Additional show info for PCA (#90)

* Additional `show` info for PCA

Co-authored-by: Zachary Christensen <zchristensen@nsc-foxemacpro.urmc-sh.rochester.edu>
Co-authored-by: Milan Bouchet-Valat <nalimilan@club.fr>
Co-authored-by: Art <wildart@users.noreply.github.com>

Author: 4 people

src/MultivariateStats.jl

@@ -5,7 +5,7 @@ module MultivariateStats
     import Statistics: mean, var, cov, covm, cor
     import Base: length, size, show, dump
     import StatsBase: fit, predict, predict!, ConvergenceException, coef, weights,
-                      dof, pairwise, r2
+                      dof, pairwise, r2, CoefTable
     import SparseArrays
     import LinearAlgebra: eigvals, eigvecs
 

src/pca.jl

@@ -135,12 +135,36 @@ gives the principal components for an observation, and \$\\mathbf{P}\$ is the pr
 reconstruct(M::PCA, y::AbstractVecOrMat{T}) where {T<:Real} = decentralize(M.proj * y, M.mean)
 
 ## show & dump
-
 function show(io::IO, M::PCA)
     idim, odim = size(M)
     print(io, "PCA(indim = $idim, outdim = $odim, principalratio = $(r2(M)))")
 end
 
+function show(io::IO, ::MIME"text/plain", M::PCA)
+    idim, odim = size(M)
+    print(io, "PCA(indim = $idim, outdim = $odim, principalratio = $(r2(M)))")
+    ldgs = loadings(M)
+    rot = diag(ldgs' * ldgs)
+    ldgs = ldgs[:, sortperm(rot, rev=true)]
+    ldgs_signs = sign.(sum(ldgs, dims=1))
+    replace!(ldgs_signs, 0=>1)
+    ldgs = ldgs * diagm(0 => ldgs_signs[:])
+    print(io, "\n\nPattern matrix (unstandardized loadings):\n")
+    cft = CoefTable(ldgs, string.("PC", 1:odim), string.("", 1:idim))
+    print(io, cft)
+    print(io, "\n\n")
+    print(io, "Importance of components:\n")
+    λ = eigvals(M)
+    prp = λ ./ var(M)
+    prpv = λ ./ sum(λ)
+    names = ["SS Loadings (Eigenvalues)",
+             "Variance explained", "Cumulative variance",
+             "Proportion explained", "Cumulative proportion"]
+    cft = CoefTable(vcat(λ', prp', cumsum(prp)',  prpv', cumsum(prpv)'),
+                    string.("PC", 1:odim), names)
+    print(io, cft)
+end
+
 #### PCA Training
 
 ## auxiliary