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I'm currently working on a college project and was having trouble deciphering a formula I ran across. The problem involves the initialization of cluster centers for the K-means algorithm, and here is how it is shown:

Consider the following heuristic method for selecting the initial cluster center positions:

  1. Choose 1st center c1 as point A
  2. For k=2,...,K set enter image description here, where X is the set of data points.

I understand that you have to measure the Euclidean distance between the points and the centers, but I'm confused by what the max(min (Euclid distance)) means.

Thanks you in advance!

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Saurav Sircar
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    Loosely speaking, the heuristic selects as a new cluster center $c_k$ the point $x \in X$ that's furthest away from the previously selected centers $c_1,\dots,c_{k-1}$. This is done in two steps: (i) for each point $x$ measure the distance to the centers by finding the closest center and computing the distance (the "min" part); (ii) select the point $x$ that is furthest away, i.e., with the largest distance (the "argmax" part). – Dan Oneață Feb 27 '20 at 07:31
  • Note that argmax means the $x$ that maximizes the term in the brackets. – ViktorStein Feb 27 '20 at 07:31

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