Find similar rows but not equal at the same matrix

Hi,

I have a mx3 matrix and need to find which rows are very close one another. For example

 [a b c
 d e f
 a b c+1e-8
 d e f
 g h i
 g h+1e-5 i
 ];

ans= [1,3 ; 5,6] %ignoring the rows that hasn't at least one similar. It's something like a min_tol to accept and an max_tol to reject

I've been thinking about tolerances with find(), unique, uniquetol(), intersection(?) or perform some calculations to get it, but i have only figure it out in ways that enlarge too much my data. Any guide Thanks!

[Stephen23]

Why are rows 2 and 4 not listed in your example output?

[Libros Construccion]

Because i don't want equals rows, just similar ones. unique() clear one of them, but i get row 2 outputted when i try it.

Answer 1

[Libros Construccion]

Hey, thanks!. I'll try to follow your guides. Maybe i can combine them with this, which is getting me where i want.

 A=[1 2 3; 1+1e-5 2 3; 1 2 3;1+1e-8 2 3];
simA=find(ismember(A,uniquetol(A,1e-6,'ByRows',true),'rows')==0);

ans=4

Answer 2

[Jan]

pdist replies the pairwise distances between the rows. Then you can filter out the values:

D     = pdist(Data);
Match = (D ~= 0 & D < 1e-4);

Without the Statistics Toolbox you can calculate the distance matrix manually also. If the input is not huge, a loop might be useful also, because you can remove the unwanted element directly:

n       = 1000;
data    = rand(n, 3);
check   = true(1, n);
result  = zeros(n, 2);  % Pre-allocate
iResult = 0;
limit   = 1e-4 ^ 2;     % Squared limit to avoid SQRT
for k = 1:n
  if check(k)  % Not included before (is this wanted?!)
    dist  = sum(data(k, :) - data(k+1:n, :)).^2, 2);
    match = find(dist > 0 & dist < 1e-2);
    ...
  end
end

Sorry, I cannot finish this code, because I found some open questions. What should happen for:

a b c
d e f
a b c+1e-4
a+1e-4 b c

Or if the limit is 1e-4, what about this:

a b c
a b c+1e-4
a b c+2e-4

What is the wanted result?

Why does the output have less columns than the input?