Diffusion maps

DiffMap{T <: Real} <: AbstractDimensionalityReduction

The DiffMap type represents diffusion maps model constructed for T type data.

fit(DiffMap, data; maxoutdim=2, t=1, α=0.0, ɛ=1.0)

Fit a isometric mapping model to data.

Arguments

• data::Matrix: a $d \times n$matrix of observations. Each column of data is

an observation, d is a number of features, n is a number of observations.

Keyword arguments

• kernel::Union{Nothing, Function}: the kernel function.

It maps two input vectors (observations) to a scalar (a metric of their similarity). by default, a Gaussian kernel. If kernel set to nothing, we assume data is instead the $n \times n$ precomputed Gram matrix.

• ɛ::Real=1.0: the Gaussian kernel variance (the scale parameter). It's ignored if the custom kernel is passed.
• maxoutdim::Int=2: the dimension of the reduced space.
• t::Int=1: the number of transitions
• α::Real=0.0: a normalization parameter

Examples

X = rand(3, 100)     # toy data matrix, 100 observations

# default kernel
M = fit(DiffMap, X)  # construct diffusion map model
R = transform(M)     # perform dimensionality reduction

# custom kernel
kernel = (x, y) -> x' * y # linear kernel
M = fit(DiffMap, X, kernel=kernel)

# precomputed Gram matrix
kernel = (x, y) -> x' * y # linear kernel
K = ManifoldLearning.pairwise(kernel, eachcol(X), symmetric=true)
M = fit(DiffMap, K, kernel=nothing)

predict(R::DiffMap)

Transforms the data fitted to the diffusion map model R into a reduced space representation.

Returns the kernel matrix of the diffusion maps model R