fixed pairwise for non-symmetric kernels

.github/workflows/ci.yml

@@ -13,7 +13,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.0'
+          - '1.1'
           - '1' # automatically expands to the latest stable 1.x release of Julia
           - 'nightly'
         os:

Project.toml

@@ -14,9 +14,9 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]
-Arpack = "0.3, 0.4"
+Arpack = "0.3, 0.4, 0.5"
 StatsBase = "0.29, 0.30, 0.31, 0.32, 0.33"
-julia = "1"
+julia = "1.1"
 
 [extras]
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

src/MultivariateStats.jl

@@ -1,9 +1,9 @@
 module MultivariateStats
     using LinearAlgebra
-    using StatsBase: SimpleCovariance, CovarianceEstimator
+    using StatsBase: SimpleCovariance, CovarianceEstimator, pairwise, pairwise!
     import Statistics: mean, var, cov, covm
     import Base: length, size, show, dump
-    import StatsBase: RegressionModel, fit, predict, ConvergenceException, dof, coef, weights
+    import StatsBase: RegressionModel, fit, predict, ConvergenceException, dof, coef, weights, pairwise
     import SparseArrays
     import LinearAlgebra: eigvals
 

src/cmds.jl

@@ -95,7 +95,7 @@ function transform(M::MDS{T}, x::AbstractVector{<:Real}; distances=false) where
     end
 
     # get distance matrix
-    D = isnan(M.d) ? M.X  : pairwise((x,y)->norm(x-y), M.X)
+    D = isnan(M.d) ? M.X : pairwise((x,y)->norm(x-y), eachcol(M.X), symmetric=true)
     d = d.^2
 
     # b = 0.5*(ones(n,n)*d./n - d + D*ones(n,1)./n - ones(n,n)*D*ones(n,1)./n^2)
@@ -142,7 +142,7 @@ function fit(::Type{MDS}, X::AbstractMatrix{T};
 
     # get distance matrix and space dimension
     D, d = if !distances
-        pairwise((x,y)->norm(x-y), X), size(X,1)
+        pairwise((x,y)->norm(x-y), eachcol(X), symmetric=true), size(X,1)
     else
         X, NaN
     end
@@ -203,8 +203,8 @@ end
 
 function stress(M::MDS)
     # calculate distances if original data was stored
-    DX = isnan(M.d) ? M.X : pairwise((x,y)->norm(x-y), M.X)
-    DY = pairwise((x,y)->norm(x-y), transform(M))
+    DX = isnan(M.d) ? M.X : pairwise((x,y)->norm(x-y), eachcol(M.X), symmetric=true)
+    DY = pairwise((x,y)->norm(x-y), eachcol(transform(M)), symmetric=true)
     n = size(DX,1)
     return sqrt(2*sum((DX - DY).^2)/sum(DX.^2));
 end

src/common.jl

@@ -121,30 +121,5 @@ function calcscattermat(Z::DenseMatrix)
 end
 
 # calculate pairwise kernel
-function pairwise!(K::AbstractVecOrMat{<:Real}, kernel::Function,
-                   X::AbstractVecOrMat{<:Real}, Y::AbstractVecOrMat{<:Real})
-    n = size(X, 2)
-    m = size(Y, 2)
-    for j = 1:m
-        aj = view(Y, :, j)
-        for i in j:n
-            @inbounds K[i, j] = kernel(view(X, :, i), aj)[]
-        end
-        j <= n && for i in 1:(j - 1)
-            @inbounds K[i, j] = K[j, i]   # leveraging the symmetry
-        end
-    end
-    K
-end
-
-pairwise!(K::AbstractVecOrMat{<:Real}, kernel::Function, X::AbstractVecOrMat{<:Real}) =
-    pairwise!(K, kernel, X, X)
-
-function pairwise(kernel::Function, X::AbstractVecOrMat{<:Real}, Y::AbstractVecOrMat{<:Real})
-    n = size(X, 2)
-    m = size(Y, 2)
-    K = similar(X, n, m)
-    pairwise!(K, kernel, X, Y)
-end
-
-pairwise(kernel::Function, X::AbstractVecOrMat{<:Real}) = pairwise(kernel, X, X)
+pairwise(kernel::Function, X::AbstractMatrix, x::AbstractVector; kwargs...) =
+    [kernel(x,y) for y in eachcol(X)]

src/kpca.jl

@@ -50,7 +50,7 @@ principalvars(M::KernelPCA) = M.λ
 
 """Calculate transformation to kernel space"""
 function transform(M::KernelPCA, x::AbstractVecOrMat{<:Real})
-    k = pairwise(M.ker, M.X, x)
+    k = pairwise(M.ker, eachcol(M.X), eachcol(x))
     transform!(M.center, k)
     return projection(M)'*k
 end
@@ -63,7 +63,7 @@ function reconstruct(M::KernelPCA, y::AbstractVecOrMat{<:Real})
         throw(ArgumentError("Inverse transformation coefficients are not available, set `inverse` parameter when fitting data"))
     end
     Pᵗ = M.α' .* sqrt.(M.λ)
-    k = pairwise(M.ker, Pᵗ, y)
+    k = pairwise(M.ker, eachcol(Pᵗ), eachcol(y))
     return M.inv*k
 end
 
@@ -88,7 +88,7 @@ function fit(::Type{KernelPCA}, X::AbstractMatrix{T};
 
     # set kernel function if available
     K = if isa(kernel, Function)
-        pairwise(kernel, X)
+        pairwise(kernel, eachcol(X), symmetric=true)
     elseif kernel === nothing
         @assert issymmetric(X) "Precomputed kernel matrix must be symmetric."
         inverse = false
@@ -126,7 +126,7 @@ function fit(::Type{KernelPCA}, X::AbstractMatrix{T};
     Q = zeros(T, 0, 0)
     if inverse
         Pᵗ = α' .* sqrt.(λ)
-        KT = pairwise(kernel, Pᵗ)
+        KT = pairwise(kernel, eachcol(Pᵗ), symmetric=true)
         Q = (KT + diagm(0 => fill(β, size(KT,1)))) \ X'
     end
 

test/cmds.jl

@@ -9,7 +9,7 @@ using Test
     n = 10
     X0 = randn(d, n)
     G0 = X0'X0
-    D0 = MultivariateStats.pairwise((x,y)->norm(x-y), X0)
+    D0 = MultivariateStats.pairwise((x,y)->norm(x-y), eachcol(X0), symmetric=true)
 
     ## conversion between dmat and gram
 
@@ -35,7 +35,7 @@ using Test
 
     X = transform(M)
     @test size(X) == (3,n)
-    @test MultivariateStats.pairwise((x,y)->norm(x-y), X) ≈ D0
+    @test MultivariateStats.pairwise((x,y)->norm(x-y), eachcol(X0), symmetric=true) ≈ D0
 
     @test_throws DimensionMismatch transform(M, rand(d+1))
     y = transform(M, X0[:, 1])
@@ -49,11 +49,11 @@ using Test
 
     X = transform(M)
     @test size(X) == (3,n)
-    @test MultivariateStats.pairwise((x,y)->norm(x-y), X) ≈ D0
+    @test MultivariateStats.pairwise((x,y)->norm(x-y), eachcol(X0), symmetric=true) ≈ D0
 
     @test_throws AssertionError transform(M, X0[:, 1])
     @test_throws DimensionMismatch transform(M, rand(d+1); distances = true)
-    d = MultivariateStats.pairwise((x,y)->norm(x-y), X0, X0[:,2]) |> vec
+    d = MultivariateStats.pairwise((x,y)->norm(x-y), X0, X0[:,2]) #|> vec
     y = transform(M, d, distances=true)
     @test X[:, 2] ≈ y
 
@@ -95,18 +95,18 @@ using Test
 
     M = fit(MDS, sqrt.(D), maxoutdim=2, distances=true)
     X = transform(M)
-    @test D ≈ MultivariateStats.pairwise((x,y)->sum(abs2, x-y), X)
+    @test D ≈ MultivariateStats.pairwise((x,y)->sum(abs2, x-y), eachcol(X), symmetric=true)
     @test eltype(X) == Float32
 
     a = Float32[0.5, 0.5, 0.5, 0.5]
     A = vcat(hcat(D, a), hcat(a', zeros(Float32, 1, 1)))
     M⁺ = fit(MDS, sqrt.(A), maxoutdim=2, distances=true)
     X⁺ = transform(M⁺)
-    @test A ≈ MultivariateStats.pairwise((x,y)->sum(abs2, x-y), X⁺)
+    @test A ≈ MultivariateStats.pairwise((x,y)->sum(abs2, x-y), eachcol(X⁺), symmetric=true)
 
     y = transform(M, a, distances=true)
     Y = [X y]
-    @test A ≈ MultivariateStats.pairwise((x,y)->sum(abs2, x-y), Y)
+    @test A ≈ MultivariateStats.pairwise((x,y)->sum(abs2, x-y), eachcol(Y), symmetric=true)
     @test eltype(Y) == Float32
 
     # different input types

test/kpca.jl

@@ -34,18 +34,10 @@ import Random
     end
 
     # kernel calculations
-    K = MultivariateStats.pairwise((x,y)->norm(x-y), X, X[:,1:2])
-    @test size(K) == (n, 2)
-    @test K[1,1] == 0
-    @test K[3,2] == norm(X[:,3] - X[:,2])
-
-    K = MultivariateStats.pairwise((x,y)->norm(x-y), X[:,1:3], X)
-    @test size(K) == (3, n)
-    @test K[1,1] == 0
-    @test K[3,2] == norm(X[:,2] - X[:,3])
+    ker  = (x,y)->norm(x-y)
 
     K = similar(X, n, n)
-    MultivariateStats.pairwise!(K, (x,y)->norm(x-y), X)
+    MultivariateStats.pairwise!(ker, K, eachcol(X))
     @test size(K) == (n, n)
     @test K[1,1] == 0
     @test K[2,1] == norm(X[:,2] - X[:,1])
@@ -54,7 +46,7 @@ import Random
     Iₙ = ones(n,n)/n
     @test MultivariateStats.transform!(KC, copy(K)) ≈ K - Iₙ*K - K*Iₙ + Iₙ*K*Iₙ
 
-    K = MultivariateStats.pairwise((x,y)->norm(x-y), X, X[:,1])
+    K = MultivariateStats.pairwise(ker, X, X[:,1])[:,1:1]
     @test size(K) == (n, 1)
     @test K[1,1] == 0
     @test K[2,1] == norm(X[:,2] - X[:,1])
@@ -88,15 +80,15 @@ import Random
     M = fit(KernelPCA, X, inverse=true)
     @test all(isapprox.(reconstruct(M, transform(M)), X, atol=0.75))
 
-    # use rbf kernel
+    # use RBF kernel
     γ = 10.
     rbf=(x,y)->exp(-γ*norm(x-y)^2.0)
     M = fit(KernelPCA, X, kernel=rbf)
     @test indim(M) == d
     @test outdim(M) == d
 
     # use precomputed kernel
-    K = MultivariateStats.pairwise((x,y)->x'*y, X)
+    K = MultivariateStats.pairwise((x,y)->x'*y, eachcol(X), symmetric=true)
     @test_throws AssertionError fit(KernelPCA, rand(1,10), kernel=nothing) # symmetric kernel
     M = fit(KernelPCA, K, maxoutdim = 5, kernel=nothing, inverse=true) # use precomputed kernel
     M2 = fit(PCA, X, method=:cov, pratio=1.0)
@@ -117,7 +109,7 @@ import Random
 
     @test indim(MM) == d
     @test outdim(MM) == d
-    @test eltype(transform(MM, X[:,1])) == Float32
+    @test eltype(transform(MM, XX[:,1])) == Float32
 
     for func in (projection, principalvars)
         @test eltype(func(M)) == Float64