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19 lines
990 B
Markdown
19 lines
990 B
Markdown
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# K-Medians
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This is a variation of k-means clustering where instead of calculating the mean for each cluster to determine its centroid we are going to calculate the median instead.
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This has the effect of minimizing error over all the clusters with respect to the Manhattan norm as opposed to the Euclidean squared norm which is minimized in K-means
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### Algorithm
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Given an initial set of $k$ medians, the algorithm proceeds by alternating between two steps.
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**Assignment step**: Assign each observation to the cluster whose median has the leas Manhattan distance.
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- Intuitively this is finding the nearest median
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**Update Step**: Calculate the new medians to be the centroids of the observations in the new clusters
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The algorithm is known to have converged when assignments no longer change. There is no guarantee that the optimum is found using this algorithm.
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The result depends on the initial clusters. It is common to run this multiple times with different starting conditions.
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