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I have data of 90 persons.

Data of a person:
- x coordinate
- y coordinate
- score (1 to 6)

I want to form groups of 9 people each so that:
- the distance between people in one group is as small as possible
- people with the same coordinates are in different groups
- people within a group should have different scores

I am not expecting a full-fledged algorithm but rather hints in the right direction. So far I am using a simple k-means algorithm which forms groups so that the distance between people gets minimized however the two other constraints are not considered, unfortunately.

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2 Answers 2

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I found this article on "Clustering with Constraints" to be a helpful resource to what you're talking about:

Credit: Clustering with Constraints Incorporating Prior Knowledge into Clustering Adapted from a Tutorial of Sugato Basu and Ian Davidson (SDM 2005)

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You are describing a variation on optimization, maximize a real function by systematically choosing input values from within an allowed set and computing the value of the function. Specifically, a variation called linear programming where you to maximize the similarity (similarity is the inverse of distance) subject to a couple of constraints:

enter image description here

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  • $\begingroup$ I thought about defining a cost function and then minimize it. But I couldn't figure out how to properly do updates. I can't compute a gradient and use gradient descent. Do you have recommendations on how to do updates? $\endgroup$
    – siva
    Commented Apr 6, 2018 at 21:06
  • $\begingroup$ Gradient descent is not the best optimization technique for clustering. Expectation–maximization (EM) is superior for clustering. $\endgroup$ Commented Apr 7, 2018 at 4:13

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