Add Gabor kernel using KernelProduct

Author: sharanry

src/KernelFunctions.jl

@@ -14,7 +14,7 @@ export ExponentiatedKernel
 export MaternKernel, Matern32Kernel, Matern52Kernel
 export LinearKernel, PolynomialKernel
 export RationalQuadraticKernel, GammaRationalQuadraticKernel
-export MahalanobisKernel
+export MahalanobisKernel, GaborKernel
 export KernelSum, KernelProduct
 export TransformedKernel, ScaledKernel
 

src/kernels/gabor.jl

@@ -3,18 +3,40 @@
 
 Gabor kernel with length scale ell and period p. Given by
 ```math
-    κ(x,y) =  h(x-z), h(t) = exp(-sum(t.^2./(2*ell.^2)))*cos(2*pi*sum(t./p))
+    κ(x,y) =  h(x-z), h(t) = exp(-sum(t.^2./(ell.^2)))*cos(pi*sum(t./p))
 ```
 
 """
-struct GaborKernel{T<:Real} <: BaseKernel
+struct GaborKernel{T<:Real, K<:Kernel} <: BaseKernel
     ell::T
     p::T
+    κ::K
     function GaborKernel(;ell::T=1.0, p::T=1.0) where {T<:Real}
-        new{T}(ell, p)
+        k = transform(SqExponentialKernel(), 1/ell)*transform(CosineKernel(), 1/p)
+        new{T, typeof(k)}(ell, p, k)
     end
 end
 
-kappa(κ::GaborKernel, d::T) where {T<:Real} = exp(-sum(d.^2 ./(2*κ.ell.^2)))*cospi(2*sum(d)./ κ.p)
+kappa(κ::GaborKernel, x, y) where {T<:Real} = kappa(κ.κ, x ,y)
 
-metric(::GaborKernel) = Euclidean()
+function kernelmatrix(
+    κ::GaborKernel,
+    X::AbstractMatrix;
+    obsdim::Int=defaultobs)
+    kernelmatrix(κ.κ, X; obsdim=obsdim)
+end
+
+function kernelmatrix(
+    κ::GaborKernel,
+    X::AbstractMatrix,
+    Y::AbstractMatrix;
+    obsdim::Int=defaultobs)
+    kernelmatrix(κ.κ, X, Y; obsdim=obsdim)
+end
+
+function kerneldiagmatrix(
+    κ::GaborKernel,
+    X::AbstractMatrix;
+    obsdim::Int=defaultobs) #TODO Add test
+    kerneldiagmatrix(κ.κ, X; obsdim=obsdim)
+end

test/test_kernels.jl

@@ -68,6 +68,11 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
             @test k(v1,v2) ≈ exp(dot(v1,v2))
         end
     end
+    @testset "Gabor" begin
+        k = GaborKernel(ell=2.0, p=2.0)
+        # @info kappa(k,v1,v2)
+        # @info k(v1,v2)
+    end
     @testset "Matern" begin
         @testset "MaternKernel" begin
             ν = 2.0