Hierarchical clustering methods

Distance optimizing combinatorial/agglomerative procedures

• Single link (nearest neighbor)
• Complete link (farthest neighbor)
• Average link (UPGMA)
• Single link (WPGMA)
• Centroid
• Median
• beta-Flexible
• Flexible UPGMA

Homogeneity-optimizing combinatorial/agglomerative methods

• Incremental sum of squares (Ward)
• Min. sum of squares in new clusters
• Incremental variance
• Minimum variance in new clusters
• Minimum average distance in new clusters
• Minimum increase of average distance
• lambda-Flexible

Information theory clustering

• Min. pooled entropy in new clusters
• Min. increase of pooled entropy
• Min. mutual information of vars in new clusters
• Min. increase of mutual information
• Division by pooled entropy
• Division by mutual information

Miscellaneous techniques

• Global optimization
• Ordinal clustering
• Minimum spanning trees
• Neighbor joining (unrooted, midpoint rooted, outgroup rooted)

Non-hierarchical clustering (partitioning)

k-means clustering

• Initialization from random or input partitions, random or input seed objects or from farthest points.

Multiple partitioning

Quick clustering

• About 15 coefficients used.

Global optimization

• More than 30 coefficients used.

• Initialization from random or input partitions, random or input seed objects or from farthest points.

Ordinal clustering

• Best suited to ordinal coefficients.

Fuzzy c-means clustering

• Ternary plots showing classification for three clusters.
• Best method for finding less separated clusters.

Ordination methods and their options

Principal components analysis (PCA)

• Standardized, centered, non-centered variants.
• Rohlf, Euclidean and Mahalanobis biplots.

Principal coordinates analysis (PCoA) and Nonmetric Multidimensional Scaling (NMDS)

• More than 30 coefficients employed.

Correspondence analysis (CoA)

• Symmetric weighting, variables at barycenter of objects or vice versa in joint plots.

Canonical correspondence analysis (CCoA)

• WA scores: Symmetric weighting, variables at barycenter of objects or vice versa.
• LC scores.

Canonical correlation analysis (COR)

Rendundancy analysis (RDA)

Canonical variates analysis (CVA)

• Spherized vs non-spherized scores.