Classification of Imbalanced Data Using Deep Learning with Adding Noise

This paper proposes a method to treat the classification of imbalanced data by adding noise to the feature space of convolutional neural network (CNN) without changing a data set (ratio of majority and minority data). Besides, a hybrid loss function of crossentropy and KL divergence is proposed. The proposed approach can improve the accuracy of minority class in the testing data. In addition, a simple design method for selecting structure of CNN is first introduced and then, we add noise in feature space of CNN to obtain proper features by a training process and to improve the classification results. From comparison results, we can find that the proposed method can extract the suitable features to improve the accuracy of minority class. Finally, illustrated examples of multiclass classification problems and the corresponding discussion in balance ratio are presented. Our approach performs well with smaller network structure compared with other deep models. In addition, the performance is improved over 40% in defective accuracy by adding noise approach. Finally, the accuracy is higher than 96%; even the imbalanced ratio (IR) is one hundred.

A branch & bound algorithm to determine optimal bivariate splits for oblique decision tree induction

Univariate decision tree induction methods for multiclass classification problems such as CART, C4.5 and ID3 continue to be very popular in the context of machine learning due to their major benefit of being easy to interpret. However, as these trees only consider a single attribute per node, they often get quite large which lowers their explanatory value. Oblique decision tree building algorithms, which divide the feature space by multidimensional hyperplanes, often produce much smaller trees but the individual splits are hard to interpret. Moreover, the effort of finding optimal oblique splits is very high such that heuristics have to be applied to determine local optimal solutions. In this work, we introduce an effective branch and bound procedure to determine global optimal bivariate oblique splits for concave impurity measures. Decision trees based on these bivariate oblique splits remain fairly interpretable due to the restriction to two attributes per split. The resulting trees are significantly smaller and more accurate than their univariate counterparts due to their ability of adapting better to the underlying data and capturing interactions of attribute pairs. Moreover, our evaluation shows that our algorithm even outperforms algorithms based on heuristically obtained multivariate oblique splits despite the fact that we are focusing on two attributes only.

Computer Implementation of Genetic Programming

This chapter presents the computer implementation of the tree-based genetic programming in C# programming language. Since C# is a common object-oriented programming language, with little modification the source code presented in the chapter can be easily transformed into Java or C++ programming languages. The chapter covers all aspects of the implementation: node, chromosome, population, function set, and terminal set class implementations. The chapter is carefully structured, so at the end of the chapter fully working GP computer program will be implemented which can solve regression and multiclass classification problems. The reader should not worry about specific operating system, or development environment, since all code implementations are based on cross-OS and open source integrated development environment visual studio code which can run on Windows, Mac, or Linux.