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## CLUSTER ANALYSIS (K MEANS) |

In addition to the ORGAN SEPARATION method which incorporates prior knowledge, PSEG offers k-means clustering as a general method for subdividing a volume into clusters of "kinetically similar" pixels [7]. The time-weighted Euclidean distance is used as the measure of dissimilarity (or distance) between TACs. In PSEG, the procedure performs the following steps for the pixels within a mask, given a prescribed number N of clusters

1.N non-background pixels serving as initial cluster centroids are randomly assigned.

2.Each pixel is assigned to that centroid with minimal distance between the TACs, thus forming N initial clusters.

3.For each cluster a new centroid TAC is calculated as the average TAC of all pixels in the cluster.

4.An iterative process with a maximal number of iterations is started which repeats the following two steps:

a.Each pixel TAC is compared with all centroid TACs and assigned to the cluster with minimal distance.

b.All centroid TACs are recalculated to reflect the updated cluster population.

The iterations are repeated until no pixels are re-assigned to a different cluster, or the maximal number of iterations is exhausted.

Note that because no geometric information is used for the clustering, spatially disconnected pixels will most likely be included in the resulting clusters.