… We implemented a diffusion map algorithm in the Python programming language. The code
was adapted for the machine learning framework Elefant (Efficient Learning, Large Scale …

… This function oscillates 12 times along the z-axis, and by employing an f -driven diffusion,
we were able to generate the function the function ψ1(ϕ,θ) = cos(θ) as the first nontrivial …

… For each of the data sets I used in this dissertation I implemented this scheme to get an
appropriate ε before I implemented the diffusion map algorithm. Figure 2.1 and 2.2 show a …

… Additionally, if X ⊂ R d is high dimensional, yet lies on a low dimensional manifold, the
diffusion map gives an embedding into Euclidean space that parameterizes the data in terms of …

… Diffusion maps generate a mapping, called an embedding, from the original shape space …
for using diffusion maps is derived from the fact that this framework generates a mapping that …

… This result was used in the diffusion maps … on an embedding of the manifold in Euclidean
space). If a data set is assumed to lie on or near an embedded manifold, the diffusion maps …

… Abstract—In this paper we propose an efficient … of diffusion maps defined on sets of data,
as established in [10]. In section III we describe how the eigenfunctions of the diffusion map are …

… a diffusion operator whose eigendecomposition produces an embedding of the data into R"
via a diffusion map. In … that they also all have an interpretation in terms of diffusion process. …

… the problem by using diffusion maps, a machine learning algorithm, to learn the map’s
geometry … The main contributions of this work are 1) development of an efficient motion planning …

… That is, we assume there exists an effective drift f(ψ1) and an effective diffusion
coefficient D(ψ1), such that the time evolution of ψ1(x(t)) approximately satisfies the Itô SDE …