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Octave clustering demo part 5: hierarchical clustering

[This post is part of the Octave clustering demo series]

So, if you read this you probably have already unpacked the tgz file containing the demo and read the previous article about k-medoids clustering. If you want to check out the older Octave clustering articles, here they are: part 0 - part 1 - part 2 - part 3.

Run the hierarchicalDemo script (if launched without input parameters, it will open the "crescents.mat" data file by default). The script will plot the dataset, then it will try to perform clustering using first k-means and then an agglomerative hierarchical clustering algorithm. Run the algorithm with all the datasets available (note that you will need to modify the code to make it work with different numbers of clusters).

Questions:

1. how does k-means perform on the non-globular datasets (crescents, circles01, and circles02)? What is the reason of this performance? how does hierarchical algorithm perform instead?
2. now let us play with the "agglomerative" dataset. Information is missing so you know neither the number of clusters in advance nor the ground truth about points (i.e. which class they belong to). First of all, run the hclust function with different numbers of clusters and plot the results. Are you satisfied with them? What do you think is the reason of this "chaining" phenomenon?
3. complete the code in hclust.m so it also calculates complete and average linkage, and run the algorithm again. How do clustering results change? Plot and comment them.