Efficient moving average of scattered data

Question

Chad Greene 2016-6-28

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https://ww2.mathworks.cn/matlabcentral/answers/292799-efficient-moving-average-of-scattered-data

回答： Chris Turnes 2017-3-9

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')

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Walter Roberson 2016-6-28

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.

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Answer 1

Chad Greene 2016-6-30

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

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Chad Greene 2016-6-30

And a 2D version called scatstat2.

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Answer 2

Chris Turnes 2017-3-9

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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).

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Answer 3

Walter Roberson 2016-6-28

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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.