We propose a 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 preclustered feature space, via a trained rotation matrix. The rotation matrix is obtained through an iterative quantization process, where the input data, inclined to different classes, is clustered to the respective vertices of the feature space with maximum purity. In the feature space, orthogonal hyperplanes, which are employed at the split nodes of the decision trees in a random forest, can effectively tackle the clustering problems. 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 (SR) specifically because the transformed, compact features are more discriminative to the clustering-regression scheme. Experimental results on several public datasets also showed that the JMPF-based image SR scheme is consistently superior to recent state-of-the-art image SR algorithms.

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