Clustering Methods

Clustering

• Clustering aims to find natural groupings within data.
• Samples within a group are more similar to each other than samples from different groups.
• Expressed visually using dendrograms (tree diagrams).
• Clustering imposes structure, which may not always be present in the data.

Applications of Clustering

• Classification of species (taxonomy).
• Classification of vegetation communities.
• Classification of soil types.
• Used to classify areas for sampling.
• Less suitable for ecological communities where there are intermediate cases.

Clustering vs. Discriminant Function Analysis

• Clustering:
  • Identifies groups without predefined categories.
  • An unsupervised method, using the data to define the groups.
• Discriminant Function Analysis:
  • Predefines groups and determines the differences between them.
  • A supervised method.
  • Not covered but similar to principal components analysis with predefined groups.

Steps in Clustering Analysis

1. Generate distance or dissimilarity matrices.
2. Choose a clustering approach.

Types of Clustering Approaches

• Agglomerative vs. Divisive.
  • Agglomerative: Builds up clusters by adding samples.
  • Divisive: Starts with one big group and divides it.
• Hierarchical vs. Non-Hierarchical.
  • Hierarchical: Once a sample is in a group, it stays there.
  • Non-Hierarchical: Samples can switch groups based on an iterative measure.
• Weighted: Emphasizes certain groupings.

Hierarchical Agglomerative Cluster Analysis

• Starts with a pairwise similarity or dissimilarity matrix.
• The most similar samples join first, then builds up.
• Groups are combined until there is one large group.
• Represented in a dendrogram.

Types of Linkage in Hierarchical Clustering

• Single Linkage:
  • Uses the smallest dissimilarity.
  • Also known as the nearest neighbor method.
  • Produces cluster chains and elongated dendrograms.
• Complete Linkage:
  • Uses the largest dissimilarity.
  • Sensitive to outliers.
• Average Linkage:
  • Uses the group means.
  • Most common is the UPGMA (Unweighted Pair Group Method with Arithmetic Averages).

UPGMA (Unweighted Pair Group Method with Arithmetic Averages)

• Uses averages of different linkages.
• A step-by-step process is used for understanding.
• Weighted pair group mean methods can also be used, weighting some of the differences.
• Unweighted paired groups method uses centroids.
• Ward's minimal variance: Forms clusters by minimizing the within-cluster sum of squares; similar sized clusters.
  • Uses Euclidean distance.
  • The others can use any type.

Example of UPGMA

• Using a matrix with samples and species.
• Bay Curtis similarities are produced.
• Identify the highest similarity to form the first cluster.
• Calculate the next cluster by averaging the differences.
• Use proportional averaging to get the final clusters.

Non-Hierarchical Clustering

• Uses iterative processes and randomization.
• Samples are rearranged until the optimal cluster is achieved.
• K-means clustering is a common method, where K is the number of clusters.
• Membership is evaluated by defined criteria.
• K-means is based on metric Euclidean data.

Determining the Number of Clusters (K)

• Elbow Plot (Scree Plot):
  • Plots the weighted sum of squares.
  • Look for the elbow to determine the optimal number of clusters.
• Calinsky-Harabasz Criterion:
  • KolinskyHarabasz = \frac{BetweenClusterVariance}{WithinClusterVariance}
  • Uses the ratio of between-cluster variance to within-cluster variance.
  • Higher values mean distinct and well-separated Clusters.
  • Optimal K is the peak on the Calinsky-Harabasz plot.
• Silhouette Width:
  • Method compares how similar objects are within clusters compared to others.
• Gap Statistic:
  • Method compares the total within variation for different clusters and compares that under a different reference distribution.

Applications and Limitations of Cluster Analysis

• Useful for classifying things like soil samples, species, vegetation communities.
• Less useful for environmental scientists and ecologists due to its rigid classification.
• Ordinal methods are better for clinal data and gradients.