Memory-Efficient Minimax Distance Measures

Minimax distance measure is a transitive-aware measure that allows us to extract elongated manifolds and structures in the data in an unsupervised manner. Existing methods require a quadratic memory with respect to the number of data points to compute the pairwise Minimax distances. In this paper, we investigate two memory-efficient approaches to reduce the memory requirement and achieve linear space complexity. The first approach proposes a novel hierarchical representation of the data that requires only O(N) memory and from which the pairwise Minimax distances can be derived in a memory-efficient manner. The second approach is an efficient sampling method that adapts well to the proposed hierarchical representation of the data. This approach accurately recovers the majority of Minimax distances, especially the most important ones. It still works in O(N) memory, but with a substantially lower computational cost, and yields impressive results on clustering benchmarks, as a downstream task. We evaluate our methods on synthetic and real-world datasets from a variety of domains.