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content/research/clusteranalysis/notes/lec11-2.md

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+# K-Medoids
+
+A medoid can be defined as the object of a cluster whose average dissimilarity to all the objects in the cluster is minimal.
+
+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.
+
+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.
+
+## Algorithms
+
+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.
+
+### Partitioning Around Medoids (PAM)
+
+1. Select $k$ of the $n$ data points as medoids
+2. Associate each data point to the closes medoid
+3. While the cost of the configuration decreases:
+   1. For each medoid $m$, for each non-medoid data point $o$:
+      1. Swap $m$ and $o$, recompute the cost (sum of distances of points to their medoid)
+      2. If the total cost of the configuration increased in the previous step, undo the swap
+
+
+
+### Voronoi Iteration Method
+
+1. Select $k$ of the $n$ data points as medoids
+2. While the cost of the configuration decreases
+   1. In each cluster, make the point that minimizes the sum of distances within the cluster the medoid
+   2. Reassign each point to the cluster defined by the closest medoid determined in the previous step.
+
+
+
+### Clustering Large Applications (CLARA
+
+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.
+
+
+
+## R Implementations
+
+Both PAM and CLARA are defined in the `cluster` package in R.
+
+```R
+clara(x, k, metric = "euclidean", stand = FALSE, samples = 5, 
+      sampsize = min(n, 40 + 2 * k), trace = 0, medoids.x = TRUE,
+      keep.data = medoids.x, rngR = FALSE)
+```
+
+```R
+pam(x, k, metric = "euclidean", stand = FALSE)
+```
+