使用dbscan对角度数据进行聚类

Question

I need to cluster data-points in the form of X,Y,Phi. Right now I use DBSCAN (sklearn). The clustering works except for one thing: Phi is angular data, which is modulo 2*Pi. As a result the clustering near Phi=0 is incorrect. Is there a trick to fix this? I could not find one or make one up myself that worked.

Thank you.

Answer 1

Circular boundary conditions are not easy to implement practically outside a Fourier framework.

You could try reparametrizing by replacing X, Y, Phi with X, Y, a * cos(Phi), a * sin(Phi) , where a > 0 , a sort of scale factor, needs to be chosen correctly in order for this projection into 2D space to act the way you need in clustering. Start by checking a = 1 (if it worked OK for pure Phi , then this is a good candidate) and then a on the order of magnitude of your remaining data X, Y .

The idea behind this is to replace Phi by its 'true' complex 'meaning' of phase , ie exp(1j * Phi) , but keeping it real all the while.

You then proceed to calculate a distance based on this reparametrization, eg euclidean:

dist = ((np.array([X1, Y1, a* np.cos(Phi1), a * np.sin(Phi1)]) - np.array([X2, Y2, a * np.cos(Phi2), a * np.sin(Phi2)])) ** 2).sum()

This you do for every pair before feeding it to your DBSCAN object.

Answer 2

DBSCAN can work with arbitary distances .

So first define a distance function (which will likely involve some trigonometric functions), then plug this into DBSCAN as similarity.

You could probably use something like this:

distance = (x1-x2)**2 + (y1-y1)**2 + factor * sin(phi1-phi2)**2

but you need to carefully choose your weight factor , as the angular difference is on a different scale as your X and Y axes, I guess.

Don't use Euclidean distance on this data set, for the obvious reasons.