diffusion_map(P, d; t=1)
diffusion_map(X, kernel, d; t=1)

compute diffusion map.

two call signatures:

• the data matrix X is passed in. examples are in the columns.
• the right-stochastic matrix P is passed in. (eg. for a precomputed kernel matrix)

arguments

• d: dim
• t: # of steps

example

# define kernel
kernel(xᵢ, xⱼ) = gaussian_kernel(xᵢ, xⱼ, 0.5)

# data matrix (100 data pts, 2D vectors)
X = rand(2, 100)

# diffusion map to 1D
X̂ = diff_map(X, kernel, 1)

normalize_to_stochastic_matrix!(P, check_symmetry=true)

normalize a kernel matrix P so that rows sum to one.

checks for symmetry.