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+---
+id: Hierarchical Clustering
+aliases:
+  - Hierarchical Clustering: Basic Concepts
+tags: []
+---
+
+## Hierarchical Clustering: Basic Concepts
+
+- Hierarchical clustering
+  - Generate a clustering hierarchy (drawn as a **dendrogram**)
+  - Not required to specify _K_, the number of clusters
+  - More deterministic
+  - No iterative refinement
+- Two categories of algorithms:
+  - **[[#Agglomerative Clustering Algorithm|Agglomerative]]**: Start with
+    sigleton clusters, continuously merge two clusters at a time to build a
+    **bottom-up** hierarchy of clusters
+  - **Divisive**: Start with a huge macro-cluster, split it continuously into
+    two groups, generating a **top-down** hierarchy of clusters
+
+## Dendrogram: Shows How Clusters are Merged
+
+![[CleanShot 2023-10-24 at 22.11.21@2x.png]]
+
+## Strengths of Hierarchical Clustering
+
+- Do not have to assume any particular number of clusters
+  - Any desired number of clusters can be obtained by 'cutting' the dendrogram
+    at the proper level
+- They may correspond to meaningful taxonomies
+  - Example in biological sciences (e.g., animal kingdom, phylogeny
+    reconstruction, ...)
+
+## Agglomerative Clustering Algorithm
+
+![[CleanShot 2023-10-24 at 22.14.30@2x.png]] ![[CleanShot 2023-10-24 at
+22.14.45@2x.png]] ![[CleanShot 2023-10-24 at 22.15.07@2x.png]] ![[CleanShot
+2023-10-24 at 22.15.23@2x.png]]
+
+## Extensions to Hierarchical Clustering
+
+- Major weaknesses of hierarchical clustering methods
+  - Can never undo what was done previously
+  - Do not scale well
+    - Time complexity of at least $O(n^2)$, where $n$ is the number of total
+      objects
+- Other hierarchical clustering algorithms
+  - BIRCH (1996): Use CF-tree and incrementally adjust the quality of
+    sub-clusters
+  - CURE (1998): Represent a cluster using a set of well-scattered
+    representative points
+  - CHAMELEON (1999): Use graph partitioning methods on the K-nearest neighbor
+    graph of the data