Transitive distance is an ultrametric with elegant properties for clustering. Conventional transitive distance can be found by referring to the minimum spanning tree (MST). We show that such distance metric can be generalized onto a minimum spanning random forest (MSRF) with element-wise max pooling over the set of transitive distance matrices from an MSRF. Our proposed approach is both intuitively reasonable and theoretically attractive. Intuitively, max pooling alleviates undesired short links with single MST when noise is present. Theoretically, one can see that the distance metric obtained max pooling is still an ultrametric, rendering many good clustering properties. Comprehensive experiments on data clustering and image segmentation show that MSRF with max pooling improves the clustering performance over single MST and achieves state of the art performance on the Berkeley Segmentation Dataset.
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