Fisher Discriminant analysis - issues with classes

Question

Adam 2023-2-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1904285-fisher-discriminant-analysis-issues-with-classes

评论： KSSV 2023-2-1

Writing a program to do Fisher's discriminant analysis. The data file I'm using is 3 x 500, so n = 3.

The dataset is given in form of a large matrix X = [X1X2 . . . XC] ∈ R n×Ck, where Xc ∈ R n×k is the data for each of the classes c = 1, 2, . . . , C. C = 5 and k = 100

1. Compute mean µc of each class, for c = 1, 2, . . . , C.

2. Compute within class scatter matrix Sw and between class scatter matrix Sb

3. Perform generalized eigen-value decomposition using [V,D] = eig(Sb,Sw,‘chol’);

4. Reorder solution using V = fliplr(V) and D = flipud(fliplr(D)).

5. Set U = V(:,1:d) and project Z = U T X. Plot of the eigenvalues and show a colored 2D scatter plot of the projected data.

What I have so far

% Define parameters
C = 5; % number of classes
k = 100; % number of features
[n,~] = size(X); % number of samples
d = 2; % dimension for projection
% Compute mean of each class
mu = zeros(k,C);
for c = 1:C
    Xc = X(:,(c-1)*k+1:c*k);
    mu(:,c) = mean(Xc,2);
end
% Compute within class scatter matrix Sw and between class scatter matrix Sb
Sw = zeros(k,k);
Sb = zeros(k,k);
for c = 1:C
    Xc = X(:,(c-1)*k+1:c*k);
    Nc = size(Xc,2);
    dmu = bsxfun(@minus, Xc, mu(:,c));
    Sw = Sw + dmu * dmu';
    Sb = Sb + Nc * (mu(:,c) - mean(mu,2)) * (mu(:,c) - mean(mu,2))';
end
% Perform generalized eigen-value decomposition
[V,D] = eig(Sb,Sw,'chol');
% Reorder solution
V = fliplr(V);
D = flipud(fliplr(D));
% Set U and project Z
U = V(:,1:d);
Z = U' * X;
% Plot the eigenvalues
figure;
plot(diag(D),'o');
title('Eigenvalues');
% Show a colored 2D scatter plot of the projected data
figure;
colors = ['r','g','b','c','m'];
for c = 1:C
    Zc = Z(:,(c-1)*n+1:c*n);
    scatter(Zc(1,:),Zc(2,:),[],colors(c));
    hold on;
end
title('2D scatter plot of the projected data');
end

i am getting this error message and I'm unsure how to fix it

Unable to perform assignment because the size of the left side is 100-by-1 and the size of the right side is 3-by-1.
Error in (line 12)
    mu(:,c) = mean(Xc,2);

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Answer 1

KSSV 2023-2-1

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https://ww2.mathworks.cn/matlabcentral/answers/1904285-fisher-discriminant-analysis-issues-with-classes#answer_1160970

在 MATLAB Online 中打开

You should use:

% Compute mean of each class
mu = zeros(k,C);  % k = 3 i.e. number rows and C is number of classes i.e.5 
for i = 1:k   % loop for each row 
    for j = 1:C   % loop for each class 
        idx = X(i,:)==j ; % get classes j in row i 
        mu(i,j) = mean(Xc(i,idx));
    end
end

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Adam 2023-2-1

在 MATLAB Online 中打开

Thanks! When I use that section I get the error message

Arrays have incompatible sizes for this operation.
Error in (line 22)
    Sw = Sw + dmu * dmu';

KSSV 2023-2-1

This is a different error. Your need to think on your code. You see, how I am selecting the classes. You are using indexing to select the classes. Why?

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