Unique vectors in cell based on tolerance - matlab

Question

I'm trying to make a search algorithm which finds the unique columns of a cell based on a tolerance level. The unique function of MATLAB (R2012a), does not provide a tolerance input. Below is the code which I have so far; I have limited myself to checking uniqueness based on the first identity (j=1) for now, however, this needs to be updated later.
The output is: I obtain a store cell which contains all the vector expect the duplicates of [0;1;0]. However other duplicate are maintained (e.g. [1;0;-0.4])
clear all; close all; clc;
%%
tolerance=1e-6;
U_vector{1} = [0 1 0 1 1 0 1 0 1 1;
1 0 1 0 0 1 0 1 0 0;
0 -0.4238 0 0.4238 -0.4238 0 0.4238 0 0.8161001 -0.8161];
for i = 1:1:size(U_vector,2)
k=1;
store{i}(:,k) = U_vector{i}(:,k);
for j=1;%:1:(size(U_vector{i},2))
for m=j:1:(size(U_vector{i},2))
if (abs(U_vector{i}(:,j)-U_vector{i}(:,m)) >= tolerance)
k=k+1;
store{i}(:,k) = U_vector{i}(:,m);
end
end
end
end

Answer 1

There's an undocumented function to merge similar points, which works on rows too:
>> u = [0 1 0 1 1 0 1 0 1 1;
1 0 1 0 0 1 0 1 0 0;
0 -0.4238 0 0.4238 -0.4238 0 0.4238 0 0.8161001 -0.8161];
>> uMerged = builtin('_mergesimpts',u.',0.3).'
uMerged =
0 1.0000 1.0000 1.0000 1.0000
1.0000 0 0 0 0
0 -0.8161 -0.4238 0.4238 0.8161
Just get u = U_vector{1}; in your case, then pack the result in a cell too (out{1} = uMerged;).
Also, the function can take a vector tolerance indicating a tolerance for each column. From the command line message from this function:
Tolerance must be a scalar or a vector with the same number of columns as the first input 'X'.
So this works too:
uMerged = builtin('_mergesimpts',u.',[eps eps 0.3]).'
BTW: There will probably be an official function for this in the future, but we're not allowed to discuss :).

Answer 2

You do not need so many nested loops. This works with the sample you provided.
It uses a working table which is reduced as duplicates are found.
for ii = 1:1:size(U_vector,2)
A = U_vector{ii} ; %// create a working copy of the current table
store{ii} = [] ; %// initialize the result cell array
endOfTable = false ;
while ~endOfTable
store{ii}(:,end+1) = A(:,1) ; %// save the first column of the table
idx = logical( sum( abs( bsxfun(#minus,A(:,2:end),A(:,1))) >= tolerance ) ) ; %// find the indices of the columns not within the tolerance
A = A(:, [false idx] ) ; %// remove the duplicate columns in A
if size(A,2) < 2 ; endOfTable = true ; end %// exit loop if we reached the last column
end
%// store last column if it remained unmatched
if size(A,2) == 1
store{ii}(:,end+1) = A(:,1) ;
end
end
Which output with your data:
>> store{1}
ans =
0 1.0000 1.0000 1.0000 1.0000
1.0000 0 0 0 0
0 -0.4238 0.4238 0.8161 -0.8161

Answer 3

What about this?!:
u = cell2mat(U_vector{1});
i=1;
while i<=size(u,2)
test=repmat(u(:,i),1,size(u,2)); % compare matrix entries to current column i
differentCols = ~all(same); % column indices that are not equal to column i
differentCols(i)=1; % ensure one such column stays in u
u=u(:,differentCols); % new u-> keep different columns
i=i+1; % next column
end
u % print u
Seems to work for me, but no guarantees.