kNN graph Laplacians with self-tuned affinity achieve operator pointwise convergence to the manifold operator at rate O(N^{-2/(d+6)}) when epsilon and k scale optimally.
The expectation of the former sum, which is its population counterpart, is ϵ−d/2 Z M k0 ∥x − y∥2 ϵϕ(¯ρr(x), ¯ρr(y))2 p(y)dV (y)
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Improved convergence rate of kNN graph Laplacians: differentiable self-tuned affinity
kNN graph Laplacians with self-tuned affinity achieve operator pointwise convergence to the manifold operator at rate O(N^{-2/(d+6)}) when epsilon and k scale optimally.