mirror of
https://github.com/Brandon-Rozek/website.git
synced 2024-12-24 18:32:25 +00:00
38 lines
2.1 KiB
Markdown
38 lines
2.1 KiB
Markdown
---
|
|
title: Introduction to Connectivity Based Models
|
|
showthedate: false
|
|
---
|
|
|
|
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.
|
|
|
|
|
|
|
|
## 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.
|