Thresholding-based subspace clustering (TSC)

tsc(X::AbstractMatrix{<:Real}, K::Integer;
    max_nz = max(4, cld(size(X, 2), max(1, K))),
    max_chunksize = 1000,
    rng = default_rng(),
    kmeans_nruns = 10,
    kmeans_opts = (;))

Cluster the N data points in the D×N data matrix X into K clusters via the Thresholding-based Subspace Clustering (TSC) algorithm with affinity matrix formed using at most max_nz neighbors. Output is a TSCResult containing the resulting cluster assignments with the internally computed affinity matrix, embedding matrix, and K-means runs.

TSC seeks to cluster data points by treating them as nodes of a weighted graph with weights given by a thresholded affinity matrix formed by thresholding the (transformed) absolute cosine similarities between every pair of points at max_nz neighbors then symmetrizing. Cluster assignments are then obtained via normalized spectral clustering of the graph.

Keyword arguments

• max_nz::Integer = max(4, cld(size(X, 2), max(1, K))): maximum number of neighbors
• max_chunksize::Integer = 1000: chunk size used in tsc_affinity
• rng::AbstractRNG = default_rng(): random number generator used by K-means
• kmeans_nruns::Integer = 10: number of K-means runs to perform
• kmeans_opts = (;): additional options for kmeans

See also TSCResult, tsc_affinity, tsc_embedding.

" TSCResult{ TA<:AbstractMatrix{<:Real}, TE<:AbstractMatrix{<:Real}, TK<:KmeansResult, Tc<:AbstractVector{<:Integer}}

The output of tsc.

Fields

• affinity::TA : N×N TSC affinity matrix
• embedding::TE : K×N TSC embedding matrix
• kmeans_runs::Vector{TK} : vector of outputs from batched K-means
• assignments::Tc : vector of final assignments