# Measuring novel configuration of points

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.

## 1 Answer

You can define different measures in this way:

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

• I think in the first or third one, Novelty will be directly proportional to the measure, but not so sure about the second and fourth one, because I think these two won't be very good in differentiating between novel and non novel configuration. Oct 15 '20 at 16:50