Prediction-based classification using learning on Riemannian manifolds

This paper is concerned with learning from predictions. Predictions are obtained by ensemble of classifiers such as random forests (RF) or extra-trees. One assumes that estimators are semi independent so that they can be considered as prediction space. Hence we project our feature vector to the space of estimators obtaining responses from each of them. The responses for RFs are conditional class probabilities. The responses might be considered as projections onto some direction in quasi-orthogonal space which are decision trees of a RF. After that one creates the connected Riemannian manifold by computing a matrix of pairwise products of predictions for all trees in the RF. These matrices are symmetric and positive definite which is a necessary and sufficient condition to have a connected Riemannian manifold (R manifold). Because outputs of trees are conditional probabilities we have to create as many such matrices as there are classes. Stacking all these matrices together we obtain a tensor which is passed to Convolutional Neural Networks (CNN) for learning. We tested our algorithm on 11 datasets from UCI repository representing difficult classification problems. The results show very fast learning and convergence of loss and prediction accuracy. The proposed algorithm outperforms feature-based classical classifier ensembles (RFs and extra-trees) for every tested dataset from UCI repository.