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High-dimensional data with very few instances are typical in many application domains. Selecting a highly discriminative subset of the original features is often the main interest of the end user. The widely-used feature selection protocol for such type of data consists of two steps. First, features are selected from the data (possibly through cross-validation), and, second, a cross-validation protocol is applied to test a classifier using the selected features. The selected feature set and the testing accuracy are then returned to the user. For the lack of a better option, the same low-sample-size dataset is used in both steps. Questioning the validity of this protocol, we carried out an experiment using 24 high-dimensional datasets, three feature selection methods and five classifier models. We found that the accuracy returned by the above protocol is heavily biased, and therefore propose an alternative protocol which avoids the contamination by including both steps in a single cross-validation loop. Statistical tests verify that the classification accuracy returned by the proper protocol is significantly closer to the true accuracy (estimated from an independent testing set) compared to that returned by the currently favoured protocol. ; project RPG-2015-188 funded by The Leverhulme Trust, UK and by project TIN2015-67534-P (MINECO/FEDER, UE) funded by the Ministerio de Economía y Competitividad of the Spanish Government and European Union FEDER funds

This paper studies the effects that combinations of balancing and feature selection techniques have on wide data (many more attributes than instances) when different classifiers are used. For this, an extensive study is done using 14 datasets, 3 balancing strategies, and 7 feature selection algorithms. The evaluation is carried out using 5 classification algorithms, analyzing the results for different percentages of selected features, and establishing the statistical significance using Bayesian tests. Some general conclusions of the study are that it is better to use RUS before the feature selection, while ROS and SMOTE offer better results when applied afterwards. Additionally, specific results are also obtained depending on the classifier used, for example, for Gaussian SVM the best performance is obtained when the feature selection is done with SVM-RFE before balancing the data with RUS. ; "La Caixa" Foundation, under agreement LCF/PR/PR18/51130007. This work was also supported by the Junta de Castilla León under project BU055P20 (JCyL/FEDER, UE) and by the Ministry of Science and Innovation under project PID2020-119894GB-I00, co-financed through European Union FEDER funds .

Datasets are growing in size and complexity at a pace never seen before, forming ever larger datasets known as Big Data. A common problem for classification, especially in Big Data, is that the numerous examples of the different classes might not be balanced. Some decades ago, imbalanced classification was therefore introduced, to correct the tendency of classifiers that show bias in favor of the majority class and that ignore the minority one. To date, although the number of imbalanced classification methods have increased, they continue to focus on normal-sized datasets and not on the new reality of Big Data. In this paper, in-depth experimentation with ensemble classifiers is conducted in the context of imbalanced Big Data classification, using two popular ensemble families (Bagging and Boosting) and different resampling methods. All the experimentation was launched in Spark clusters, comparing ensemble performance and execution times with statistical test results, including the newest ones based on the Bayesian approach. One very interesting conclusion from the study was that simpler methods applied to unbalanced datasets in the context of Big Data provided better results than complex methods. The additional complexity of some of the sophisticated methods, which appear necessary to process and to reduce imbalance in normal-sized datasets were not effective for imbalanced Big Data. ; "la Caixa" Foundation, Spain, under agreement LCF/PR/PR18/51130007. This work was supported by the Junta de Castilla y León, Spain under project BU055P20 (JCyL/FEDER, UE) co-financed through European Union FEDER funds, and by the Consejería de Educación of the Junta de Castilla y León and the European Social Fund, Spain through a pre-doctoral grant (EDU/1100/2017).

One of the main goals of Big Data research, is to find new data mining methods that are able to process large amounts of data in acceptable times. In Big Data classification, as in traditional classification, class imbalance is a common problem that must be addressed, in the case of Big Data also looking for a solution that can be applied in an acceptable execution time. In this paper we present Approx-SMOTE, a parallel implementation of the SMOTE algorithm for the Apache Spark framework. The key difference with the original SMOTE, besides parallelism, is that it uses an approximated version of k-Nearest Neighbor which makes it highly scalable. Although an implementation of SMOTE for Big Data already exists (SMOTE-BD), it uses an exact Nearest Neighbor search, which does not make it entirely scalable. Approx-SMOTE on the other hand is able to achieve up to 30 times faster run times without sacrificing the improved classification performance offered by the original SMOTE. ; "La Caixa" Foundation, under agreement LCF/PR/PR18/51130007. This work was supported by the Junta de Castilla y León under project BU055P20 and by the Ministry of Science and Innovation of Spain under project PID2020-119894 GB-I00, co-financed through European Union FEDER funds. It also was supported through Consejería de Educación of the Junta de Castilla y León and the European Social Fund through a pre-doctoral grant (EDU/1100/2017). This material is based upon work supported by Google Cloud.

The Rotation Forest classifier is a successful ensemble method for a wide variety of data mining applications. However, the way in which Rotation Forest transforms the feature space through PCA, although powerful, penalizes training and prediction times, making it unfeasible for Big Data. In this paper, a MapReduce Rotation Forest and its implementation under the Spark framework are presented. The proposed MapReduce Rotation Forest behaves in the same way as the standard Rotation Forest, training the base classifiers on a rotated space, but using a functional implementation of the rotation that enables its execution in Big Data frameworks. Experimental results are obtained using different cloud-based cluster configurations. Bayesian tests are used to validate the method against two ensembles for Big Data: Random Forest and PCARDE classifiers. Our proposal incorporates the parallelization of both the PCA calculation and the tree training, providing a scalable solution that retains the performance of the original Rotation Forest and achieves a competitive execution time (in average, at training, more than 3 times faster than other PCA-based alternatives). In addition, extensive experimentation shows that by setting some parameters of the classifier (i.e., bootstrap sample size, number of trees, and number of rotations), the execution time is reduced with no significant loss of performance using a small ensemble. ; This work was supported through project TIN2015-67534-P (MINECO/FEDER, UE) of the Ministerio de Economía y Competitividad of the Spanish Government, projects BU085P17 and BU055P20 (JCyL/FEDER, UE) of the Junta de Castilla y León, Spain (both projects co-financed through European Union FEDER funds), and by the Consejería de Educación of the Junta de Castilla y León, Spain and the European Social Fund through a pre-doctoral grant (EDU/1100/2017). The project leading to these results has received also funding from "la Caixa" Foundation, Spain , under agreement LCF/PR/PR18/51130007. This material is based upon work supported by Google Cloud.