Merge pull request #54 from sharanry/maha

Add Mahalanobis distance-based kernel

Author: theogf

src/KernelFunctions.jl

@@ -14,6 +14,7 @@ export ExponentiatedKernel
 export MaternKernel, Matern32Kernel, Matern52Kernel
 export LinearKernel, PolynomialKernel
 export RationalQuadraticKernel, GammaRationalQuadraticKernel
+export MahalanobisKernel
 export KernelSum, KernelProduct
 export TransformedKernel, ScaledKernel
 
@@ -44,7 +45,7 @@ include("distances/dotproduct.jl")
 include("distances/delta.jl")
 include("transform/transform.jl")
 
-for k in ["exponential","matern","polynomial","constant","rationalquad","exponentiated","cosine"]
+for k in ["exponential","matern","polynomial","constant","rationalquad","exponentiated","cosine","maha"]
     include(joinpath("kernels",k*".jl"))
 end
 include("kernels/transformedkernel.jl")

src/kernels/maha.jl

@@ -0,0 +1,21 @@
+"""
+    MahalanobisKernel(P::AbstractMatrix)
+
+    Mahalanobis distance-based kernel given by
+```math
+    κ(x,y) =  exp(-r^2), r^2 = maha(x,P,y) = (x-y)'*inv(P)*(x-y)
+```
+where the matrix P is the metric.
+
+"""
+struct MahalanobisKernel{T<:Real, A<:AbstractMatrix{T}} <: BaseKernel
+    P::A
+    function MahalanobisKernel(P::AbstractMatrix{T}) where {T<:Real}
+        LinearAlgebra.checksquare(P)
+        new{T,typeof(P)}(P)
+    end
+end
+
+kappa(κ::MahalanobisKernel, d::T) where {T<:Real} = exp(-d) 
+
+metric(κ::MahalanobisKernel) = SqMahalanobis(κ.P)

src/trainable.jl

@@ -16,6 +16,8 @@ trainable(k::PolynomialKernel) = (k.d, k.c)
 
 trainable(k::RationalQuadraticKernel) = (k.α,)
 
+trainable(k::MahalanobisKernel) = (k.P,)
+
 #### Composite kernels
 
 trainable(κ::KernelProduct) = κ.kernels

test/test_kernels.jl

@@ -113,6 +113,13 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
             @test kappa(PolynomialKernel(d=1.0,c=c),x) ≈ kappa(LinearKernel(c=c),x)
         end
     end
+    @testset "Mahalanobis" begin
+        P = rand(3,3)
+        k = MahalanobisKernel(P)
+        @test kappa(k,x) == exp(-x)
+        @test k(v1,v2) ≈ exp(-sqmahalanobis(v1,v2, k.P))
+        @test kappa(ExponentialKernel(),x) == kappa(k,x)
+    end
     @testset "RationalQuadratic" begin
         @testset "RationalQuadraticKernel" begin
             α = 2.0