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+---
+id: SSE
+aliases:
+  - Partitioning Algorithms: Basic Concepts
+tags: []
+---
+
+## Partitioning Algorithms: Basic Concepts
+
+- <u>Partitioning method</u>: Discovering the groupings in the data by
+  optimizing a specific ==objective function== and ==iteratively== improving the
+  quality of partitions
+- _K-partitioning_ method: Partitioning a dataset _**D**_ of _**n**_ objects
+  into a set of _**K**_ clusters so that an objective function is optimized
+  (e.g., the sum of squared distances is minimized within each cluster, where
+  $C_k$ is the centroid or medoid of cluster $C_k$)
+  - A typical objective function: **Sum of Squared Errors (SSE)** $$ SSE(C) =
+    \sum*{k=1}^{K}\sum*{x\_{i\in{C_k}}}||x_i - c_k||^2$$
+- **Problem definition**: Given _K_, find a partition of _K clusters_ that
+  optimizes the chosen partitioning criterion
+  - Global optimal: Needs to exhaustively enumerate all partitions
+  - Heuristic methods (i.e., greedy algorithms): _[[K-Means]], [[K-Medians]],
+    [[K-Medoids]], etc_