… local intrinsic dimension of a distribution, denoted as ID-Entropy, can serve as a robust
entropy measure for continuous spaces, while capturing the data dimensionality. We find that ID-…

… to the limits of tail measures of entropy, divergence or distance, so as to produce formulations
that depend only on the local intrinsic dimensions of the functions involved. All three …

… estimates, we apply neighborhood smoothing and recursive entropy estimation as described
above. The results, illustrated in Fig. 15(a), lead us to define an ideal neighborhood size of …

… Knowing the intrinsic dimension and relative entropy of these manifolds is important for …
new family of entropic graph methods to the estimation of intrinsic dimension and entropy of …

… |'—dimerrsional manifold, this intrinsic entropy can be usefrrl for … on deriving intrinsic dimension
and entropy estimators based … nonlinea.1' dimension reduction via local tangent space a-…

… local intrinsic dimension (LID) as formulated in [22, 23], and in particular, establishing how it
relates to entropy… In its essence, entropy can be regarded as a measure of the uncertainty of …

… Several local intrinsic … dimension (ED) [25], the generalized expansion dimension (GED)
[19], the minimum neighbor distance (MiND) [31], and local continuous intrinsic dimension (…

… dimensional values to different locations in the data domain. Our focus in this paper is on the
local intrinsic dimension … between local intrinsic dimensionality and several forms of entropy …

… manifold’s intrinsic dimension and the intrinsic entropy of the … They are based on local
approximation of the geometry of the … have better stability than local methods when the number of …

… intrinsic dimension is not always required to be very precise. The existing approaches to
estimating the intrinsic dimension … a global or local PCA, with intrinsic dimension determined by …