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+---
+id: external
+aliases:
+  - Measuring Clustering Quality: ==External== Methods
+tags: []
+---
+
+## Measuring Clustering Quality: ==External== Methods
+
+- Given the **ground truth** _T, Q(C, T)_ is the **quality measure** for a
+  clustering C
+- _Q(C, T)_ is good if it satisfies the following **four** essential criteria
+  - **Cluster homogeneity**
+    - The purer, the better
+  - **Cluster completeness**
+    - Assign objects belonging to the same category in the ground truth to the
+      same cluster
+  - **Rag bag better than alien**
+    - Putting a heterogeneous object into a pure cluster should be penalized
+      **more** than putting it into a _rag bag_ (i.e., "miscellaneous" or
+      "other" category)
+  - **Small cluster preservation**
+    - Splitting a small category into pieces is more harmful than splitting a
+      large category into pieces
+
+## Commonly Used External Measures
+
+- **Matching-based measure**
+  - Purity, maximum matching, [[F-measure]]
+- **Entropy-Based Measures**
+  - Conditional entropy
+  - <u>Normalized mutual information (NMI)</u>
+  - Variation of information
+- **Pairwise measures**
+  - Four possibilities: True positive (TP), FN, FP, TN
+  - Jaccard coefficient, Rand statistic, Fowlkes-Mallow measure
+- **Correlation measures**
+  - Discretized Huber static, normalized discretized Huber static
+- Purity vs Maximum Matching ![[CleanShot 2023-10-25 at 15.57.30@2x.png]]
+- [[F-measure]] ![[CleanShot 2023-10-25 at 15.57.51@2x.png]] ![[CleanShot
+2023-10-25 at 15.58.04@2x.png]] ![[CleanShot 2023-10-25 at 15.58.19@2x.png]]
+  ![[CleanShot 2023-10-25 at 15.58.40@2x.png]]