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# Kernel Density for 2D data

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Devinya Herath on 15 Oct 2011
Edited: Tunde on 20 Oct 2016
I have two series of data(both of type double). I want to generate a kernel density plot from these. Pls help. My coding is given below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
curs1 = exec(conn, 'select sp_x, sp_y from road_part6_trajectories_oneway2_new_segments_cartesian2');
format long;
curs1 = fetch(curs1);
AA = curs1.Data;
x = [AA{:,1}]';
y = [AA{:,2}]';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
I want to generate the kernel density or any other suitable density plot for x and y. pls advise.
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### Accepted Answer

the cyclist on 15 Oct 2011
The function ksdensity() will do kernel density estimation. It's not clear to me what your x and y represent, so it's hard to give more specific advice than that.
In response to comments, here is some code with an example of 2-d kernel density estimation, with a plot of the results. Important note: this assumes that x and y are independent from each other.
% Generate some normally distributed data
x = randn(50,1);
y = randn(50,1);
% Estimate a continuous pdf from the discrete data
[pdfx xi]= ksdensity(x);
[pdfy yi]= ksdensity(y);
% Create 2-d grid of coordinates and function values, suitable for 3-d plotting
[xxi,yyi] = meshgrid(xi,yi);
[pdfxx,pdfyy] = meshgrid(pdfx,pdfy);
% Calculate combined pdf, under assumption of independence
pdfxy = pdfxx.*pdfyy;
% Plot the results
mesh(xxi,yyi,pdfxy)
set(gca,'XLim',[min(xi) max(xi)])
set(gca,'YLim',[min(yi) max(yi)])
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Bjorn Gustavsson on 24 Oct 2011
Then you should start with a two-dimensional histogram. There are several contributions with such tools on the file exchange. To use the cyclist's code you have to show that the variables are independent. A quick look with a 2-D histogram will help you get a look of that.

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### More Answers (1)

Tunde on 20 Oct 2016
Edited: Tunde on 20 Oct 2016
Very helpful. After changing x and y to variables from my data. I have this diagram Is there any way to change the z-axis to normalized density estimates or probabilities?
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