An emerging trend in feature selection is the development of two-objective algorithms that analyze the tradeoff between the number of features and the classification performance of the model built with these features. Since these two objectives are conflicting, a typical result stands in a set of Pareto-efficient subsets, each having a different cardinality and a corresponding discriminating power. However, this approach overlooks the fact that, for a given cardinality, there can be several subsets with similar information content. The study reported here addresses this problem, and introduces a novel multiobjective feature selection approach conceived to identify: 1) a subset that maximizes the performance of a given classifier and 2) a set of subsets that are quasi equally informative, i.e., have almost same classification performance, to the performance maximizing subset. The approach consists of a wrapper [Wrapper for Quasi Equally Informative Subset Selection (W-QEISS)] built on the formulation of a four-objective optimization problem, which is aimed at maximizing the accuracy of a classifier, minimizing the number of features, and optimizing two entropy-based measures of relevance and redundancy. This allows conducting the search in a larger space, thus enabling the wrapper to generate a large number of Pareto-efficient solutions. The algorithm is compared against the mRMR algorithm, a two-objective wrapper and a computationally efficient filter [Filter for Quasi Equally Informative Subset Selection (F-QEISS)] on 24 University of California, Irvine, (UCI) datasets including both binary and multiclass classification. Experimental results show that W-QEISS has the capability of evolving a rich and diverse set of Pareto-efficient solutions, and that their availability helps in: 1) studying the tradeoff between multiple measures of classification performance and 2) understanding the relative importance of each feature. The quasi equally informative subsets are identified at the cost of a marginal increase in the computational time thanks to the adoption of Borg Multiobjective Evolutionary Algorithm and Extreme Learning Machine as global optimization and learning algorithms, respectively.

No abstract

No abstract

This work investigates the uncertainty associated to the presence of multiple subsets of predictors yielding data-driven models with the same, or similar, predictive accuracy. To handle this uncertainty eectively, we introduce a novel input variable selection algorithm, called Wrapper for Quasi Equally Informative Subset Selection (W-QEISS), specically conceived to identify all alternate subsets of predictors in a given dataset. The search process is based on a four-objective optimisation problem that minimises the number of selected predictors, maximises the predictive accuracy of a data-driven model and optimises two information theoretic metrics of relevance and redundancy, which guarantee that the selected subsets are highly informative and with little intra-subset similarity. The algorithm is rst tested on two synthetic test problems and then demonstrated on a real-world streamow prediction problem in the Yampa River catchment (US). Results show that complex hydro-meteorological datasets are characterised by a large number of alternate subsets of predictors, which provides useful insights on the un

No abstract