Subspace partitioning plays a fundamental role in the design of effective classification methods. A novel subspace learning machine (SLM) was recently proposed. It projects feature vectors into a 1D feature subspace and partitions it into two disjoint sets. To effectively generalize the SLM method to high-dimensional feature space, SLM with soft partitioning, denoted by SLM/SP, is proposed in this work. By incorporating the Soft Decision Tree (SDT) data structure for decision learning, the SLM/SP begins with the adaptive learning of a tree structure using local greedy subspace partitioning. Once the tree structure is finalized, all parameters are globally updated. To apply SLM/SP to image classification tasks, we propose modulated designs for the topology of the SDT and a novel module for efficient local representation learning in the subspace learning diagram. The SLM/SP methodology offers efficient training, high classification accuracy, and small model size, underscored by experimental results on image classification benchmarks.