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
- Finding the object that is furthest away from the others within a group and using that as a seed for a splinter group.
- 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.
- The step is then repeated.
This process has been developed into a program named
DIANA (DIvisive ANAlysis Clustering) which is implemented in
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
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.
CUREstarts with a random sample of points and represents clusters by a smaller number of points that capture the shape of the cluster
- Which are then shrunk towards the centroid as to dampen the effect of the outliers
- 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.