How to construct a weighed 2D histogram?

Hey,

I am finding it hard to construct a weighed 2D histogram.

Let us assume that we have two vectors, X and Y, of equal length N such that the entries in each of X and Y are not necessarily unique. Similarly, let's assume that W represents an array of N non-unique, non-integer values weighing each sample point [ X(i), Y(i) ].

To construct a standard 2D histogram, I am aware one can simply use

H = histogram2( X, Y ) 

to plot (along the z-axis) the sum/count of number of points per bin.

My question: how can I modify this to account for the weight of every sample point within a bin? That is, for the result to be the sum of the weights of all points within a bin.

(Note that this is not equivalent to merely weighing the count per bin by a constant value)

Thanks for any suggestions!

Answer 1

[John D'Errico]

Just use accumarray to sum the weights in each bin.

[Antranik Sefilian]

Hey, thanks for the reply!

I'd appreciate it very much if you could provide an example describing how to do so.

[John D'Errico]

Did you read the help for accumarray? Why not? Note that there are 8 examples of use of accumarray, here:

help accumarray

There will be more complete examples and explanations in

doc accumarray

READ THE HELP!

You will find that you first need to use discretize to bin each sample, so do that twice, once for each dimension. But again, you will find examples in the help. I cannot do better than to re-write the help, and how will that gain you or me?

help discretize

[Antranik Sefilian]

Hey John,

Thanks for referring me to accumarray. I now have a piece of code which serves my needs partially; that is, without weighing individual points [x(i), y(i)].

% Create random data
x = randn(1e3,1);    y = randn(1e3,1)*2 ;

% Centers of bins (I use integers)
xbins = floor(min(x)):1:ceil(max(x));  NumBins_x = numel(xbins);
ybins = floor(min(y)):1:ceil(max(y));  NumBins_y = numel(ybins);

% Mapping data to bin indices
Xi = round( interp1(xbins, 1:NumBins_x, x, 'linear', 'extrap') );
Yi = round( interp1(ybins, 1:NumBins_y, y, 'linear', 'extrap') );

% Limit indices to the range [1, NumBins]
Xi = max( min(Xi,NumBins_x), 1);
Yi = max( min(Yi,NumBins_y), 1);

% Use accumarray to count number of points/bin
H = accumarray([Yi(:) Xi(:)], 1, [NumBins_y NumBins_x]);

% Plotting 
[XX, YY] = meshgrid(xbins, ybins);
figure(1); surf(XX, YY, H); 
shading interp; colorbar; colormap jet; view(0,90);
% hold on; plot(x,y, 'r.', 'MarkerSize',10) ; To visualize underlying data

Update: I gather that I can sum the weights (rather than the number of points) in each bin by the following:

w = randn(1e3, 1) ; % Define weights: same size as [x] & [y]
H = accumarray([Yi(:) Xi(:)], w, [NumBins_y NumBins_x]); %i.e. vals = w, not 1

I'd appreciate it if you can provide your feedback on this.

Answer 2

[andrepiz]

you can use histweight available on MATLAB exchange.

The call would be:

[bins, counts, edges] = histweight([X;Y], W)

Example for random points attached.

Disclaimer: I am the author of the toolbox.