Hybrid extreme rotation forest.

This paper proposes the Hybrid Extreme Rotation Forest (HERF), an innovative ensemble learning algorithm for classification problems, combining classical Decision Trees with the recently proposed Extreme Learning Machines (ELM) training of Neural Networks. In the HERF algorithm, training of each individual classifier involves two steps: first computing a randomized data rotation transformation of the training data, second, training the individual classifier on the rotated data. The testing data is subjected to the same transformation as the training data, which is specific for each classifier in the ensemble. Experimental design in this paper involves (a) the comparison of factorization approaches to compute the randomized rotation matrix: the Principal Component Analysis (PCA) and the Quartimax, (b) assessing the effect of data normalization and bootstrapping training data selection, (c) all variants of single and combined ELM and decision trees, including Regularized ELM. This experimental design effectively includes other state-of-the-art ensemble approaches in the comparison, such as Voting ELM and Random Forest. We report extensive results over a collection of machine learning benchmark databases. Ranking the cross-validation results per experimental dataset and classifier tested concludes that HERF significantly improves over the other state-of-the-art ensemble classifier. Besides, we find some other results such as that the data rotation with Quartimax improves over PCA, and the relative insensitivity of the approach to regularization which may be attributable to the de facto regularization performed by the ensemble approach.