In this paper, we introduce a new distance computed from the construction of dual-rooted minimal spanning trees (MSTs). This distance extends Grikschat's approach, exhibits attractive properties and allows to account for both local and global neighborhood information. Furthermore, a function measuring the probability that a point belongs to a detected class is proposed. Some connections with diffusion maps are outlined. The dual-rooted tree-based distance (DRPT) allows us to construct a new affinity matrix for use in a spectral clustering algorithm, or leads to a new data analysis method. Results are presented on benchmark datasets.