MATLAB find and apply function to values of repeated indices

Question

I have a 352x11 matrix, indexed by column 1 with 10 data points. Some of the index values are repeated. I\'d like to find the repeated indices and calculate the mean data po

Answer 1

You might find accumarray with @mean useful:

Assuming first column holds values 1 .. k for some k <= size(x,1), you may compute each column of the output using

col = accumarray( x(:,1), x(:,2), [], @mean ); % second column

Answer 2

You can apply accumarray to multiple columns as shown here

labels = x(:,1) - min(x(:, 1)) + 1; 
labels = [repmat(labels(:),size(x,2),1), kron(1:size(x,2),ones(1,numel(labels))).'];             
totals = accumarray(labels,x(:),[], @mean);

This is adapted from Gnovice's code.

To get it to work for your code you then need to delete all the zeros in the front

totals(find(mean((totals == zeros(size(totals)))')), :) = [];

which results in the desired

   26.0000   77.5700   17.9735   32.7200
   27.0000   40.5887   16.6100   31.5800
   28.0000   48.0609   22.8699   44.2100
   29.0000   95.3448   19.0000   37.7300
   30.0000   82.7273   30.4394   39.1400

Answer 3

A more general approach would employ unique to find the unique index values:

[U, ix, iu] = unique(x(:, 1));

and then accumarray:

[c, r] = meshgrid(1:size(x, 2), iu);
y = accumarray([r(:), c(:)], x(:), [], @mean);

Explanation

The input values to process are actually the second parameter of accumarray.

The first parameter of accumarray is a matrix, each row being a set of indices in the (accumulated) output matrix, and it corresponds to a value from the matching row in the vector given as the second parameter.

Think of the output as a cell array. The second parameters are the input values, and each row in the first parameter tells in which cell of the output matrix accumarray should store the corresponding input value. When output "cell array" is finished, a function (mean in our case) is applied to each cell.

Example

Here's a short example with a smaller matrix:

x = [27, 10, 8;
     28, 20, 10;
     28, 30, 50];

We find the unique values by:

[U, ix, iu] = unique(x(:, 1));

Vector U stores the unique values, and iu indicates which index of the value associated with each row (note that in this solution we have no use for ix ). In our case we get that:

U = 
    27
    28

iu =
    1
    2
    2

Now we apply accumarray:

[c, r] = meshgrid(1:size(x, 2), iu);
y = accumarray([r(:), c(:)], x(:), [], @mean);

The fancy trick with meshgrid and [r(:), c(:)] produces a set of indices:

[r(:), c(:)] =
     1     1
     2     1
     2     1
     1     2
     2     2
     2     2
     1     3
     2     3
     2     3

and these are the indices for the input values x(:), which is a column-vector equivalent of x:

x(:) =
    27
    28
    28
    10
    20
    30
     8
    10
    50

The process of accumulation:

• The first value 27 goes to cell <1,1> in the output matrix.
• The second value 28 goes to cell <2,1> in the output matrix.
• The third value 28 goes to cell <2,1> in the output matrix.

See what just happened? Both values 28 get accumulated in the same cell (and eventually they will be averaged). The process continues:

• The fourth value 10 goes to cell <1,2> in the output matrix.

and so on...

Once all values are stored in cells, the function mean is applied on each cell and we get the final output matrix:

y =
    27    10     8
    28    25    30

Answer 4

Given you input

x = [ ...
    26   77.5700   17.9735   32.7200; ...
    27   40.5887   16.6100   31.5800; ...
    28   60.4734   18.5397   33.6200; ...
    28   35.6484   27.2000   54.8000; ...
    29   95.3448   19.0000   37.7300; ...
    30   82.7273   30.4394   39.1400];

You can create an array of indexes where duplicated vgalues share the same index, using the third output of unique.

%Get index of unique values (1 - N)
[~, ~, ix] = unique(x(:,1))

Then you can use this array to rebuild your matrix, combining duplicated values with the function of your choice.

%Use accumarry to rebuild the matrix one column at a time
result = [...
    accumarray( ix, x(:,1), [], @max )  ...  %Many functions works here, as all inputs are the same.  E.G.  @mean, @max, @min
    accumarray( ix, x(:,2), [], @mean ) ...  %Use mean to combine data, per problem statement.
    accumarray( ix, x(:,3), [], @mean ) ...
    accumarray( ix, x(:,4), [], @mean ) ...
    ]