Plot a curve that splits data into two sets

Hello,

I have data points which represent 2 classes (collisions avoided and probable collisions). My goal is to plot a curve (polynomial equation), that would split the data points say in a chosen ratio (Say 90% collisions avoided to 10% probable collisions). Note that data points corresponding to two classes are very close.

I have tried using 'fit' funciton in matlab, and for a polynomial of degree 8, here is what I get (refer image). But it doesn't split the data as required.

I am looking at Support Vector Machines for Binary Classification (I am not an expert in this domain), I am not sure if it would help. How can I get the data seggregation I want?

Best,

Raj

Answer 1

[Greg Heath]

Your data is extremely discontinuous. The best you can hope for is a decision tree.

Hope this helps

Thank you for formally acceptingmy answer

Greg

[RPatel]

Thanks Greg for your suggestion, but it will not help my study...

[Image Analyst]

Too bad because I think that's your best shot at a possible solution. Since your data is so overlapping, I think that those two parameters are not enough to do the discrimination. You'd best try to look for a third or fourth parameter, like acceleration, velocity vector angles, or something. If you can't, then I think a treebagger/random forest/decision tree type of approach is the best you can hope for, like Greg said. See the scatterplot example on https://www.mathworks.com/help/stats/ensemble-methods.html#bsx62vu Actually your ad hoc convex hull example is somewhat related to a treebagger type of solution. It also sounds a bit like dbscan https://en.wikipedia.org/wiki/DBSCAN

Answer 2

[John D'Errico]

But why would a polynomial regression fit have any chance of satisfying this goal? It would be pure random chance if it came even close. It is especially wrong to hope that such a fit, based on purely distance as the independent variable would have a chance.

It seems you are looking for a nonlinear discriminant curve, based on both velocity and distance. I'd suggest neural nets, but just because you want to see a 90% success rate does not mean any such function exists. You could have as easily have insisted on a 99.99% target success rate. If wishes were horses, beggars would ride.

What you need to be modeling is a boolean result, thus collision or not, as a function of TWO independent variables, vehicle velocity and inter-vehicle distance. Again, use a tool of your choice. But a polynomial regression is still NOT the tool I would ever advise here.

[RPatel]

Hello John,

I never had to do something of this sort before, and I have no idea about the diverse tools matlab offers to solve this kind of an issue. 'Polynomial regression fit' is just one of them I came across and I tried.

Indeed, I would like to have a different curve, for different percentage of success rate (90 %, 99%, etc.).

I will have a look at neural nets to see if it helps. Thanks for your comments :)

Answer 3

[RPatel]

As there doesn't seem to be any solution to this, here is what I did:

I found the centroid, chose x % of the closest points. Then I plot a convexhull around those points. Next, I check whether a particular point of interest lies in or out of the convex hull. Using this, I manage to get the percentage of collisions avoided to probable collisions (of points inside the hull)..

Hope this helps to others who might face a similar situation...