PCA Whitening

[wildart]

Provide a separate implementation of PCA whitening similar to Whitening, and remove duplicated code:

MultivariateStats.jl/src/whiten.jl

Lines 148 to 159 in 99ee965

	function _invsqrtm!(C::AbstractMatrix{<:Real})
	n = size(C, 1)
	size(C, 2) == n || error("C must be a square matrix.")
	E = eigen!(Symmetric(C))
	U = E.vectors
	evs = E.values
	for i = 1:n
	@inbounds evs[i] = 1.0 / sqrt(sqrt(evs[i]))
	end
	rmul!(U, Diagonal(evs))
	return U * transpose(U)
	end

Note: double sqrt application

MultivariateStats.jl/src/ica.jl

Lines 238 to 243 in 99ee965

	C = rmul!(Z * transpose(Z), 1.0 / (n - 1))
	Efac = eigen(C)
	ord = sortperm(Efac.values; rev=true)
	(v, P) = extract_kv(Efac, ord, k)
	W0 = rmul!(P, Diagonal(1 ./ sqrt.(v)))
	Z = W0'Z

MultivariateStats.jl/src/lda.jl

Lines 380 to 389 in 99ee965

	function _lda_whitening!(C::AbstractMatrix{T}, regcoef::T) where T<:Real
	n = size(C,1)
	E = eigen!(Symmetric(C))
	v = E.values
	a = regcoef * maximum(v)
	for i = 1:n
	@inbounds v[i] = 1.0 / sqrt(v[i] + a)
	end
	return rmul!(E.vectors, Diagonal(v))
	end