This is a summary of the third part of Ecological Methods (WEC31806), namely Applied Statistics. The summary shows all the lectures in the applied part and has been made extra visual in order to understand the material quickly and properly. In addition, with sufficient examples.
16. Cluster analysis
Clustering: grouping data points based on similarity
Data points within a cluster are similar to each other, and dissimilar do data points in other clusters
→ useful to find groups that are assumed to exist in reality (e.g. vegetation type, animal behaviour)
Clustering = partitioning (same term)
- Clustering is not about revealing gradients
→ ordination is about revealing gradients
→ clustering is about detecting discrete groups with small differences between members
- Clustering is not the same as classification
→ classification is about creating groups based on known labels
Similarity and dissimilarity are essential components of clustering analysis
Distance between pairs of:
→ points
→ cluster of points
Types of clustering:
- Flat clustering (K-means clustering): creates a flat set of clusters without any structure
- Hierarchical clustering: creates a hierarchy of clusters (thus within internal structure)
Flat clustering (K-means)
K-means: the simplest clustering algorithm, where we must define a target number K, which refers to
the number of means (centers) we want our dataset to partition around.
→ Each observation is assigned to the cluster with the nearest mean
→ Only deals with difference between clusters and not within clusters
Steps:
1. Randomly locates initial cluster centers
2. Assign records to nearest cluster mean
3. Compute new cluster means
4. Repeats 2 & 3 a few iterations
→ new data points can be assigned to the cluster
with the nearest center
→ disadvantage: number of clusters is assigned by
eye
Learning algorithm: algorithm that learns; tries a
few times and then knows a definite outcome.
→ does not necessarily result in exactly the same outcome when the analyses is repeated
,Hierarchical clustering
Hierarchical clustering does not require us to pre-
specify the number of clusters to be generated,
and results in a dendrogram
Dendrogram: tree-like diagram that records the
sequences of merges or splits
Root node: upper node where all samples belong to
Leaf (terminal node): cluster with only one sample
→ similarity of two observations is bases on the height where branches containing those two
observations first are fused
→ we cannot use the proximity of two observations along the horizontal axis for similarity
Types of hierarchical clustering:
- Agglomerative clustering (merges): builds nested clusters by merging smaller cluster with a
bottom-up approach
- Divisive clustering (splits): builds nested cluster by merging smaller clusters with a top-down
approach
Disadvantage: when a new datapoint is
added, the entire dendrogram needs to
be recalculated
,Similarity and dissimilarity
Distance between pairs
Euclidean How the crow flies
Manhattan How the taxi drives
→ distance along the axis
Jaccard Intersection/union: relative similarity
→ for binary data
Jaccard distance:
0.67 → 4 out of 6 species differ between the sites
, If variables differ in measure (e.g. temperature and weight), scale the columns to mean = 0, sd = 1
→ same scal
Linkage: how we quantify the dissimilarity between clusters:
- Single: minimum distance between clusters
- Often leading to clusters with different size
- Shape of clusters can become elongated
- Complete: maximum distance between clusters
- Size of clusters become more compact
- Average: average between clusters - Handles outliers and noise well
- Ward: minimum variance method - Lead to more uniformly sized clusters
- More difficult to compute, thus slower for
large datasets
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