Proximity mapping: Criteria

The Criteria tab specifies the algorithmic settings that control the dimensionality of the solution, the convergence behavior of the optimization process, and post-solution standardization and orientation of the resulting configuration.

Dimensionality

Sets the number of dimensions in the common space. The value must be 2 or greater and less than the number of objects - 1. Increasing the number of dimensions may improve fit, but that can reduce interpretability.

Algorithm Convergence

These settings determine when the iterative optimization stops.

Field	Description	Default value
Function Minimum	Sets the threshold for the loss function value below which the solution is accepted. If the value of the loss function drops below this minimum, iteration stops. The value must be greater than or equal to zero.	1.0 × 10-6
Function Difference	Sets the convergence criterion based on change in the loss function between iterations. If the absolute difference in function values falls below this value, the algorithm is considered to have converged. The value must be greater than or equal to zero.	1.0 × 10-12
Configuration Difference	Sets the convergence threshold for changes in the configuration between iterations. If the total movement of object positions falls below this value, the algorithm stops. The value must be greater than or equal to zero.	1.0 × 10-6
Maximum Iterations	Specifies the maximum number of iterations that the algorithm may perform. If convergence is not reached by this number, iteration stops regardless. The value must be greater than or equal to zero.	1000

Standardization

Specifies how multivariate variables (if used to derive proximities) are standardized before distance computation. The option also applies to attribute and property variables.

• By default Sum of Squares = N is selected.
• Select Sum of Squares = N−1 if you want consistency with other statistical procedures.

Dimension

Specifies how the common space configuration is oriented in the coordinate space.

Radio button	Description
None / As Is	No constraints are applied. The orientation is in principal axes orientation, where signs for dimensions are arbitrary.
Positive Correlation between Dimensions	Sets the reflection of the configuration to maximize positive correlation between dimensions and the data.
Positive Quadrant for Greatest Absolute Coordinate	Reflects dimensions to ensure that the object with the largest coordinate appears in the positive quadrant of the space.
Per Dimension	You can set reflections individually for each dimension. Select the checkbox next to a dimension to apply reflection to that specific axis.