Hi Sunil,
I understand that you want an explanation of the given MATLAB code, which involves transforming a label vector into an indicator matrix and computing the mean of each cluster, followed by assigning samples to clusters.
The first line of the code creates a sparse indicator matrix "E" from a label vector. The matrix "E" is of size "n" by "k", where "n" is the number of samples and "k" is the number of clusters. Each row corresponds to a sample, and each column corresponds to a cluster. The entry "E(i, j)" is 1 if sample "i" belongs to cluster "j" and 0 otherwise.
E = sparse(1:n, label, 1, n, k, n);
% "1:n" specifies the row indices.
% "label" specifies the column indices.
% "1" specifies the values to be placed at the specified indices.
The second line computes the mean "m" of each cluster. This is done by multiplying the data matrix "X" with a normalized indicator matrix. The normalization is achieved by dividing each column of "E" by the sum of the elements in that column, which is done using "spdiags".
m = X * (E * spdiags(1 ./ sum(E, 1)', 0, k, k));
% "spdiags" creates a sparse diagonal matrix.
% "1 ./ sum(E, 1)'" computes the inverse of the sum of each column.
% "m" is a matrix where each column represents the mean of a cluster.
The third line assigns each sample to the nearest cluster by calculating the distance between each sample and the cluster means. This is achieved using "bsxfun" to subtract the squared norm of the means from the dot product of the means and the data matrix "X". The "max" function identifies the cluster with the maximum value for each sample, effectively assigning the sample to that cluster.
[~, label] = max(bsxfun(@minus, m' * X, dot(m, m, 1)' / 2), [], 1);
% "m' * X" computes the dot product of the transposed mean matrix with "X".
% "dot(m, m, 1)' / 2" computes half the squared norm of each mean.
% "bsxfun(@minus, ...)" applies element-wise subtraction.
% "max(..., [], 1)" finds the cluster with the maximum value for each sample.
Refer to the documentation of "sparse" for creating sparse matrices: https://www.mathworks.com/help/matlab/ref/sparse.html
Refer to the documentation of "spdiags" for creating sparse diagonal matrices: https://www.mathworks.com/help/matlab/ref/spdiags.html
Refer to the documentation of "bsxfun" for applying element-wise operations: https://www.mathworks.com/help/matlab/ref/bsxfun.html
Refer to the documentation of "dot" for computing dot products: https://www.mathworks.com/help/matlab/ref/dot.html
Hope this helps!
