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Random Balance strategy (RandBal) has been recently proposed for constructing classifier ensembles for imbalanced, two-class data sets. In RandBal, each base classifier is trained with a sample of the data with a random class prevalence, independent of the a priori distribution. Hence, for each sample, one of the classes will be undersampled while the other will be oversampled. RandBal can be applied on its own or can be combined with any other ensemble method. One particularly successful variant is RandBalBoost which integrates Random Balance and boosting. Encouraged by the success of RandBal, this work proposes two approaches which extend RandBal to multiclass imbalance problems. Multiclass imbalance implies that at least two classes have substantially different proportion of instances. In the first approach proposed here, termed Multiple Random Balance (MultiRandBal), we deal with all classes simultaneously. The training data for each base classifier are sampled with random class proportions. The second approach we propose decomposes the multiclass problem into two-class problems using one-vs-one or one-vs-all, and builds an ensemble of RandBal ensembles. We call the two versions of the second approach OVO-RandBal and OVA-RandBal, respectively. These two approaches were chosen because they are the most straightforward extensions of RandBal for multiple classes. Our main objective is to evaluate both approaches for multiclass imbalanced problems. To this end, an experiment was carried out with 52 multiclass data sets. The results suggest that both MultiRandBal, and OVO/OVA-RandBal are viable extensions of the original two-class RandBal. Collectively, they consistently outperform acclaimed state-of-the art methods for multiclass imbalanced problems., Ministerio de Economía yCompetitividad[http://dx.doi.org/10.13039/501100003329] of theSpanishGovernmentthroughprojectTIN2015-67534-P(MINECO/FEDER, UE) and the Junta de Castilla y León through projectBU085P17 (JCyL/FEDER, UE)

Detecting change in multivariate data is a challenging problem, especially when class labels are not available. There is a large body of research on univariate change detection, notably in control charts developed originally for engineering applications. We evaluate univariate change detection approaches —including those in the MOA framework — built into ensembles where each member observes a feature in the input space of an unsupervised change detection problem. We present a comparison between the ensemble combinations and three established ‘pure’ multivariate approaches over 96 data sets, and a case study on the KDD Cup 1999 network intrusion detection dataset. We found that ensemble combination of univariate methods consistently outperformed multivariate methods on the four experimental metrics., project RPG-2015-188 funded by The Leverhulme Trust, UK; Spanish Ministry of Economy and Competitiveness through project TIN 2015-67534-P and the Spanish Ministry of Education, Culture and Sport through Mobility Grant PRX16/00495. The 96 datasets were originally curated for use in the work of Fernández-Delgado et al. [53] and accessed from the personal web page of the author5. The KDD Cup 1999 dataset used in the case study was accessed from the UCI Machine Learning Repository [10]

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

We consider a problem where a set X of N objects (instances) coming from c classes have to be classified simultaneously. A restriction is imposed on X in that the maximum possible number of objects from each class is known, hence we dubbed the problem who-is-there? We compare three approaches to this problem: (1) independent classification whereby each object is labelled in the class with the largest posterior probability; (2) a greedy approach which enforces the restriction; and (3) a theoretical approach which, in addition, maximises the likelihood of the label assignment, implemented through the Hungarian assignment algorithm. Our experimental study consists of two parts. The first part includes a custom-made chess data set where the pieces on the chess board must be recognised together from an image of the board. In the second part, we simulate the restricted set classification scenario using 96 datasets from a recently collated repository (University of Santiago de Compostela, USC). Our results show that the proposed approach (3) outperforms approaches (1) and (2)., Spanish Ministry of Economy and Competitiveness through project TIN 2015-67534-P

Publisher Summary This chapter considers the point prototype construction for the nearest prototype classifier design. The distinctions between pre and post-supervised learning and also between selection and extraction of point prototypes are discussed. Numerical examples based on the Iris data are given to contrast and compare various models. Calculations suggest that the pre-supervision yields better nearest prototype classifiers than post-supervision, independent of the type of prototypes chosen; selection is better than extraction for finding point prototypes for classification; post-supervised sequential methods such as vector quantization may produce better prototypes than batch methods such as fuzzy c-means when the number of prototypes is larger than the number of labeled classes; and among post-supervised designs, self-organizing feature maps produce classifiers that are intermediate among those based on local and global prototype updating.