�

​

​

​

​

Data Mining_Anoop Chaturvedi

1

Swayam Prabha

Course Title

Multivariate Data Mining- Methods and Applications

Lecture 28

Hierarchical Clustering Techniques

By

Anoop Chaturvedi

Department of Statistics, University of Allahabad

Prayagraj (India)

​

Slides can be downloaded from https://sites.google.com/view/anoopchaturvedi/swayam-prabha

Data Mining_Anoop Chaturvedi

2

Data Mining_Anoop Chaturvedi

3

Data Mining_Anoop Chaturvedi

4

Example: The following table gives the proportions of two populations of red Campion:

​

Data Mining_Anoop Chaturvedi

5

Data Mining_Anoop Chaturvedi

6

Data Mining_Anoop Chaturvedi

7

Data Mining_Anoop Chaturvedi

8

Iris Data: Cluster Dendrogram

Data Mining_Anoop Chaturvedi

9

Data Mining_Anoop Chaturvedi

10

Data Mining_Anoop Chaturvedi

11

Data Mining_Anoop Chaturvedi

12

Data Mining_Anoop Chaturvedi

13

Data Mining_Anoop Chaturvedi

14

Data Mining_Anoop Chaturvedi

15

Data Mining_Anoop Chaturvedi

16

Shortcomings of single linkage clustering

• In order to merge two groups, only need one pair of points to be close. Clusters can be too spread out. Can’t discern poorly separated clusters.
• Suffers from the Chaining Effect where clusters are extended by connecting individual points that are close to each other but may not necessarily belong to the same cluster.
• Sensitive to outliers. Even a single outlier can significantly affect the clustering results by connecting distant points into the same cluster.

Data Mining_Anoop Chaturvedi

17

• If the density of points within the cluster may vary or there may be empty spaces between clusters, it struggles with identifying clusters.
• Can lead to fragmented clusters, especially in datasets with varying densities or non-convex shapes.
• Choice of distance metric can greatly influence the clustering results.
• Does not provide a clear criterion for determining the optimal number of clusters.

​

Data Mining_Anoop Chaturvedi

18

Data Mining_Anoop Chaturvedi

19

Shortcomings of complete linkage clustering

• Avoids chaining, but suffers from crowding. Its score is based on the worst-case dissimilarity between pairs, a point can be closer to points in other clusters than to points in its own cluster. Clusters are compact, but not far enough apart.
• Tends to produce clusters of approximately equal diameter. Struggle with clusters that have significantly different sizes or densities.
• Tends to produce compact clusters, but is not suitable for detecting irregularly shaped clusters.

​

Data Mining_Anoop Chaturvedi

20

• Sensitivity to Outliers.
• It may merge clusters that are connected by a few points even if the majority of points within each cluster are far apart.
• Tends to suffer from the "cluster fusion problem," where small, well-separated clusters may be merged into larger clusters due to the presence of a few points that are relatively close to each other.
• Subjectivity in Determining Number of Clusters.

​

Data Mining_Anoop Chaturvedi

21

Data Mining_Anoop Chaturvedi

22

Shortcomings of average linkage

• Not has simple interpretations like Single and complete linkage trees.
• Sensitivity to Outliers.
• Tendency to produce Clusters of approximately equal sizes, resulting in merging of distinct clusters or the fragmentation of single clusters.
• Difficulty in handling Non-Globular Clusters, where the distance between points within a cluster is not uniform.
• Dependency on Distance Metric.
• Inability to Detect Complex Structures such as hierarchical relationships or nested clusters within larger clusters.
• Subjectivity in Determining Number of Clusters

Data Mining_Anoop Chaturvedi

23

Data Mining_Anoop Chaturvedi

24

Data Mining_Anoop Chaturvedi

25

Single linkage Average linkage Complete linkage

​

Data Mining_Anoop Chaturvedi

26