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Publication date: 11/10/2021

Spatial Measures

To use the Add Spatial Measures option, your data must be stacked and contain two attribute columns that correspond to spatial coordinates. Some of the spatial measures are constructed using the Hough transform. See White et al. (2008) and Ballard (1981). See Example of Wafer Defect Classification Using Spatial Measures.

Choose Spatial Components Window

The Choose Spatial Components window appears if you do the following in the launch window:

Select the Data is stacked data structure

Specify two columns as Attribute ID that correspond to spatial coordinates

Specify an Object ID

Select Add Spatial Measures

In the Choose Spatial Components window, you select and weight spatial components for your cluster analysis. These components are used to construct the variables used in the cluster analysis. A new table with a row for each object opens. This table contains the calculated spatial components for each object.


The types of variables that are constructed and used in the cluster analysis. The variables are constructed using spatial components and the response, Y.


The value of the Y variable calculated at each location for each object, as defined by the two Attribute ID variables.

Angle, Pie

Variables that reflect wedge shapes or hemispherical shapes.

Radius, Circle

The variables that reflect circular shapes.

Streak Angle

The variables that reflect streaks that have the same angle.

Streak Position

The variables that reflect streaks with the same spatial position.

Position in Shot

The variables that are based on the position of the die in the shot. Position in Shot variables are represented as ShotPos[vShotSize, hShotSize], where vShotSize and hShotSize are the defined vertical and horizontal shot sizes.


The variables that identify which rectangle an object is in, where you specify the number of horizontal and vertical positions of objects in the rectangle. The term shot is used in semiconductor wafer data to identify which dies are imaged together across a wafer.

Enter values for Shot Horizontal Size and Shot Vertical Size. Specifying a horizontal shot size of 4 and a vertical shot size of 5 indicates that there are up to 20 dies in a shot. The total number of identifiers created is calculated as follows:

floor[(hSize+hShotSize-1)/hShotSize]* floor[(vSize+vShotSize-1)/vShotSize]

where hSize and vSize are the maximum numbers of horizontal and vertical positions, respectively, hShotSize = Shot Horizontal Size, and vShotSize = Shot Vertical Size.

Note: Shot variables are represented as Shot[vert, horiz], where vert and horiz represent the vertical and horizontal die locations, respectively.


The total number of variables of the given type that are constructed.


A measure of importance for the given type of variable used in determining the clusters.

Spatial Measures Reports

When you click OK in the Choose Spatial Components window, two windows appear.

Hierarchical Clustering Report

When you conduct an analysis with stacked data and two Attribute IDs, the Cluster Summary report shows spatial maps of the Y variable. Each plot is a two-dimensional plot that displays the cluster mean for each location defined by the Attribute ID variables. The plot uses a Blue to Gray to Red color gradient with a Quantile scale. Using the quantile scale mitigates the effect of outliers.

Spatial Data Table

The data table for Spatial measures has a row for each unique Object ID. Columns are displayed using a Blue to Gray to Red default color gradient to show the Y variable. The table contains the following columns:


An expression column that shows a heat map of the Y variable at each spatial location defined by the two Attribute ID variables.


An expression column that shows a heat map of the Hough space for each object. See White et al. (2008).

Spatial Measures

A column for each spatial measure that shows the computed values for each object. Cells are colored by value.

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