Deleting X-Y points that are not near other points on a field of data points

I have a set of data. This data is around 900 rows of two columns. Each row has an X and a Y value which specifies a point on the X-Y plane. The X-Y plane is from 0 to 100 and 0 to 100 respectively. All of these points are randomly scattered throughout the X-Y plane. My problem is there are too many X-Y points cluttering up the scatter plot. So what I want to do is have Matlab look at each point and say: Is this point a distance of 10 or less to another point. If it is then keep it. If it isn’t then delete the row containing that X, Y value. A shortened example of my data:

X=[1 2 3 4 20];
Y=[1 3 4 3 59];

Since (20,59) is more than a distance of 10 away from the other points, delete it and return the following:

X2=[1 2 3 4];
Y2=[1 3 4 3];

If anyone knows how I could do this, It would be a very great thing.

Answer 1

[per isakson]

See Doug's video Advanced: making a 2d or 3d histogram to visualize data density and search the FEX for "hist2"

I failed to find a solution in the FEX. Here is a naive code with "10" hard-coded in the magic number "100".

    X=[1,2,3,4,20];
    Y=[1,3,4,3,59];

    to_be_removed = false(size(X));
    for ii = 1 : length(X)
        is = (X-X(ii)).^2+(Y-Y(ii)).^2 <= 100; 
        is(ii) = false;
        if not( any( is ) )
            to_be_removed(ii) = true;
        end
    end
    X(to_be_removed)=[];
    Y(to_be_removed)=[];

[charles atlas]

I had to tweak the code a little bit to fit my actual data,.. but it worked well, Thank you

Answer 2

[Geoff]

Naive (brute force) implementation given by per isakson looks sufficient for this problem. O(N^2) is okay for 900 rows. For larger sets, I'd consider partitioning the points into a quad tree.

However, without making things complicated, I would say that the number of candidates for removal will be small due to your X and Y range. You could easily speed up the naive algorithm by first approximating the local point-density into a 21x21 array (cel-sizes of 5 with extra one for the ends) and then only do a search on points that are unique to a cel address.

[charles atlas]

Sorry I havent been able to get into the office and test the code until today.

the read data is latitude and longitudes but for simplicity's sake, I said it was 0 to 100 on the X and Y axis (which would actually be the longitude and latitude axes respectively.

The code did what it was supposed to do when I tested it, but It neglected half the values that were jumbled together (that is at a distance of about 600 yards away, aka <= .005 as a difference in lat and long squared, added and then square rooted.

[charles atlas]

That is; I used isakson's code from above.

Answer 3

[Image Analyst]

If you displayed it as an image instead of a scatterplot, you wouldn't have that problem. Why not give it a try?

[per isakson]

That's what Doug shows