<h1>Introduction to Connectivity Based Models</h1>
<p>Hierarchical algorithms combine observations to form clusters based on their distance.</p>
<h2>Connectivity Methods</h2>
<p>Hierarchal Clustering techniques can be subdivided depending on the method of going about it.</p>
<p>First there are two different methods in forming the clusters <em>Agglomerative</em> and <em>Divisive</em></p>
<p><u>Agglomerative</u> is when you combine the n individuals into groups through each iteration</p>
<p><u>Divisive</u> is when you are separating one giant group into finer groupings with each iteration.</p>
<p>Hierarchical methods are an irrevocable algorithm, once it joins or separates a grouping, it cannot be undone. As Kaufman and Rousseeuw (1990) colorfully comment: <em>"A hierarchical method suffers from the defect that it can never repair what was done in previous steps"</em>. </p>
<p>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.</p>
<p>At different distances, different clusters are formed and are more readily represented using a <strong>dendrogram</strong>. These algorithms do not provide a unique solution but rather provide an extensive hierarchy of clusters that merge or divide at different distances.</p>
<h2>Linkage Criterion</h2>
<p>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.</p>
<p>Do you want to group based on the nearest points in each cluster? Nearest Neighbor Clustering</p>
<p>Or do you want to based on the farthest observations in each cluster? Farthest neighbor clustering.</p>
<p>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.</p>
<p>As we go through this section, we will go into detail about the different linkage criterion and other parameters of this model.</p>
