criticized for lacking a sound theoretical justification. In this paper, we study the problem of combining predictions wit ..."
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Weighted voting is the commonly used strategy for combining predictions in pairwise classification. Even though it shows good classification performance in practice, it is often criticized for lacking a sound theoretical justification. In this paper, we study the problem of combining predictions within a formal framework of label ranking and, under some model assumptions, derive a generalized voting strategy in which predictions are properly adapted according to the strengths of the corresponding base classifiers. We call this strategy adaptive voting and show that it is optimal in the sense of yielding a MAP prediction of the class label of a test instance. Moreover, we offer a theoretical justification for weighted voting by showing that it yields a good approximation of the optimal adaptive voting prediction. This result is further corroborated by empirical evidence from experiments with real and synthetic data sets showing that, even though adaptive voting is sometimes able to achieve consistent improvements, weighted voting is in general quite competitive, all the more in cases where the aforementioned model assumptions underlying adaptive voting are not met. In this sense, weighted voting appears to be a more robust aggregation strategy.
FR3: A fuzzy rule learner for inducing reliable classifiers
 IEEE Transactions Fuzzy Systems
, 2009
"... This paper introduces a fuzzy rulebased classification method called FR3, which is short for ..."
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This paper introduces a fuzzy rulebased classification method called FR3, which is short for
Multiclass imbalanced datasets with linguistic fuzzy rule based classification systems based on pairwise learning
 Computational Intelligence for KnowledgeBased System Design
, 2010
"... Abstract. In a classification task, the imbalance class problem is present when the dataset has a very different distribution of examples among their classes. The main handicap of this type of problem is that standard learning algorithms consider a balanced training set and this supposes a bias tow ..."
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Abstract. In a classification task, the imbalance class problem is present when the dataset has a very different distribution of examples among their classes. The main handicap of this type of problem is that standard learning algorithms consider a balanced training set and this supposes a bias towards the majority classes. In order to provide a correct identification of the different classes of the problem, we propose a methodology based on two steps: first we will use the onevsone binarization technique for decomposing the original dataset into binary classification problems. Then, whenever each one of these binary subproblems is imbalanced, we will apply an oversampling step, using the SMOTE algorithm, in order to rebalance the data before the pairwise learning process. For our experimental study we take as basis algorithm a linguistic Fuzzy Rule Based Classification System, and we aim to show not only the improvement in performance achieved with our methodology against the basic approach, but also to show the good synergy of the pairwise learning proposal with the selected oversampling technique.
Grouping, overlap and generalized bientropic functions for fuzzy modeling of pairwise comparisons
 IEEE Trans. Fuzzy Syst
, 2012
"... Abstract—In this paper, we propose new aggregation functions for the pairwise comparison of alternatives in fuzzy preference modeling. More specifically, we introduce the concept of a grouping function, i.e., a specific type of aggregation function that combines two degrees of support (weak preferen ..."
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Abstract—In this paper, we propose new aggregation functions for the pairwise comparison of alternatives in fuzzy preference modeling. More specifically, we introduce the concept of a grouping function, i.e., a specific type of aggregation function that combines two degrees of support (weak preference) into a degree of information or, say, a degree of comparability between two alternatives, and we relate this new concept to that of incomparability. Grouping functions of this type complement the existing concept of overlap functions in a natural way, since the latter can be used to turn two degrees of weak preference into a degree of indifference. We also define the socalled generalized bientropic functions that allow for a unified representation of overlap and grouping functions. Apart from analyzing mathematical properties of these types of functions and exploring relationships between them, we elaborate on their use in fuzzy preference modeling and decision making. We present an algorithm to elaborate on an alternative preference ranking that penalizes those alternatives for which the expert is not sure of his/her preference. Index Terms—Decision making, generalized bientropic function, grouping function, incomparability, overlap function, pairwise comparison, preference relations. I.
Preference Learning and Ranking by Pairwise Comparison
"... This chapter provides an overview of recent work on preference learning and ranking via pairwise classification. The learning by pairwise comparison (LPC) paradigm is the natural machine learning counterpart to the relational approach to preference modeling and decision making. From a machine learn ..."
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This chapter provides an overview of recent work on preference learning and ranking via pairwise classification. The learning by pairwise comparison (LPC) paradigm is the natural machine learning counterpart to the relational approach to preference modeling and decision making. From a machine learning point of view, LPC is especially appealing as it decomposes a possibly complex prediction problem into a certain number of learning problems of the simplest type, namely binary classification. We explain how to approach different preference learning problems, such as label and instance ranking, within the framework of LPC. We primarily focus on methodological aspects, but also address theoretical questions as well as algorithmic and complexity issues.
Fuzzy Classifier: On the Synergy Between nDimensional Overlap Functions and Decomposition Strategies
"... Abstract—There are many realworld 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 cl ..."
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Abstract—There are many realworld 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 rulebased classification model for highdimensional problems (FARCHD) fuzzy classifier in multiclass classification problems using decomposition strategies, and more specifically OneversusOne (OVO) and OneversusAll (OVA) strategies. However, when these strategies are applied on FARCHD, a problem emerges due to the lowconfidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product tnorm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of
Chapter 2 Aiding to Decide: Concepts and Issues
"... Abstract This chapter is about the decision aiding process. In professional contexts, there are cases of decision problems which require using formal processes and methods. In the first part of the chapter, we identify and describe the essential steps of a decision aiding process. In the second par ..."
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Abstract This chapter is about the decision aiding process. In professional contexts, there are cases of decision problems which require using formal processes and methods. In the first part of the chapter, we identify and describe the essential steps of a decision aiding process. In the second part, we discuss four practical questions that have to be tackled by an analyst in charge of a decision aiding process. What should I do now? It is sure that you have asked yourself more than once such a question. We all face problem situations in which we need to think before acting. It is also sure that several times it happens that you address such a question to somebody else or that somebody else asks you what to do now? It is this precise situation we
Enhancing Fuzzy Rule Based Systems in MultiClassification Using Pairwise Coupling with Preference Relations
"... This contribution proposes a technique for Fuzzy Rule Based Classification Systems (FRBCSs) based on a multiclassifier approach using fuzzy preference relations for dealing with multiclass classification. The idea is to decompose the original dataset into binary classification problems using a ..."
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This contribution proposes a technique for Fuzzy Rule Based Classification Systems (FRBCSs) based on a multiclassifier approach using fuzzy preference relations for dealing with multiclass classification. The idea is to decompose the original dataset into binary classification problems using a pairwise coupling approach (confronting all pair of classes), and to obtain a fuzzy system for each one of them. Along the inference process, each FRBCS generates an association degree for its two classes, and these values are encoded into a fuzzy preference relation. The final class of the whole FRBCS will be obtained by decision making following a nondominance criterium. We show the goodness of our proposal in contrast with the base fuzzy model with an extensive experimental study following a statistical study for analysing the differences in performance among the algorithms. We will also contrast our results versus the wellknown C4.5 decision tree.