K-affine-spaces (KAS)

kas(X::AbstractMatrix{<:Number}, d::AbstractVector{<:Integer};
    maxiters = 100,
    rng = default_rng(),
    init = [(randsubspace(rng, float(eltype(X)), size(X, 1), di), zeros(float(eltype(X)), size(X, 1))) for di in d],
    showprogress = false)

Cluster the N data points in the D×N data matrix X into K clusters via the K-affine-spaces (KAS) algorithm with corresponding affine space dimensions d[1],...,d[K]. Output is a KASResult containing the resulting cluster assignments c[1],...,c[N], affine space basis matrices U[1],...,U[K], bias vectors b[1],...,b[K], and metadata about the algorithm run.

KAS seeks to cluster data points by their affine space by minimizing the following total cost

\[\sum_{i=1}^N \| X[:, i] - (U[c[i]] U[c[i]]' (X[:, i] - b[c[i]]) + b[c[i]]) \|_2^2\]

with respect to the cluster assignments c[1],...,c[N], affine space basis matrices U[1],...,U[K], and bias vectors b[1],...,b[K].

Keyword arguments

• maxiters::Integer = 100: maximum number of iterations
• rng::AbstractRNG = default_rng(): random number generator (used when reinitializing the affine space for an empty cluster)
• init::AbstractVector{<:Tuple{<:AbstractMatrix{TUb},<:AbstractVector{TUb}}} = [(randsubspace(rng, float(eltype(X)), size(X, 1), di), zeros(float(eltype(X)), size(X, 1))) for di in d]: vector of K initial pair of affine space basis matrices containing U[1],...,U[K] and bias vectors containing b[1],...,b[K] where TUb is a floating point type.
• showprogress::Bool = false: whether to log progress during the algorithm run

See also KASResult.

KASResult{
    TUb<:Union{AbstractFloat,Complex{<:AbstractFloat}},
    TU<:AbstractVector{<:AbstractMatrix{TUb}},
    Tb<:AbstractVector{<:AbstractVector{TUb}},
    Tc<:AbstractVector{<:Integer},
    T<:Real}

The output of kas.

Fields

• U::TU: vector of affine space basis matrices U[1],...,U[K]
• b::Tb: vector of bias vectors b[1],...,b[K]
• c::Tc: vector of cluster assignments c[1],...,c[N]
• iterations::Int: number of iterations performed
• totalcost::T: final value of total cost function
• counts::Vector{Int}: vector of cluster sizes counts[1],...,counts[K]
• converged::Bool: final convergence status