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Diffusion maps (DM) constitute a classic dimension reduction technique, fordata lying on or close to a (relatively) low-dimensional manifold embedded in amuch larger dimensional space. The DM procedure consists in constructing aspectral parametrization for the manifold from simulated random walks ordiffusion paths on the data set. However, DM is hard to tune in practice. Inparticular, the task to set a diffusion time t when constructing the diffusionkernel matrix is critical. We address this problem by using the semigroupproperty of the diffusion operator. We propose a semigroup criterion forpicking t. Experiments show that this principled approach is effective androbust.

Diffusion Maps : Using the Semigroup Property for Parameter Tuning