Advances in random forests with application to classification
Arnu Pretorius · SUNScholar (Stellenbosch University) · 2016
ENGLISH SUMMARY : Since their introduction, random forests have successfully been employed in a vast array of application areas. Fairly recently, a number of algorithms that adhere to Leo Breiman’s definition of a random forest have been proposed in the literature. Breiman’s popular random forest algorithm (Forest-RI), and related ensemble classification algorithms which followed, form the focus of this study. A review of random forest algorithms that were developed since the introduction of Forest-RI is given. This includes a novel taxonomy of random forest classification algorithms, which is based on their sources of randomization, and on deterministic modifications. Also, a visual conceptualization of contributions to random forest algorithms in the literature is provided by means of multidimensional scaling. Towards an analysis of advances in random forest algorithms, decomposition of the expected prediction error into bias and variance components is considered. In classification, such decompositions are not as straightforward as in the case of using squared-error loss for regression. Hence various definitions of bias and variance for classification can be found in the literature. Using a particular bias-variance decomposition, an empirical study of ensemble learners, including bagging, boosting and Forest-RI, is presented. From the empirical results and insights into the way in which certain mechanisms of random forests affect bias and variance, a novel random forest framework, viz. oblique random rotation forests, is proposed. Although not entirely satisfactory, the framework serves as an example of a heuristic approach towards novel proposals based on bias-variance analyses, instead of an ad hoc approach, as is often found in the literature. The analysis of comparative studies regarding advances in random forest algorithms is also considered. It is of interest to critically evaluate the conclusions that can be drawn from these studies, and to infer whether novel random forest algorithms are found to significantly outperform Forest-RI. For this purpose, a meta-analysis is conducted in which an evaluation is given of the state of research on random forests based on all (34) papers that could be found in which a novel random forest algorithm was proposed and compared to already existing random forest algorithms. Using the reported performances in each paper, a novel two-step procedure is proposed, which allows for multiple algorithms to be compared over multiple data sets, and across different papers. The meta analysis results indicate weighted voting strategies and variable weighting in high-dimensional settings to provide significantly improved performances over the performance of Breiman’s popular Forest-RI algorithm.