1. Comparison of main classical clustering algorithms

1. Inside R environment, place yourself into your local copy of the "examples" directory:
• setwd("examples")
  
  
  
2. Load into R the 5 data files Atom, Lsun, WingNut, Chainlink, TwoDiamonds (visualized above):
• tmp = read.table("xxx.lrn", comment.char = "%")  # where xxx must successivement be set as: Atom Lsun WingNut Chainlink et TwoDiamonds 
• true_data_xxx =tmp[,-1]


3. Experiment the K-means algorithm on these 5 different datasets:
   • km_xxx = kmeans(true_data_xxx,K)  # where K is the desired number of clusters (to be manually chosen by you !) into which data shall be partuitionned
   • plot(true_data_xxx,col=km_xxx$cluster)
   QUESTION 1: Does the K-means algo always produce the expected result?
   By analyzing and comparing the SHAPES of clusters in the datasets on which K-measn works best and worse, try to understand for which type of point distribution K-means is NOT well-suited. You can confirm this by relaunching K-means with increasing values for K on datasets over which it produces bad results, and checking the shapes of produced clusters.
   QUESTION 2: What is the only shape of cluster that K-means is capable of isolating?
   
   
4. Now, experiment with the Hierarchical Agglomerative Clustering (HAC) methods (hclust function):
   dist2_xxx=dist(true_data_xxx)
   hs_xxx=hclust(dist2_xxx,method="single")
   plot(hs_xxx) # For visualizing the DENDROGRAM
   labS_xxx=cutree(hs_xxx,K) # K = number of desired clusters, which shall determine the height at which the dendrogram will be cut
   plot(true_data_xxx,col=labS_xxx)
   
   hc_xxx=hclust(dist2_xxx,method="complete")
   plot(hc_xxx) # To visualize the DENDROGRAM 
   labC_xxx=cutree(hc_xxx,K) # K = number of desired clusters, which shall determine the height at which the dendrogram will be cut
   plot(true_data_xxx,col=labC_xxx)
   
   
   QUESTION 3: On which dataset does "single-linkage" HAC produce an excellent result? Why is it logical?
   QUESTION 4: Conversely, on which dataset does "single-linkage" HAC perform very badly, and why is it expected?
   QUESTION 5: By comparing with what you had observed for K-means, which variant of HAC (between single-linkage and complete-linkage) seems to be the most complementary to K-means?
   
   
5. Finally, experiment spectral clustering (specc function, accessible after having executed the "library(kernlab)" command in R):
   
   • library(kernlab)
   • sc_xxx_K = specc(true_data_xxx, centers=K)     # where K is the desired number of clusters
   • plot(true_data_xxx, col=sc_xxx_K)
   • help(specc)     # To get complete help on all possible parameters of the function
     
   
   
6. Optionnally, you can also experiment the above clustering methods on other datasets included in the "examples" directory.