YZ Sözlüğü
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Gaussian kernel
Exponential kernel function used to compute local similarities between data points, defined by K(x,y) = exp(-||x-y||²/σ²) where σ is the bandwidth parameter.
Diffusion eigenvectors
Eigenfunctions of the diffusion operator serving as coordinates to embed data into a lower-dimensional space preserving the diffusion geometry.
Diffusion time scale
Parameter t controlling the number of steps in the diffusion process, allowing exploration of data structure at different resolutions from local to global.
Laplace-Beltrami operator
Generalization of the Laplacian operator to differentiable manifolds, approximated by Diffusion Maps to capture the underlying Riemannian geometry of data.
Random walk on graph
Stochastic process where a particle moves randomly between nodes of the data graph according to transition probabilities, forming the basis of Diffusion Maps.
Row-stochastic normalization
Normalization procedure of the affinity matrix to obtain a transition matrix where each row sums to 1, ensuring valid transition probabilities.
Underlying manifold
Low-dimensional geometric structure on which data are sampled, which Diffusion Maps seek to discover and represent.
k-nearest neighbors graph
Structure connecting each point to its k nearest neighbors, used to sparsify the affinity matrix and improve computational efficiency of Diffusion Maps.
Effective conductance
Measure of connectivity between sets of points in the diffusion graph, related to the ease with which the diffusion process can propagate between these sets.