Multivariate & Spatial Statistics

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Abstractions about matrix-valued distributions, multivariate dependence, random matrices, correlation, spatial association, dimension reduction, and whitening.

13 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Cokurtosis — Measure fourth-order joint variation by taking standardized expectations of products containing four centered random-variable factors, retaining how extreme deviations co-occur beyond covariance and coskewness.
• Euclidean random matrix — A random matrix whose entries are deterministic functions of randomly placed points in Euclidean space, coupling matrix statistics to spatial geometry.
• Functional correlation — A family of dependence measures for paired random functions that reduces infinite-dimensional covariance structure to interpretable associations between curves or functional components.
• Geary's C — Measure global spatial autocorrelation by comparing weighted squared differences between neighboring observations with overall variance.
• Matrix t-distribution — A heavy-tailed probability distribution for random matrices that generalizes the multivariate t distribution with separate row and column scale structure.
• Matrix variate Dirichlet distribution — A probability law on several positive-definite matrices whose sum remains below the identity, generalizing scalar Dirichlet and matrix beta distributions.
• Multivariate t-distribution — An elliptically contoured heavy-tailed distribution for random vectors, parameterized by location, positive-definite scale matrix and degrees of freedom.
• Orthogonal Procrustes problem — A least-squares alignment problem seeking the orthogonal transformation that best maps one matrix configuration to another.
• Random indexing — An incremental dimensionality-reduction method that assigns sparse random index vectors to items and accumulates their contextual vectors, approximating high-dimensional distributional geometry in fixed space.
• Regularized canonical correlation analysis — A canonical-correlation method that stabilizes singular or ill-conditioned covariance estimates by adding penalties, commonly ridge terms, before solving for paired linear variates.
• Spatial Analysis of Principal Components — A multivariate ordination method that finds genetic or ecological components maximizing variance while weighting either positive or negative spatial autocorrelation.
• Whitening transformation — A linear transformation that maps a centered random vector with nonsingular covariance to variables having identity covariance.
• Wigner semicircle distribution — A compactly supported probability distribution whose density is proportional to a semicircle and which governs limiting eigenvalue spectra of many random symmetric matrices.