Imposing connectivity constraints adds additional requirements in regards to which observations can be connected and merged into an existing cluster beyond just the distance metric used. Without connectivity constraints, clusters are merged simply based on satisfying the linkage criteria chosen. In high-dimensional data, not using connectivity constraints can fail to distinguish between regions that are similar based on distance but might practically represent different constructs within the data. A simple example of a connectivity constraint is to restrict candidate observations that can be merged into a cluster to a pre-defined number of observations or nearest neighbors.
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