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How to sample columns from matrix based on norm squared sampling?

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Clarisha Nijman
Clarisha Nijman on 19 Oct 2018
I want to do some random column sampling. This technique samples n columns of a matrix based on the probability distribution that is related to the norm of the column and the matrix. The code that I have samples the columns BUT WITH REPLACEMENT.But a column should be selected once. Can somebody give me some feedback on the code or any other suggestion. Thank you in advance.
This is the code:
Araw=importdata('File.csv'); A=Araw(:,2:size(Araw,2));%Columns that can be selected
m=norm(A,'fro');%compute frobenius norm n=10;%number of the columns that should be selected/sampled
%compute for each column the probability to be selected p=[]; %initiate list sith probabilities for i=1:size(A,2) prob=norm(A(:,i),2)/m; p=[p prob]; end
v = 1:size(A,2);%initiate list with column numbers c = cumsum([0,p(:).']);%compute cumulative distribution c = c/c(end); % make sure the cumulative is 1 [~,i] = histc(rand(1,n),c); r = v(i); % map to v values, r is the number of coluns that are selected
AScetched=A(:,r); ARate=sum(A,1)/size(A,2); AScetchedRate=sum(AScetched,2)/n;
d=ARate-AScetchedRate; MeanError=norm(d,2)/n;


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