Node splitting is an important issue in Random Forest but robust splitting requires a large number of training samples. Existing solutions fail to properly partition the feature space if there are insufficient training data. In this paper, we present semi-supervised splitting to overcome this limitation by splitting nodes with the guidance of both labeled and unlabeled data. In particular, we derive a nonparametric algorithm to obtain an accurate quality measure of splitting by incorporating abundant unlabeled data. To avoid the curse of dimensionality, we project the data points from the original high-dimensional feature space onto a low-dimensional subspace before estimation. A unified optimization framework is proposed to select a coupled pair of subspace and separating hyper plane such that the smoothness of the subspace and the quality of the splitting are guaranteed simultaneously. The proposed algorithm is compared with state-of-the-art supervised and semi-supervised algorithms for typical computer vision applications such as object categorization and image segmentation. Experimental results on publicly available datasets demonstrate the superiority of our method.
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