  In this paper, we propose a novel random-forest scheme, namely Joint Maximum
Purity Forest (JMPF), for classification, clustering, and regression tasks. In
the JMPF scheme, the original feature space is transformed into a compactly
pre-clustered feature space, via a trained rotation matrix. The rotation matrix
is obtained through an iterative quantization process, where the input data
belonging to different classes are clustered to the respective vertices of the
new feature space with maximum purity. In the new feature space, orthogonal
hyperplanes, which are employed at the split-nodes of decision trees in random
forests, can tackle the clustering problems effectively. We evaluated our
proposed method on public benchmark datasets for regression and classification
tasks, and experiments showed that JMPF remarkably outperforms other
state-of-the-art random-forest-based approaches. Furthermore, we applied JMPF
to image super-resolution, because the transformed, compact features are more
discriminative to the clustering-regression scheme. Experiment results on
several public benchmark datasets also showed that the JMPF-based image
super-resolution scheme is consistently superior to recent state-of-the-art
image super-resolution algorithms.
