How Cluster and Outlier Analysis (Anselin Local Moran's I) works

Given a set of weighted features, the Cluster and Outlier Analysis tool identifies spatial clusters of features with attribute values similar in magnitude. The tool also identifies spatial outliers. To do this, the tool calculates a local Moran's I value, a z-score, a p-value, and a code representing the cluster type for each feature. The z-scores and p-values represent the statistical significance of the computed index values.


Local Moran's I mathematics

View additional mathematics for the local Moran's I statistic.


A positive value for I indicates that a feature has neighboring features with similarly high or low attribute values; this feature is part of a cluster. A negative value for I indicates that a feature has neighboring features with dissimilar values; this feature is an outlier. In either instance, the p-value for the feature must be small enough for the cluster or outlier to be considered statistically significant. For more information on determining statistical significance, see What is a z-score? What is a p-value? Note that the local Moran's I index (I) is a relative measure and can only be interpreted within the context of its computed z-score or p-value.

The output field, cluster/outlier type (COType), distinguishes between a statistically significant (0.05 level) cluster of high values (HH), cluster of low values (LL), outlier in which a high value is surrounded primarily by low values (HL), and outlier in which a low value is surrounded primarily by high values (LH).


This tool creates a new output feature class with the following attributes for each feature in the input feature class: local Moran's I index, z-score, p-value, and COType. The field names of these attributes are also returned as derived tool string outputs for potential use in custom models or scripts.

When this tool runs in ArcMap, the output feature class is automatically added to the table of contents (TOC) with default rendering applied to the COType field. The rendering applied is defined by a layer file in <ArcGIS>/ArcToolbox/Templates/Layers. You can reapply the default rendering, if needed, by importing the template layer symbology.

Best practice guidelines

Potential applications

The Cluster and Outlier Analysis (Anselin Local Moran's I) tool identifies concentrations of high values, concentrations of low values, and spatial outliers. It can help you answer questions such as these:

Applications can be found in many fields including economics, resource management, biogeography, political geography, and demographics.

Additional resources

Anselin, Luc. "Local Indicators of Spatial Association—LISA," Geographical Analysis 27(2): 93–115, 1995.

Mitchell, Andy. The ESRI Guide to GIS Analysis, Volume 2. ESRI Press, 2005.