PCA

PCA(ncomps; options...)
PCA(;ncomps=nothing, options...)

Use principal components analysis (PCA) to form a low-rank orthonormal basis of the input. Uses deterministic singular-value decomposition (SVD) to decompose data.

If ncomps is nothing, the basis will not be truncated (i.e. ncomps is equal to the number of frames). ncomps can be set to :noise or :pratio to automatically choose the number of components using the residual frame noise or principal ratio, respectively. For more information, see the extended help.

References

1. Soummer, Pueyo, and Larkin (2012) "Detection and Characterization of Exoplanets and Disks Using Projections on Karhunen-Loève Eigenimages"

Extended help

Optimizing ncomps

There are a few ways to optimize ncomps using the input data. Additional options for the optimization are listed below

1. ncomps=:noise - residual noise optimization
2. ncomps=:pratio - principal ratio optimization

Residual noise optimization

This technique progressively increases ncomps at each step measuring the pixel-to-pixel noise (standard deviation) in the residual data. Iteration will stop when the noise is not improving beyond a threshold. This is suited for data with similar statistical characteristics, such as an annulus more so than a full-frame cube.

• collapse=false - if true, the temporal median of the residual data will be used for measuring the noise.
• noise_error=1e-3 - the threshold for the minimal noise improvement looking back 2 iterations

Principal ratio optimization

This technique chooses the number of components required to explain some ratio of the total variance in the data. This is known as the principal ratio or the explained variance ratio. The explained variance is measured by transforming the singular values of the SVD decomposition (Λ = @. S^2 / (n - 1)).

• pratio=0.9 - the target principal ratio (between 0 and 1)