ExpectationMaximizationPCA.jl (EMPCA) is a Julia rewrite of empca which provides weighted Expectation Maximization PCA, an iterative method for solving PCA while properly weighting data.
The most current, tagged version of ExpectationMaximizationPCA.jl can be easily installed using Julia's Pkg
Pkg.add("ExpectationMaximizationPCA")If you would like to contribute to the package, or just want to run the latest (untagged) version, you can use the following
Pkg.develop("ExpectationMaximizationPCA")import ExpectationMaximizationPCA as EMPCA
## making data
nx = 200 # dimensionality of observations
nt = 50 # number of observations
σ = ((((((1:nx) .- nx/2).^2) ./ (nx/2)^2) .+ 1)* ones(nt)') ./ 3 # noise, edges are twice as noisy as the center
data = rand(nt)' .* sin.(((1:nx) ./ nx) * 2π) + (0.2 .* rand(nt)') .* cos.(((1:nx) ./ nx) * 2π) # a mixture of sin and cos signals
data .+= σ .* randn(size(data)) # add Gaussian noise
## performing EMPCA
nb = 2 # number of basis vectors
μ = vec(mean(data; dims=2)) # mean observation
weights = 1 ./ σ.^2 # use inverse variance as the weights
# weights = ones(size(data)) # uniform weights replicates PCA
basis_vecs, scores = EMPCA.EMPCA(μ, nb, data, weights) # perform EMPCA on `data` .- `μ` with `nb` basis vectors using `weights` for weightingThe documentation for this package is available here.
The original python version can be found here.
The paper S. Bailey 2012, PASP, 124, 1015 describes the underlying math and is available as a pre-print at: http://arxiv.org/abs/1208.4122
If you use this code in an academic paper, please include a citation as described in CITATION.txt, and optionally an acknowledgement such as:
This work uses the Weighted EMPCA code by Stephen Bailey, available at https://github.com/sbailey/empca/