Efficient moving average of scattered data

I have some scattered data and I'd like to take something similar to a moving average, where I average all values with in some radius of each point. I can do this with a loop, but I'd like a more efficient approach. Any ideas?

Here's a working example I'd like to make more efficient:

x = randi(100,45,1) + 20+3*randn(45,1) ; 
y = 15*sind(x) + randn(size(x)) + 3;  

figure
plot(x,y,'bo')

radius = 10;

ymean = NaN(size(x)); 
for k = 1:length(x)

     % Indicies of all points within specified radius: 
     ind = abs(x-x(k))<radius; 

     % Mean of y values within radius:  
     ymean(k) = mean(y(ind)); 
  end

hold on
plot(x,ymean,'ks')
legend('scattered data','radial average','location','southeast')

[Walter Roberson]

When I read the title I thought you might mean "sparse", and was thinking about how I might do an efficient moving average on sparse data.

Answer 1

[Chad Greene]

I turned this into a generalized function called scatstat1, which is on the file exchange here.

[Chad Greene]

And a 2D version called scatstat2.

Answer 2

[Chris Turnes]

If you can upgrade to R2017a, this functionality can now be achieved through the 'SamplePoints' name-value pair in the moving statistics. For your example, you would do something like movmean(y, 2*radius, 'SamplePoints', x); (though you'd need to sort your x values first).

Answer 3

[Walter Roberson]

pdist() to get all of the distances simultaneously. Compare to the radius. Store the resulting mask. Multiply the mask by repmat() of the y value, and sum along a dimension. sum the mask along the same dimension and divide the value sum by that count. Result should be the moving average.

[Chad Greene]

Interesting idea! I got your solution working, but for N of 20,000 points the pdist function takes a bit of time. As it turns out, looping is a faster.

[Walter Roberson]

I wonder if looping pdist2() would be efficient? Eh, it probably just adds unnecessary overhead to a simple Euclidean calculation.

[Chad Greene]

Also adds a Stats Toolbox dependency. I'll have to keep pdist in mind for future applications though. Thanks for the suggestion!