Diffusion Maps : Using the Semigroup Property for Parameter Tuning
This addresses a practical tuning problem in a classic dimension reduction technique, but it is incremental as it builds on existing methods.
The paper tackles the difficulty of tuning the diffusion time parameter in diffusion maps by proposing a semigroup criterion for selecting it, and experiments demonstrate the approach is effective and robust.
Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral parametrization for the manifold from simulated random walks or diffusion paths on the data set. However, DM is hard to tune in practice. In particular, the task to set a diffusion time t when constructing the diffusion kernel matrix is critical. We address this problem by using the semigroup property of the diffusion operator. We propose a semigroup criterion for picking t. Experiments show that this principled approach is effective and robust.