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content/research/clusteranalysis/notes/lec5.md

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+# Introduction to Connectivity Based Models
+
+Hierarchical algorithms combine observations to form clusters based on their distance.
+
+## Connectivity Methods
+
+Hierarchal Clustering techniques can be subdivided depending on the method of going about it.
+
+First there are two different methods in forming the clusters *Agglomerative* and *Divisive*
+
+<u>Agglomerative</u> is when you combine the n individuals into groups through each iteration
+
+<u>Divisive</u> is when you are separating one giant group into finer groupings with each iteration.
+
+Hierarchical methods are an irrevocable algorithm, once it joins or separates a grouping, it cannot be undone. As Kaufman and Rousseeuw (1990) colorfully comment: *"A hierarchical method suffers from the defect that it can never repair what was done in previous steps"*. 
+
+It is the job of the statistician to decide when to stop the agglomerative or decisive algorithm, since having one giant cluster containing all observations or having each observation be a cluster isn't particularly useful.
+
+At different distances, different clusters are formed and are more readily represented using a **dendrogram**. These algorithms do not provide a unique solution but rather provide an extensive hierarchy of clusters that merge or divide at different distances.
+
+## Linkage Criterion
+
+Apart from the method of forming clusters, the user also needs to decide on a linkage criterion to use. Meaning, how do you want to optimize your clusters.
+
+Do you want to group based on the nearest points in each cluster? Nearest Neighbor Clustering
+
+Or do you want to based on the farthest observations in each cluster? Farthest neighbor clustering.
+
+![http://www.multid.se/genex/onlinehelp/clustering_distances.png](http://www.multid.se/genex/onlinehelp/clustering_distances.png)
+
+## Shortcomings
+
+This method is not very robust towards outliers, which will either show up as additional clusters or even cause other clusters to merge depending on the clustering method.
+
+As we go through this section, we will go into detail about the different linkage criterion and other parameters of this model.