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Input Transforms

Overview

Transforms are designed to change input data before passing it on to a kernel object.

It can be as standard as IdentityTransform returning the same input, or multiplying the data by a scalar with ScaleTransform or by a vector with ARDTransform. There is a more general FunctionTransform that uses a function and applies it to each input.

You can also create a pipeline of Transforms via ChainTransform, e.g.,

LowRankTransform(rand(10, 5)) ∘ ScaleTransform(2.0)

A transformation t can be applied to a single input x with t(x) and to multiple inputs xs with map(t, xs).

Kernels can be coupled with input transformations with transform. It falls back to creating a TransformedKernel but allows more optimized implementations for specific kernels and transformations.

List of Input Transforms

KernelFunctions.ScaleTransform — Type
ScaleTransform(l::Real)

Transformation that multiplies the input elementwise with l.

Examples

julia> l = rand(); t = ScaleTransform(l); X = rand(100, 10);

julia> map(t, ColVecs(X)) == ColVecs(l .* X)
true
source
KernelFunctions.ARDTransform — Type
ARDTransform(v::AbstractVector)

Transformation that multiplies the input elementwise by v.

Examples

julia> v = rand(10); t = ARDTransform(v); X = rand(10, 100);

julia> map(t, ColVecs(X)) == ColVecs(v .* X)
true
source
KernelFunctions.LinearTransform — Type
LinearTransform(A::AbstractMatrix)

Linear transformation of the input realised by the matrix A.

The second dimension of A must match the number of features of the target.

Examples

julia> A = rand(10, 5); t = LinearTransform(A); X = rand(5, 100);

julia> map(t, ColVecs(X)) == ColVecs(A * X)
true
source
KernelFunctions.FunctionTransform — Type
FunctionTransform(f)

Transformation that applies function f to the input.

Make sure that f can act on an input. For instance, if the inputs are vectors, use f(x) = sin.(x) instead of f = sin.

Examples

julia> f(x) = sum(x); t = FunctionTransform(f); X = randn(100, 10);

julia> map(t, ColVecs(X)) == ColVecs(sum(X; dims=1))
true
source
KernelFunctions.SelectTransform — Type
SelectTransform(dims)

Transformation that selects the dimensions dims of the input.

Examples

julia> dims = [1, 3, 5, 6, 7]; t = SelectTransform(dims); X = rand(100, 10);

julia> map(t, ColVecs(X)) == ColVecs(X[dims, :])
true
source
KernelFunctions.ChainTransform — Type
ChainTransform(ts::AbstractVector{<:Transform})

Transformation that applies a chain of transformations ts to the input.

The transformation first(ts) is applied first.

Examples

julia> l = rand(); A = rand(3, 4); t1 = ScaleTransform(l); t2 = LinearTransform(A);

julia> X = rand(4, 10);

julia> map(ChainTransform([t1, t2]), ColVecs(X)) == ColVecs(A * (l .* X))
true

julia> map(t2 ∘ t1, ColVecs(X)) == ColVecs(A * (l .* X))
true
source
KernelFunctions.PeriodicTransform — Type
PeriodicTransform(f)

Transformation that maps the input elementwise onto the unit circle with frequency f.

Samples from a GP with a kernel with this transformation applied to the inputs will produce samples with frequency f.

Examples

julia> f = rand(); t = PeriodicTransform(f); x = rand();

julia> t(x) == [sinpi(2 * f * x), cospi(2 * f * x)]
true
source