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make nystrom work with AbstractVector (#427)
* make nystrom work with AbstractVector * add test * Update test/approximations/nystrom.jl Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> * patch bump * Update test/approximations/nystrom.jl Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> * Apply suggestions from code review Co-authored-by: David Widmann <[email protected]> * Apply suggestions from code review * deprecate * Apply suggestions from code review Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> * Apply suggestions from code review Co-authored-by: David Widmann <[email protected]> * Apply suggestions from code review Co-authored-by: Théo Galy-Fajou <[email protected]> * Update src/approximations/nystrom.jl Co-authored-by: Théo Galy-Fajou <[email protected]> * Update src/approximations/nystrom.jl Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> Co-authored-by: David Widmann <[email protected]> Co-authored-by: Théo Galy-Fajou <[email protected]>
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‎Project.toml

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,6 +1,6 @@
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name = "KernelFunctions"
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uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
3-
version = "0.10.27"
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version = "0.10.28"
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[deps]
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ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

‎src/approximations/nystrom.jl

Lines changed: 35 additions & 21 deletions
Original file line numberDiff line numberDiff line change
@@ -1,25 +1,29 @@
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# Following the algorithm by William and Seeger, 2001
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# Cs is equivalent to X_mm and C to X_mn
33

4-
function sampleindex(X::AbstractMatrix, r::Real; obsdim::Integer=defaultobs)
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function sampleindex(X::AbstractVector, r::Real)
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0 < r <= 1 || throw(ArgumentError("Sample rate `r` must be in range (0,1]"))
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n = size(X, obsdim)
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n = length(X)
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m = ceil(Int, n * r)
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S = StatsBase.sample(1:n, m; replace=false, ordered=true)
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return S
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end
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function nystrom_sample(
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k::Kernel, X::AbstractMatrix, S::Vector{<:Integer}; obsdim::Integer=defaultobs
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)
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obsdim ∈ [1, 2] ||
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throw(ArgumentError("`obsdim` should be 1 or 2 (see docs of kernelmatrix))"))
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Xₘ = obsdim == 1 ? X[S, :] : X[:, S]
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C = kernelmatrix(k, Xₘ, X; obsdim=obsdim)
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@deprecate sampleindex(X::AbstractMatrix, r::Real; obsdim::Integer=defaultobs) sampleindex(
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vec_of_vecs(X; obsdim=obsdim), r
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) false
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function nystrom_sample(k::Kernel, X::AbstractVector, S::AbstractVector{<:Integer})
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Xₘ = @view X[S]
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C = kernelmatrix(k, Xₘ, X)
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Cs = C[:, S]
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return (C, Cs)
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end
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23+
@deprecate nystrom_sample(
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k::Kernel, X::AbstractMatrix, S::Vector{<:Integer}; obsdim::Integer=defaultobs
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) nystrom_sample(k, vec_of_vecs(X; obsdim=obsdim), S) false
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function nystrom_pinv!(Cs::Matrix{T}, tol::T=eps(T) * size(Cs, 1)) where {T<:Real}
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# Compute eigendecomposition of sampled component of K
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QΛQᵀ = LinearAlgebra.eigen!(LinearAlgebra.Symmetric(Cs))
@@ -63,38 +67,48 @@ function NystromFact(W::Matrix{<:Real}, C::Matrix{<:Real})
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end
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@doc raw"""
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nystrom(k::Kernel, X::Matrix, S::Vector; obsdim::Int=defaultobs)
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nystrom(k::Kernel, X::AbstractVector, S::AbstractVector{<:Integer})
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Computes a factorization of Nystrom approximation of the square kernel matrix of data
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matrix `X` with respect to kernel `k`. Returns a `NystromFact` struct which stores a
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Nystrom factorization satisfying:
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Compute a factorization of a Nystrom approximation of the square kernel matrix
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of data vector `X` with respect to kernel `k`, using indices `S`.
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Returns a `NystromFact` struct which stores a Nystrom factorization satisfying:
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```math
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\mathbf{K} \approx \mathbf{C}^{\intercal}\mathbf{W}\mathbf{C}
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```
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"""
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function nystrom(k::Kernel, X::AbstractMatrix, S::Vector{<:Integer}; obsdim::Int=defaultobs)
76-
C, Cs = nystrom_sample(k, X, S; obsdim=obsdim)
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function nystrom(k::Kernel, X::AbstractVector, S::AbstractVector{<:Integer})
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C, Cs = nystrom_sample(k, X, S)
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W = nystrom_pinv!(Cs)
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return NystromFact(W, C)
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end
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@doc raw"""
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nystrom(k::Kernel, X::Matrix, r::Real; obsdim::Int=defaultobs)
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nystrom(k::Kernel, X::AbstractVector, r::Real)
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Computes a factorization of Nystrom approximation of the square kernel matrix of data
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matrix `X` with respect to kernel `k` using a sample ratio of `r`.
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Compute a factorization of a Nystrom approximation of the square kernel matrix
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of data vector `X` with respect to kernel `k` using a sample ratio of `r`.
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Returns a `NystromFact` struct which stores a Nystrom factorization satisfying:
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```math
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\mathbf{K} \approx \mathbf{C}^{\intercal}\mathbf{W}\mathbf{C}
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```
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"""
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function nystrom(k::Kernel, X::AbstractVector, r::Real)
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S = sampleindex(X, r)
97+
return nystrom(k, X, S)
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end
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100+
function nystrom(
101+
k::Kernel, X::AbstractMatrix, S::AbstractVector{<:Integer}; obsdim::Int=defaultobs
102+
)
103+
return nystrom(k, vec_of_vecs(X; obsdim=obsdim), S)
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end
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91106
function nystrom(k::Kernel, X::AbstractMatrix, r::Real; obsdim::Int=defaultobs)
92-
S = sampleindex(X, r; obsdim=obsdim)
93-
return nystrom(k, X, S; obsdim=obsdim)
107+
return nystrom(k, vec_of_vecs(X; obsdim=obsdim), r)
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end
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"""
97-
nystrom(CᵀWC::NystromFact)
111+
kernelmatrix(CᵀWC::NystromFact)
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Compute the approximate kernel matrix based on the Nystrom factorization.
100114
"""

‎test/approximations/nystrom.jl

Lines changed: 8 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -2,10 +2,16 @@
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dims = [10, 5]
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X = rand(dims...)
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k = SqExponentialKernel()
5+
for obsdim in [1, 2]
6+
Xv = vec_of_vecs(X; obsdim=obsdim)
7+
@assert Xv isa Union{ColVecs,RowVecs}
8+
@test kernelmatrix(k, Xv) ≈ kernelmatrix(nystrom(k, Xv, 1.0))
9+
@test kernelmatrix(k, Xv) ≈ kernelmatrix(nystrom(k, Xv, collect(1:dims[obsdim])))
10+
end
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for obsdim in [1, 2]
612
@test kernelmatrix(k, X; obsdim=obsdim) ≈
7-
kernelmatrix(nystrom(k, X, 1.0; obsdim=obsdim))
13+
kernelmatrix(nystrom(k, X, 1.0; obsdim=obsdim))
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@test kernelmatrix(k, X; obsdim=obsdim) ≈
9-
kernelmatrix(nystrom(k, X, collect(1:dims[obsdim]); obsdim=obsdim))
15+
kernelmatrix(nystrom(k, X, collect(1:dims[obsdim]); obsdim=obsdim))
1016
end
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end

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