Skip to content
GPU Spatial Primitives

Getis-Ord hotspots

The Getis-Ord Gi* statistic — a Local Indicator of Spatial Association (LISA). For each cell it asks whether the neighbourhood sum is significantly higher or lower than a random shuffle would give.

What it means

Section titled “What it means”

A z-score per cell:

  • large positive → a hot spot (a cluster of high values)
  • large negative → a cold spot
  • near zero → unremarkable

|z| > 1.96 is significant at p < 0.05. Directly readable as a map.

GPU approach

Section titled “GPU approach”

A composition and a render-then-compute example:

  1. the windowed neighbourhood sum is a separable box convolution (GPU);
  2. the global mean/variance and the closed-form standardisation are cheap CPU.

pointHotspotsGpu chains it onto the KDE splat, so a raw point cloud becomes a hotspot map in one call.

Usage

Section titled “Usage”
import { getisOrdGpu, pointHotspotsGpu } from 'intraspatial/gpu/spatial/getisOrd';


// on an existing grid
const { z } = await getisOrdGpu(grid, w, h, { radius: 2 });


// or straight from points:  points → splat → window → z
const hot = await pointHotspotsGpu(xs, ys, { width: 64, height: 64, sigma: 3, radius: 2 });

A box window gives the classic binary-weights Gi*; a Gaussian window gives a softer, “fuzzier” LISA — the windowing idea again.

Status: ✅ implemented and validated (CPU golden + hot/cold + end-to-end) · src/gpu/spatial/getisOrd.ts