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K-medians

Same as K-means but with medians instead of means to compute the centroids.

Question: do the centroids lie in between data points or on data points?

  • Three red points are the dataset points
  • median on orange horizontal axis is 0, median([0, 0, 1]) = 0
  • median on green vertical axis is 1, median([0, 1, 2]) = 1
  • Thus, the centroid is (0, 1) (yellow star)
  • There is no (0, 1) point in the dataset
  • So the answer is no, the centroids may not be within dataset points.