Geary's C¶
Measure global spatial autocorrelation by comparing weighted squared differences between neighboring observations with overall variance.
Core Idea¶
Geary's C is a global spatial autocorrelation statistic formed from weighted squared differences across spatially linked observations, normalized by total variance. Neighbor differences contribute to the numerator, so similar adjacent values lower C and dissimilar adjacent values raise it relative to a random-spatial-association reference near one. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
The load-bearing residual is not the broad topic of spatial statistics. It is the exact Geary normalization and neighbor-difference sensitivity, not spatial correlation generally.
Scope of Application¶
Geary's C belongs to spatial statistics and is useful where the analyst can specify values observed on spatial units plus a declared spatial weights matrix with zero diagonal, then evaluate C is computed from the declared weights and the ratio of weighted pairwise squared differences to centered global sum of squares. The scope is broad within that domain but bounded by the need for C is computed from the declared weights and the ratio of weighted pairwise squared differences to centered global sum of squares. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making C is computed from the declared weights and the ratio of weighted pairwise squared differences to centered global sum of squares the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Geary's C can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Geary's C. Geary's C compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: values observed on spatial units plus a declared spatial weights matrix with zero diagonal. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express C is computed from the declared weights and the ratio of weighted pairwise squared differences to centered global sum of squares independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of spatial statistics because they reuse values observed on spatial units plus a declared spatial weights matrix with zero diagonal, Neighbor differences contribute to the numerator, so similar adjacent values lower C and dissimilar adjacent values raise it relative to a random-spatial-association reference near one., and publish the weights matrix and normalization, check zero variance and islands, compute numerator and denominator consistently, and use an explicit randomization or asymptotic null for inference. A theorem, diagnostic, or modeling warning can travel when those roles remain literal.
Relationships to Other Abstractions¶
Current abstraction Geary's C Domain-specific
Parents (1) — more general patterns this builds on
-
Geary's C is a kind of Correlation Prime
The proposed strict upward parent is
prime:correlation.
Hierarchy path (1) — routes to 1 parentless root
- Geary's C → Correlation
Neighborhood in Abstraction Space¶
Geary's C sits in a moderately populated region (56th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Multivariate & Spatial Statistics (13 abstractions)
Nearest neighbors
- Spatial Analysis of Principal Components — 0.91
- Moran's I — 0.89
- Euclidean random matrix — 0.87
- Spatial distribution — 0.87
- Spatial heterogeneity — 0.87
Computed from structural-signature embeddings · 2026-09-08