Feature construction as a bi-level optimization problem

Feature selection and construction are important pre-processing techniques in data mining. They allow not only dimensionality reduction but also classification accuracy and efficiency improvement. While feature selection consists in selecting a subset of relevant features from the original feature set, feature construction corresponds to the generation of new high-level features, called constructed features, where each one of them is a combination of a subset of original features. However, different features can have different abilities to distinguish different classes. Therefore, it may be more difficult to construct a better discriminating feature when combining features that are relevant to different classes. Based on these definitions, feature construction could be seen as a BLOP (Bi-Level optimization Problem) where the feature subset should be defined in the upper level and the feature construction is applied in the lower level by performing mutliple followers, each of which generates a set class dependent constructed features. In this paper, we propose a new bi-level evolutionary approach for feature construction called BCDFC that constructs multiple features which focuses on distinguishing one class from other classes using Genetic Programming (GP). A detailed experimental study has been conducted on six high-dimensional datasets. The statistical analysis of the obtained results shows the competitiveness and the outperformance of our bi-level feature construction approach with respect to many state-of-art algorithms.