Given non-uniformly sampled data points on a toroidal helix (top), the first two Diffusion Map coordinates with Laplace–Beltrami normalization are plotted (bottom). The Diffusion Map unravels the toroidal helix recovering the underlying intrinsic circular geometry of the data.
Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon[1][2][3][4] which computes a family of embeddings of a data set into Euclidean space (often low-dimensional) whose coordinates can be computed from the eigenvectors and eigenvalues of a diffusion operator on the data. The Euclidean distance between points in the embedded space is equal to the "diffusion distance" between probability distributions centered at those points. Different from linear dimensionality reduction methods such as principal component analysis (PCA), diffusion maps are part of the family of nonlinear dimensionality reduction methods which focus on discovering the underlying manifold that the data has been sampled from. By integrating local similarities at different scales, diffusion maps give a global description of the data-set. Compared with other methods, the diffusion map algorithm is robust to noise perturbation and computationally inexpensive.
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Diffusionmaps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of a...
special kind of DWI, diffusion tensor imaging (DTI), has been used extensively to map white matter tractography in the brain. In diffusion weighted imaging...
In machine learning, diffusion models, also known as diffusion probabilistic models or score-based generative models, are a class of latent variable generative...
sets. Diffusionmaps leverages the relationship between heat diffusion and a random walk (Markov Chain); an analogy is drawn between the diffusion operator...
discrete Laplace operators on point clouds for manifold learning (e.g. diffusionmap). Kernel density estimates are closely related to histograms, but can...
then be processed and reapplied to the model as a light map. To simulate diffusion, the light map texture can simply be blurred. Rendering the lighting...
using data collected by diffusion MRI. It uses special techniques of magnetic resonance imaging (MRI) and computer-based diffusion MRI. The results are presented...
aggregating CN2 algorithm Constructing skill trees Dehaene–Changeux model Diffusionmap Dominance-based rough set approach Dynamic time warping Error-driven...
spatial diffusion (1968). The diffusion of disease can be described in four patterns: expansion diffusion, contagious diffusion, hierarchal diffusion and...
Michael T.; Newman, M.E.J. (May 18, 2004). "Diffusion-based Method for Producing Density-Equalizing Maps". Proceedings of the National Academy of Sciences...
The Society for the Diffusion of Useful Knowledge (SDUK) was founded in London in 1826, mainly at the instigation of Whig MP Henry Brougham, with the...
transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)...
Isomap, which uses geodesic distances in the data space; diffusionmaps, which use diffusion distances in the data space; t-distributed stochastic neighbor...
The Bass model or Bass diffusion model was developed by Frank Bass. It consists of a simple differential equation that describes the process of how new...
In applied mathematics, Arnold diffusion is the phenomenon of instability of nearly-integrable Hamiltonian systems. The phenomenon is named after Vladimir...
believed in a direct diffusion to Syria, Crete, East Africa, Southern Arabia and Sumer, and other areas were influenced by secondary diffusion. The Neolithic...
Rotational diffusion is the rotational movement which acts upon any object such as particles, molecules, atoms when present in a fluid, by random changes...
principle used to create a shadow map. The light's view is rendered, storing the depth of every surface it sees (the shadow map). Next, the regular scene is...
deformation mechanism map will be larger than in maps with very small grains. Additionally, the larger the grains, the less diffusional creep and thus the...
In modern cosmological theory, diffusion damping, also called photon diffusion damping, is a physical process which reduced density inequalities (anisotropies)...
Graphics at SIGGRAPH conference. At Hebrew University, he wrote a paper on Diffusionmaps for edge-aware image editing. His research on tone mapping of HDR images...
algorithm. This can be for example a 2D simplex noise function or by diffusion-limited aggregation. Another method is to reconstruct heightmaps from...
associated vector spaces over the field k. A map f: X → Z is an affine map if there exists a linear map mf : V → W such that mf (x − y) = f (x) − f (y)...
Roman Empire as diffusion of innovation looks at religious change in the Roman Empire's first three centuries through the lens of diffusion of innovations...
applications, such as identifying factors involved in dangerous driving. Diffusion of innovations Discriminant analysis Marketing research Multidimensional...
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