Imbalanced classification deals with learning from data with a disproportional number of samples in its classes. Traditional classifiers exhibit poor behavior when facing this kind of data because they do not take into account the imbalanced class distribution. Four main kinds of solutions exist to solve this problem: modifying the data distribution, modifying the learning algorithm for considering the imbalance representation, including the use of costs for data samples, and ensemble methods. In this paper, we adopt the second type of solution and introduce a classification algorithm for imbalanced data that uses fuzzy rough set theory and ordered weighted average aggregation. The proposal considers different strategies to build a weight vector to take into account data imbalance. Our methods are validated by an extensive experimental study, showing statistically better results than 13 other state-of-the-art methods.

Incremental and online learning algorithms are more relevant in the data mining context because of the increasing necessity to process data streams. In this context, the target function may change overtime, an inherent problem of online learning (known as concept drift). In order to handle concept drift regardless of the learning model, we propose new methods to monitor the performance metrics measured during the learning process, to trigger drift signals when a significant variation has been detected. To monitor this performance, we apply some probability inequalities that assume only independent, univariate and bounded random variables to obtain theoretical guarantees for the detection of such distributional changes. Some common restrictions for the online change detection as well as relevant types of change (abrupt and gradual) are considered. Two main approaches are proposed, the first one involves moving averages and is more suitable to detect abrupt changes. The second one follows a widespread intuitive idea to deal with gradual changes using weighted moving averages. The simplicity of the proposed methods, together with the computational efficiency make them very advantageous. We use a Naive Bayes classifier and a Perceptron to evaluate the performance of the methods over synthetic and real data.

In this paper we propose a method to build similarity relations into extended Rough Set Theory. Similarity is estimated using ideas from Granular computing and Case-base reasoning. A new measure is introduced in order to compute the quality of the similarity relation. This work presents a study of a case of a similarity relation based on a global similarity function between two objects, this function includes the weights for each feature and local functions to calculate how the values of a given feature are similar. This approach was proved in the function approximation problem. Promissory results are obtained in several experiments.

Rough sets theory has opened new trends for the development of the incomplete information theory. Inside this one, the notion of reduct is a very significant one, but to obtain a reduct in a decision system is an expensive computing process although very important in data analysis and knowledge discovery. Because of this, it has been necessary the development of different variants to calculate reducts. The present work look into the utility that offers rough sets model and information theory in feature selection and three methods are presented with the purpose of calculate good reducts. The first algorithm is MRSReduct, a variant of the method RSReduct; both methods consist of a greedy algorithm that uses heuristics to work out good reducts in acceptable times. In this paper we propose other method to find good reducts: RSRed*; this method combines several elements of rough set theory. The new methods are compared with others which are implemented inside pattern recognition, genetic algorithm and ant colony optimization algorithms and the results of the statistical tests are shown.

The accelerated growth of the information volumes on processes, phenomena and reports brings about an increasing interest in the possibility of discovering knowledge from data sets. This is a challenging task because in many cases it deals with extremely large, inherently not structured and fuzzy data, plus the presence of uncertainty. Therefore it is required to know a priori the quality of future procedures without using any additional information. In this paper we propose new measures to evaluate the quality of training sets used by algorithms for learning of supervised classifiers. Our training set assessment relied on measures furnished by rough sets theory. Our experimental results involved three classifiers (k-NN, C-4.5 and MLP) from international data bases. New training sets are built taking into account the results of the measures and the accuracy obtained by the classifiers, with the aim of infer the accuracy that the classifiers would obtain using a new training set. This is possible using a rule generator (C4.5) and a function estimation algorithm (k-NN).

In this paper we propose a hybrid approach to feature selection based on Ant Colony System algorithm and Rough Set Theory. Rough Set Theory offers the heuristic function to measure the quality of a single subset. We have studied the influence of the setting of the parameters for this problem, in particular for finding reducts. Experimental results show this hybrid approach is a promising method for features selection.

Rough set theory (RST) is a technique for data analysis. In this paper, we use RST to improve the performance of the k-NN method. The RST is used to edit the training set. We propose two methods to edit training sets, which are based on the lower and upper approximations. Experimental results show a satisfactory performance of the k-NN using these techniques.