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51 lines
2.8 KiB
Markdown
51 lines
2.8 KiB
Markdown
---
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title: Divisive Methods Pt 2.
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showthedate: false
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---
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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.
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## Polythetic Divisive Methods
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Polythetic methods operate via a distance matrix.
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This procedure avoids considering all possible splits by
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1. Finding the object that is furthest away from the others within a group and using that as a seed for a splinter group.
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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.
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3. The step is then repeated.
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This process has been developed into a program named `DIANA` (DIvisive ANAlysis Clustering) which is implemented in `R`.
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### Similarities to Politics
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This somewhat resembles a way a political party might split due to inner conflicts.
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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.
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## Methods for Large Data Sets
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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.
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### CURE
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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
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2. Which are then shrunk towards the centroid as to dampen the effect of the outliers
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3. Hierarchical clustering then operates on the representative points
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`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.
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## Revisiting Topics: Cluster Dissimilarity
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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.
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In most methods of hierarchical clustering this is achieved by a use of an appropriate
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- Metric (a measure of distance between pairs of observations)
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- Linkage Criterion (which specifies the dissimilarities of sets as functions of pairwise distances observations in the sets)
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## Advantages of Hierarchical Clustering
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- Any valid measure of distance measure can be used
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- In most cases, the observations themselves are not required, just hte matrix of distances
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- This can have the advantage of only having to store a distance matrix in memory as opposed to a n-dimensional matrix.
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