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---
id: K-Medians
aliases:
- *K-Medians*: Handling Outliers by Computing Medians [(Youtube)]()
tags: []
---
## _K-Medians_: Handling Outliers by Computing Medians [(Youtube)]()
- Medians are less sensitive to outliers than means
- Think of the median salary vs. mean salary of a large firm when adding a few
top executives!
- _**K-Medians**_: Instead of taking the **mean** value of the object in a
cluster as a reference point, **medians** are used ($L_1$-norm is often used
as the distance measure)
- The criterion function for the _K-Medians_ algorithm: $$ S =
\sum*{k=1}^{K}\sum*{x*{i\in{C_k}}}|x*{ij} - m e d\_{kj}|$$
- The _K-Medians_ clustering algorithm:
- Select _K_ points as the initial representative objects (i.e., as initial _K
medians_)
- **Repeat**
- Assign every point to its nearest median
- Re-compute the median using the median of <u>==each individual
feature==</u>
- **Until** convergence criterion is satisfied
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