Dimensionality estimation without distances
نویسندگان
چکیده
Theorem (Consistency of EDP and ECAP) Let the regularity assumptions hold. Let D = {x1, . . . , xn} ⊆ X be an i.i.d. sample from f and G be the directed, unweighted kNN-graph on D. Given G as input and a vertex i ∈ {1, . . . , n} chosen uniformly at random, both EDP({i}) and ECAP({i}) converge to the true dimension d in probability as n→∞ if k = k(n) satisfies k ∈ o(n), logn ∈ o(k), and there exists k′ = k′(n) with k′ ∈ o(k) and logn ∈ o(k′). How can we choose k and k′? For example: k = (logn)1+τ and k′ = (logn)1+τ/2 for some τ > 0
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