Finding rows that have only two unique clusters of values with a spread of +/- 1

Hello all,

Let us assume that there is a matrix as following:

Z=[a a a a b b; a a b b b a; a a b c b b]

Also assume that we do not know apriori where the rows with just two unique values will lie in a large matrix.I can extract the rows having only two unique elements easily by using unique function in a for loop.

for i=1:size(Z,1)
    Z(unique(Z(i,:))<=2,:)
end

Now if my matrix is the following:

Z=[a-1 a+1 a+1 a b-1 b; a-1 a b b+1 b a; a a+1 b-1 c b+1 b]

The first two rows have two unique cluster of values 'a' and 'b' with a spread of maximum +/- 1. How do I extract the two rows in this case?

Thanks!

Answer 1

[Akira Agata]

How about using uniquetol function?

The following is an example:

% Sample matrix (a = 5, b = 10, c = 15 in your matrix)
Z = [5-1 5+1 5+1 5 10-1 10; 5-1 5 10 10+1 10 5; 5 5+1 10-1 15 10+1 10];

delta = 2; % -> to detect unique value within +/-1 variation
idx = false(size(Z,1),1);

% Check whether each row has <=2 unique values within +/-1 variation or not
for kk = 1:size(Z,1)
  tol = delta/max(Z(kk,:));
  if numel(uniquetol(Z(kk,:),tol)) <= 2
    idx(kk) = true;
  end
end

% Extract the target rows
Z = Z(idx,:);

[Raghavasimhan Thirunarayanan]

Thank you. But should not delta be 1? Since uniquetol itself takes only the absolute?

[Akira Agata]

As shown in the help page, uniquetol returns uniqe values based on the following rule:

C = uniquetol(A, tol) returns the unique elements in A using tolerance tol. Two values, u and v, are within tolerance if

abs(u-v) <= tol*max(abs(A(:)))

So I set delta = 2, in order to let uniquetol judge [a-1, a, a+1] as only one unique value.

That means, if you set delta = 1, uniquetol judges [a-1, a, a+1] contains two unique values.

By the way, now one question arose in my mind.

If your matrix Z contains the row [a-1 a+1 b b b b], based on your rule, the number of unique value should be two? or three??

[Guillaume]

"But should not delta be 1? Since uniquetol itself takes only the absolute?"

A few things:

• By default uniquetol use relative difference
• If you use 1 as delta, then a-1 and a+1 are not considered equal since the difference is 2. Akira is correct that the delta should be 2.
• Rather than calculating the relative tolerance by rescaling the absolute tolerance delta by the max of the array, you can just tell uniquetol to use absolute tolerance with the DataScale option:

uniquetol(Z(kk, :), delta, 'DataScale', 1)

[Akira Agata]

Hi Guillaume-san,

Thank you for your additional comment for clarification. Also, thank you for adding a better solution!

[Guillaume]

Raghavasimhan Thirunarayanan's answer moved to comment here:

https://ch.mathworks.com/matlabcentral/answers/511225-finding-rows-that-have-only-two-unique-clusters-of-values-with-a-spread-of-1#comment_811024

@ Akira-san

It should be 2 if we do not know 'a' apriori and it differs by more than 2. But in this case since I know 'a', it should be 3. I was wondering how it will affect the above solution. I will try it out once I get home so that I can access matlab.

@Guillame.. Thanks I will try it out!