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2020-06-30 20:47
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求助!求大佬帮忙用Matlab编写一段程序实现计算两个分布的Wasserstein距离

如题,需要用到Wassertein距离计算两个离散点分布之间的距离,麻烦懂的大佬动下小手帮忙做做。

可偿!可偿!可偿!

如数据集1{45,46,46,49,50,47,49,41,52,46};数据集2{49,47,42,38,53,42,47,41,45,50}。

用Matlab编写。谢谢!!!

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1条回答 默认 最新

  • i-Data 2020-07-01 15:44
    已采纳

    源代码如下:

    function wsd = ws_distance(u_samples, v_samples, p)
    % WS_DISTANCE 1- and 2- Wasserstein distance between two discrete 
    % probability measures 
    %   
    %   wsd = WS_DISTANCE(u_samples, v_samples) returns the 1-Wasserstein 
    %   distance between the discrete probability measures u and v 
    %   corresponding to the sample vectors u_samples and v_samples
    %
    %   wsd = WS_DISTANCE(u_samples, v_samples, p) returns the p-Wasserstein 
    %   distance between the discrete probability measures u and v
    %   corresponding to the sample vectors u_samples and v_samples. 
    %   p must be 1 or 2.
    %
    % from https://github.com/nklb/wasserstein-distance
    if ~exist('p', 'var')
        p = 1;
    end
    u_samples_sorted = sort(u_samples(:));
    v_samples_sorted = sort(v_samples(:));
    if p == 1
    
        all_samples = unique([u_samples_sorted; v_samples_sorted], 'sorted');
    
        u_cdf = find_interval(u_samples_sorted, all_samples(1:end-1)) ...
            / numel(u_samples);
        v_cdf = find_interval(v_samples_sorted, all_samples(1:end-1)) ...
            / numel(v_samples);
    
        wsd = sum(abs(u_cdf - v_cdf) .* diff(all_samples));
    
    elseif p == 2
    
        u_N = numel(u_samples);
        v_N = numel(v_samples);    
        all_prob = unique([(0:u_N) / u_N, (0:v_N) / v_N], 'sorted').';
    
        u_icdf = u_samples_sorted(fix(all_prob(1:end-1) * u_N) + 1);
        v_icdf = v_samples_sorted(fix(all_prob(1:end-1) * v_N) + 1);
    
        wsd = sqrt(sum((u_icdf-v_icdf).^2 .* diff(all_prob)));
    
    else
    
        error('Only p=1 or p=2 allowed.')
    
    end
    end
    
    
    %注意这里是第二部分调用函数
    function idx = find_interval(bounds, vals)
    % Given the two sorted arrays bounds and vals, the function 
    % idx = FIND_INTERVAL(bounds, vals) identifies for each vals(i) the index 
    % idx(i) s.t. bounds(idx(i)) <= vals(i) < bounds(idx(i) + 1).
    m = 0;
    bounds = [bounds(:); inf];
    idx = zeros(numel(vals), 1);
    for i = 1:numel(vals)
        while bounds(m+1) <= vals(i)
            m = m + 1;
        end
        idx(i) = m;
    end
    end
    

    运行以下:

    wsd = ws_distance([45,46,46,49,50,47,49,41,52,46], [49,47,42,38,53,42,47,41,45,50], 1)
    

    我现在电脑上没有安装matlab,所以还没实际运行过,不过我用Python算了下结果是1.9,你可以用matlab运行确认下。

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