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content/research/clusteranalysis/notes/lec8.md

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+# Divisive Methods Pt 2.
+
+Recall in the previous section that we spoke about Monothetic and Polythetic methods. Monothetic methods only looks at a single variable at a time while Polythetic looks at multiple variables simultaneously. In this section, we will speak more about polythetic divisive methods.
+
+## Polythetic Divisive Methods
+
+Polythetic methods operate via a distance matrix.
+
+This procedure avoids considering all possible splits by 
+
+1. Finding the object that is furthest away from the others within a group and using that as a seed for a splinter group.
+2. Each object is then considered for entry to that separate splinter group: any that are closer to the splinter group than the main group is moved to the splinter one. 
+3. The step is then repeated.
+
+This process has been developed into a program named `DIANA` (DIvisive ANAlysis Clustering) which is implemented in `R`.
+
+### Similarities to Politics
+
+This somewhat resembles a way a political party might split due to inner conflicts.
+
+Firstly, the most discontented member leaves the party and starts a new one, and then some others follow him until a kind of equilibrium is attained.
+
+## Methods for Large Data Sets
+
+There are two common hierarchical methods used for large data sets `BIRCH` and `CURE`. Both of these algorithms employ a pre-clustering phase in where dense regions are summarized, the summaries being then clustered using a hierarchical method based on centroids.
+
+### CURE
+
+1. `CURE` starts with a random sample of points and represents clusters by a smaller number of points that capture the shape of the cluster
+2. Which are then shrunk towards the centroid as to dampen the effect of the outliers
+3. Hierarchical clustering then operates on the representative points
+
+`CURE` has been shown to be able to cope with arbitrary-shaped clusters and in that respect may be superior to `BIRCH`, although it does require judgment as to the number of clusters and also a parameter which favors either more or less compact clusters.
+
+## Revisiting Topics: Cluster Dissimilarity
+
+In order to decide where clusters should be combined (for agglomerative), or where a cluster should be split (for divisive), a measure of dissimilarity between sets of observations is required.
+
+In most methods of hierarchical clustering this is achieved by a use of an appropriate 
+
+- Metric (a measure of distance between pairs of observations)
+- Linkage Criterion (which specifies the dissimilarities of sets as functions of pairwise distances observations in the sets)
+
+## Advantages of Hierarchical Clustering
+
+- Any valid measure of distance measure can be used
+- In most cases, the observations themselves are not required, just hte matrix of distances
+  - This can have the advantage of only having to store a distance matrix in memory as opposed to a n-dimensional matrix.