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35 lines
2.1 KiB
Markdown
35 lines
2.1 KiB
Markdown
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# Introduction to Connectivity Based Models
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Hierarchical algorithms combine observations to form clusters based on their distance.
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## Connectivity Methods
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Hierarchal Clustering techniques can be subdivided depending on the method of going about it.
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First there are two different methods in forming the clusters *Agglomerative* and *Divisive*
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<u>Agglomerative</u> is when you combine the n individuals into groups through each iteration
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<u>Divisive</u> is when you are separating one giant group into finer groupings with each iteration.
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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"*.
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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.
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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.
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## Linkage Criterion
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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.
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Do you want to group based on the nearest points in each cluster? Nearest Neighbor Clustering
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Or do you want to based on the farthest observations in each cluster? Farthest neighbor clustering.
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## Shortcomings
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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.
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As we go through this section, we will go into detail about the different linkage criterion and other parameters of this model.
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