Calculate median with accumarray

Hello,

I have an array with two columns. The rows are sorted by the values of the first column and then indexed by the use of histc. Now I want to calculate the median of every interval for the columns. Procedure for the first column is clear with accumarray but before calculating the median for the second column I have to sort every interval, right? How can I do this?

groupMedian = accumarray(ID,Measurement(:,2),[],@median);

Answer 1

[Walter Roberson]

No, you do not need to sort each interval. Just make sure that each interval is given a distinct ID vector row.

[unique_col1, ~, ID] = unique(Measurement(:,1));
group_median = accumarray(ID, Measurement(:,2), [], @median);
output = [unique_col1, group_median];

No sorting by column 1 beforehand is needed (unless you happen to need that output for a different purpose.)

Answer 2

[Bruno Luong]

Internally the median command "sort" input data and take a middle element of the sorted array (or average of two left and right for even length array). Some other technique exists, such as partial-sorting which has better complexity than SORT (I don't think MATLAB use it however the last time I check it)

You, as user don't have to sort it when calling median, that's how the function like this exists at the first hand.

Answer 3

[franky]

I read in some statistic books that it is necessary to sort the values before calculating the median. After indexing the columns column 1 is sorted but values with the same ID in column 2 are not necessary sorted. So I think this is a problem or does Matlab sort the values in the median function automatically?

[Walter Roberson]

It is not required to sort the values before calling median()

data = randi(20, 1, 1000);
>> median(data)
ans =
    11
>> median(data(randperm(length(data))))
ans =
    11