Normalization

Overview

Normalization is the process of converting different units or scales into a common scale, often used in GIS and MCDA to enable comparison and combination of diverse criteria. Normalization ensures that variables with different ranges contribute proportionally to analysis.

Key Concepts

Min-max normalization scales values to a 0-1 range. Z-score normalization centers data around mean with standard deviation units. Benefit criteria are attributes where higher values are better. Cost criteria are attributes where lower values are better (require inversion). Linear scaling applies a linear transformation to values.

Common Methods

Method	Formula	Range
Min-Max	$(x-min)/(max-min)$	0-1
Z-Score	$(x-\mu )/\sigma$	Unbounded
Max Scaling	$x/max$	0-1
Log Transform	$\log (x)$	Varies

Applications

• Multi-criteria analysis weighting
• Machine learning feature scaling
• Index creation (composite indicators)
• Raster reclassification

Appendix

Created: 2025-12-13 | Modified: 2025-12-13

See Also

• Multi-Criteria Decision Analysis (MCDA)
• Geographic Information System (GIS)

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