不同类别的Matlab协方差矩阵计算

Question

I've got 2 different files, one of them is an input matrix (X) which has 3823*63 elements (3823 input and 63 features), the other one is a class vector (R) which has 3823*1 elements; those elements have values from 0 to 9 (there are 10 classes).

I have to compute covariance matrices for every classes. So far, i could only compute mean vectors for every classes with so many nested loops. However, it leads me to brain dead.

Is there any other easy way?

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There is the code for my purpose (thanks to Sam Roberts):

xTra = importdata('optdigits.tra');
xTra = xTra(:,2:64); % first column's inputs are all zero

rTra = importdata('optdigits.tra');
rTra = rTra(:,65); % classes of the data

c = numel(unique(rTra));

for i = 1:c
    rTrai = (rTra==i-1); % Get indices of the elements from the ith class
    meanvect{i} = mean(xTra(rTrai,:)); % Calculate their mean
    covmat{i} = cov(xTra(rTrai,:)); % Calculate their covariance
end

Answer 1

Does this do what you need?

X = rand(3263,63);
R = randi(10,3263,1)-1;

numClasses = numel(unique(R));

for i = 1:numClasses
    Ri = (R==i); % Get indices of the elements from the ith class
    meanvect{i} = mean(X(Ri,:)); % Calculate their mean
    covmat{i} = cov(X(Ri,:)); % Calculate their covariance
end

This code loops through each of the classes, selects the rows of R that correspond to observations from that class, and then gets the same rows from X and calculates their mean and covariance. It stores them in a cell array, so you can access the results like this:

% Display the mean vector of class 1
meanvect{1}

% Display the covariance matrix of class 2
covmat{2}

Hope that helps!

Answer 2

Don't use mean and sum as a variable names because they are names of useful Matlab built-in functions. (Type doc mean or doc sum for usage help)

Also cov will calculate the covariance matrix for you.

You can use logical indexing to pull out the examples.

covarianceMatrices = cell(m,1);
for k=0:m-1
    covarianceMatrices{k} = cov(xTra(rTra==k,:));
end

One-liner

covarianceMatrices = arrayfun(@(k) cov(xTra(rTra==k,:)), 0:m-1, 'UniformOutput', false);

Answer 3

First construct the data matrix for each class. Second compute the covariance for each data matrix.

The code below does this.

% assume allData contains all the data you've read in, each row is one data point
% assume classVector contains the class of each data point
numClasses = 10;
data = cell(10,1);       %use cells to store each of the data matrices
covariance = cell(10,1); %store each of the class covariance matrices
[numData dummy] = size(allData);

%get the data out of allData and into each class' data matrix
%there is probably a nice matrix way to do this, but this is hopefully clearer
for i = 1:numData
  currentClass = classVector(i) + 1; %Matlab indexes from 1
  currentData = allData(i,:);
  data{currentClass} = [data{currentClass}; currentData];
end

%calculate the covariance matrix for each class
for i = 1:numClasses
  covariance{i} = cov(data{i});
end