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52 lines
2.2 KiB
Markdown
52 lines
2.2 KiB
Markdown
# K-Medoids
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A medoid can be defined as the object of a cluster whose average dissimilarity to all the objects in the cluster is minimal.
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The K-medoids algorithm is related to k-means and the medoidshift algorithm. Both the k-means and k-medoids algorithms are partition and both attempt to minimize the distance between points in the cluster to it's center. In contrast to k-means, it chooses data points as centers and uses the Manhattan Norm to define the distance between data points instead of the Euclidean.
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This method is known to be more robust to noise and outliers compared to k-means since it minimizes the sum of pairwise dissimilarities instead of the sum of squared Euclidean distances.
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## Algorithms
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There are several algorithms that have been created as an optimization to an exhaustive search. In this section, we'll discuss PAM and Voronoi iteration method.
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### Partitioning Around Medoids (PAM)
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1. Select $k$ of the $n$ data points as medoids
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2. Associate each data point to the closes medoid
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3. While the cost of the configuration decreases:
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1. For each medoid $m$, for each non-medoid data point $o$:
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1. Swap $m$ and $o$, recompute the cost (sum of distances of points to their medoid)
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2. If the total cost of the configuration increased in the previous step, undo the swap
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### Voronoi Iteration Method
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1. Select $k$ of the $n$ data points as medoids
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2. While the cost of the configuration decreases
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1. In each cluster, make the point that minimizes the sum of distances within the cluster the medoid
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2. Reassign each point to the cluster defined by the closest medoid determined in the previous step.
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### Clustering Large Applications (CLARA
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This is a variant of the PAM algorithm that relies on the sampling approach to handle large datasets. The cost of a particular cluster configuration is the mean cost of all the dissimilarities.
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## R Implementations
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Both PAM and CLARA are defined in the `cluster` package in R.
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```R
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clara(x, k, metric = "euclidean", stand = FALSE, samples = 5,
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sampsize = min(n, 40 + 2 * k), trace = 0, medoids.x = TRUE,
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keep.data = medoids.x, rngR = FALSE)
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```
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```R
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pam(x, k, metric = "euclidean", stand = FALSE)
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```
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