Measuring novel configuration of points

Question

I am trying to implement Novelty search; I understand why it can work better than the standard Genetic Algorithm based solution which just rewards according to the objective.
I am working on a problem which requires to generate a fixed number of points in a 2d box centered at the origin.
In this problem, how can I identify which is a novel configuration of points?
Note: I have thought of one way of doing this: We call the mean of one configuration of points to be the mean of all points in that configuration (let's say this tuple is $(m_x, m_y)$, we store the mean of all configurations generated till now, now for a new configuration it's novelty can be defined as the distance of the mean of this new configuration with $(m_x, m_y)$.
But I think it will not work greatly as some very different configuration of points can also have the same mean.

OmG · Answer

You can define different measures in this way:

Maximum distance of the new point with all points of the configuration ($M$)
Minimum distance of the new point with all points of the configuration ($N$)
$frac{M}{text{Maximum distance between two points of the configuration(}D)}$: normalize (1) measure
$frac{N}{D}$:normalize (2) measure

You can get more ideas from distance measures in hierarchical clustering methods. To select a proper one, you need to elaborate on the context of these points.

Measuring novel configuration of points

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