  This work introduces a transformation-based learner model for classification
forests. The weak learner at each split node plays a crucial role in a
classification tree. We propose to optimize the splitting objective by learning
a linear transformation on subspaces using nuclear norm as the optimization
criteria. The learned linear transformation restores a low-rank structure for
data from the same class, and, at the same time, maximizes the separation
between different classes, thereby improving the performance of the split
function. Theoretical and experimental results support the proposed framework.
