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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_
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