Local cluster analysis

Local Cluster Analysis compares each area’s value with its neighbors’ and reports where high values sit among high values, low among low, or one value stands out against its surroundings. This article runs it on diagnosed diabetes (% of adults) for the 3,109 US counties in the Diabetes and poverty sample. Every step below was run on Vesta Online, and the screenshots come from that run. For a shorter first run with the defaults, see the Quickstart.

The seven steps

1. 1Open a project that holds your dataOpen the Projects page, select a project and choose Open Project. This walk-through uses a copy of the Diabetes and poverty sample, whose US counties dataset has 3,109 counties. It tests one variable at a time.
2. 2Choose Local Cluster AnalysisChoose Analyze in the left rail, then Find clusters & hotspots, then Local Cluster Analysis, and choose Pick a method. The analysis has six steps: Analysis, Variables, Spatial weights, Significance, Run and Summary.
3. 3Pick the variableOn Variables choose the dataset, US counties, and the variable, Diagnosed diabetes (% of adults). Objects with a missing value are left out of the analysis, not treated as zero. Choose Next: Spatial weights.
4. 4Set the neighborsThe step asks what counts as a neighbor. Leave the definition on Detect: a grid uses its cells, point data uses nearest neighbors, polygons use shared boundaries. For counties it reports Shared boundary adjacency. The Guidance switch at the top right sets how much the step shows; Full control also shows Neighbors per object (1 to 50, used by k nearest weights and by point data; a value outside the range is set to the nearest end and a note says so, for example "51 is outside the allowed range (1 to 50); using 50."), Distance band (map units; it applies only to Distance band weights and is ignored with any other neighbor definition), Use rook contiguity (queen is the default) and Row-standardize the weights (on by default). Choose Next: Significance.
5. 5Set the significanceAlpha is the cutoff for calling an object a cluster or outlier; the default is 0.05. Randomizations are the permutations behind each pseudo-p value: the default is 100, the minimum is 99 and the maximum is 9,999. This walk-through uses 199. At Full control you can also choose a multiple-testing correction, None, False discovery rate (Benjamini-Hochberg) or Bonferroni, and a seed. Leave the seed blank for a new one on every run, or set it (here 12345) so the run can be repeated. This walk-through uses False discovery rate. Choose Run analysis when you are ready.
6. 6Run the analysisThe run happens on the server: a short run runs directly on the server; a longer one is queued for a compute worker. If you start a second run while another of yours is going, the step says Another analysis of yours is still running. The Summary then lists what was saved and what to check.
7. 7Open the result workspaceChoose Open in workspace. The result workspace has a cluster map, a category histogram, a Moran scatterplot and the written summary. The map shows Loading map features while it draws.

What you should see

The method

Analysis

Find clusters & hotspots lists Local Cluster Analysis first.

The variable

Variables

One dataset and one variable. The side card lists what the run will create.

The neighbors

Spatial weights

At Full control the step shows every option. Detect read the county polygons as shared-boundary adjacency.

The significance

Significance

The card on the right repeats the settings, including the finest p the permutations can resolve.

The summary

Summary

The run saved a report, a written summary and five variables, and counted the clusters.

The run adds five variables to the dataset: a standardized value, the local cluster statistic, its pseudo-p value, the cluster class and the spatially lagged standardized value. The cluster class is the one to map. The Summary also carries a warning from this run: 4 objects have no neighbors under queen contiguity and were not classified.

The result

Result workspace

Cluster Class on the map, with its histogram and a Moran scatterplot.

Reading the result

In this run, with False discovery rate and alpha 0.05, 784 of the 3,109 counties are in a cluster or an outlier: 363 High-High, 383 Low-Low, 14 High-Low and 24 Low-High. Another 2,321 are Not Significant, and 4 counties are islands (Dukes, Nantucket, Richmond and San Juan) that share no boundary with another county, so under shared-boundary weights they have no neighbors and are not tested. This run gives them the class No neighbors, not Missing. The 784, the 2,321 and these 4 account for all 3,109. Global Moran’s I is 0.6248 (p < 0.001), so similar values are grouped across the whole map; the local clusters show where that grouping is strongest. The classes mean this:

Class	Meaning
High-High	A high value among neighbors that are also high: a hot spot.
Low-Low	A low value among neighbors that are also low: a cold spot.
High-Low	A high value among lower neighbors: an outlier.
Low-High	A low value among higher neighbors: an outlier.
Not Significant	No clear local pattern at the alpha you chose.
No neighbors	A county with a value but no neighbors under the weights you chose, such as an island. It is not tested and not classified.

The first two are clusters; the middle two are outliers.

NoteThe analysis shows where these groups are, not why they are there. A cluster of high diabetes prevalence does not say what drives it; to explore that, try a model such as regression.

Watch outOne test is run per county, so with no correction roughly alpha times n counties look significant by chance alone. At alpha 0.05 on 3,109 counties that is about 155, and no correction is the default. False discovery rate controls the share of false positives among the counties reported; Bonferroni is stricter and reports far fewer. Say which you used when you report the map.

NoteThis walk-through used county polygons, shared-boundary neighbors and False discovery rate. Point data, Grid cells and Bonferroni were not run for it, so the screenshots do not show them.

NoteThe p-values come from random permutations, so two runs of the same configuration give slightly different pseudo-p values, and counties near the significance level can change class between runs. Set a seed when a run has to be repeatable. Two runs with different neighbor definitions can also disagree about where the clusters are, so report the definition you used.

Where next

• Your first run, with the defaults: Quickstart.
• Model what drives the pattern: Regression and GWR.
• Bring in your own data: Importing data.

Not sure which method fits your question? When the Advisor is turned on, you can describe your question on the Analysis step and let the Advisor suggest one. The Advisor is an optional AI-assisted guided workflow; see Using the Advisor.