Hi,
I am having a density-based radar database that I try to cluster with a grid-based DBSCAN algorithm.
The part of the algorithm my question focuses on is "the core point condition". Which is basically the following. To determine if a point is a core point, it needs to have more than a certain number of neighbours (MinPoints) in its epsilon-neighbourhood.
The epsilon neighbourhood can be determined as follows:
- Calculate the distance from a point P to all the other points in the database.
- Determine the epsilon-neighbourhood: All the points that are within a max. distance of eps are part of the neighbourhood. Meaning epsilon is the search radius.
- The core point condition: A point is a core point if in its epsilon-neighbourhood at least MinPoints are.
My question is now, how to determine the epsilon-neighbourhood for polar points with azimuth (azi) and range (r). I do not completely know how to calculate the distance and then from there how to determine the epsilon neighbourhood.
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I use among others the "Phased-Array Toolbox" and the "clusterDBSCAN" algorithm has to possiblity to also use a 1-by-P row vector. Where P is the number of features in the input data. Does someone know how this neighborhood search works with a vector?
Because in the end I want to have a range dependend epsilon(x,y)-vector that varients in azimuth direction with the range.
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Edit:
I implemented my own algorithm. My problem is that I do not know how to implement the ellipse equation to determine the size of the epsilon-neighbourhood. To basically how to implement the regionQuery function for an ellipse search radius. Below you find my temporary implementation were I only look at the points on the same range or azimuth angle. So it is basically a cross, but not a circual search area. P is the temporary point which has to be checked for the core point criterion.
function Neighbors=RegionQuery(P)
RANGEPOINT = Data(P,2)-min(Data(:,2))/Q_range+1;
All_Azi = find(Data(:,2) == Data(P,2));
Neighbors_azi = All_Azi(find(D_azi(P,All_Azi) <= epsilon_azi(RANGEPOINT)));
All_Range = find(Data(:,1) == Data(P,1));
Neighbors_range = All_Range(find(D_range(P,All_Range) <= epsilon_range));
Neighbors = [Neighbors_azi; Neighbors_range];
Neighbors = sort(unique(Neighbors));
end
The implementation above is as said only looking linear but not elliptical. Can you help me with that? I created a short data set of points in polar coordinates in degree and meter:
polar_corepoint = [0,6];
polar_borderpoints = [10,6;5,6.5;-5,5.5; 0,8; 0,4 ];
polar_noise = [25,6;-15,4;15,9;45,8.5;-25,8];
eps_azi = 10;
eps_range = 2;
I want to get the neighbourhood of the corepoint that only includes the boarderpoints and not the noise. So basically the size of the neighborhood should be in the end = 6 (core point + borderpoints).
Do you know how to implement that epsilon search? It does not matter which distance metric is used, I personally have used the Euclidean until now (pdist2(data,data)).
Thanks for you help
