This chapter deals with multivariate statistical methods for data reduction and clustering, commonly used in geographical analysis, including

• Principal component analysis

• Factor analysis

• Multidimensional scaling

• Hierarchical clustering

• -means clustering

• Regionalization (SKATER, REDCAP)

• Density-based clustering (DBSACN, HDBSCAN, OPTICS)

• Similarity analysis (cosine similarity)

After a thorough study of the theory and lab sections, you will be able to

• Understand why multivariate data and statistics are essential in geographical analysis such as in geodemographics

• Understand that observations in multivariate data sets are points in a multidimensional data space

• Understand what principal components are and how they can be mapped in a GIS environment

• Map multidimensional datasets to a 2-D or 3-D representation by multidimensional scaling

• Understand why hierarchical clustering is important to identify the structure of clusters

• Use the k-means algorithm in a geographical problem

• Evaluate the importance of taking into account spatial constraints when clustering (regionalization)

• Use density-based clustering to analyze large datasets of point entities

• Apply similarity analysis to identify common characteristics (profiles) on your spatial entities

• Perform principal component analysis, multidimensional scaling and hierarchical clustering in Matlab

• Conduct k-means clustering, similarity analysis and spatial clustering in ArcGIS

• Conduct k-means clusteringand spatial clustering in GeoDa