如何计算单元格数组的加权平均值? [英] How to calculate the weighted average over a cell-array of arrays?

问题描述

概括我之前的问题，如何对单元元素(即并应保留为数组的元素)进行加权平均)执行?

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我首先要修改 gnovice的答案是这样的:

dim = ndims(c{1});          %# Get the number of dimensions for your arrays
M = cat(dim+1,c{:});        %# Convert to a (dim+1)-dimensional matrix
meanArray = sum(M.*weigth,dim+1)./sum(weigth,dim+1);  %# Get the weighted mean across arrays

在此之前，请确保weight具有正确的形状.我认为需要注意的三种情况是

1. weight = 1(或任何常数)=>返回通常的平均值
2. numel(weight)== length(c)=>重量是每个单元元素c {n}(但对于固定n的每个数组元素都相等)
3. numel(weight)== numel(cell2mat(c))=>每个数组元素都有自己的权重...

第一种情况很简单，第3种情况不太可能发生，所以目前我对第2种情况感兴趣:如何将权重转换为一个数组，以使M.*weight在上述总和中具有正确的维数?当然，也可以给出显示获得加权平均值的另一种方法的答案.

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编辑实际上，如果权重与c的结构相同，则情况3比情况1更为琐碎.

这是我对情况2的意思的一个例子.

c = { [1 2 3; 1 2 3], [4 8 3; 4 2 6] };
weight = [ 2, 1 ];

应该返回

meanArray = [ 2 4 3; 2 2 4 ]

(例如，第一个元素(2 * 1 + 1 * 4)/(2 + 1)= 2)

解决方案

熟悉

In generalisation of my previous question, how can a weighted average over cell elements (that are and shall remain arrays themselves) be performed?

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I'd start by modifying gnovice's answer like this:

dim = ndims(c{1});          %# Get the number of dimensions for your arrays
M = cat(dim+1,c{:});        %# Convert to a (dim+1)-dimensional matrix
meanArray = sum(M.*weigth,dim+1)./sum(weigth,dim+1);  %# Get the weighted mean across arrays

And before that make sure weight has the correct shape. The three cases that I think need to be taken care of are

1. weight = 1 (or any constant) => return the usual mean value
2. numel(weight) == length(c) => weight is per cell-element c{n} (but equal for each array element for fixed n)
3. numel(weight) == numel(cell2mat(c)) => each array-element has its own weight...

Case one is easy, and case 3 unlikely to happen so at the moment I'm interested in case 2: How can I transform weight into a array such that M.*weight has the correct dimensions in the sum above? Of course an answer that shows another way to obtain a weighted averaged is appreciated as well.

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edit In fact, case 3 is even more trivial_{(what a tautology, apologies)} than case 1 if weight has the same structure as c.

Here's an example of what I mean for case 2:

c = { [1 2 3; 1 2 3], [4 8 3; 4 2 6] };
weight = [ 2, 1 ];

should return

meanArray = [ 2 4 3; 2 2 4 ]

(e.g. for the first element (2*1 + 1*4)/(2+1) = 2)

解决方案

After familiarizing myself with REPMAT, now here's my solution:

function meanArray = cellMean(c, weight)
% meanArray = cellMean(c, [weight=1])
% mean over the elements of a cell c, keeping matrix structures of cell
% elements etc. Use weight if given.

% based on http://stackoverflow.com/q/5197692/321973, courtesy of gnovice
% (http://stackoverflow.com/users/52738/gnovice)
% extended to weighted averaging by Tobias Kienzler
% (see also http://stackoverflow.com/q/5231406/321973)

dim = ndims(c{1});          %# Get the number of dimensions for your arrays
if ~exist('weight', 'var') || isempty(weight); weight = 1; end;
eins = ones(size(c{1})); % that is german for "one", creative, I know...
if ~iscell(weight)
    % ignore length if all elements are equal, this is case 1
    if isequal(weight./max(weight(:)), ones(size(weight)))
        weight = repmat(eins, [size(eins)>0 length(c)]);
    elseif isequal(numel(weight), length(c)) % case 2: per cell-array weigth
        weight = repmat(shiftdim(weight, -3), [size(eins) 1]);
    else
        error(['Weird weight dimensions: ' num2str(size(weight))]);
    end
else % case 3, insert some dimension check here if you want
    weight = cat(dim+1,weight{:});
end;

M = cat(dim+1,c{:});        %# Convert to a (dim+1)-dimensional matrix
sumc = sum(M.*weight,dim+1);
sumw = sum(weight,dim+1);
meanArray = sumc./sumw;  %# Get the weighted mean across arrays

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