Hello everyone? I have a problem related with sorting and grouping of elements in a matrix, but the problem is a very specific one?

I will give an example to illustrate my problem. Consider a matrix

A= [1 2; 
    2 6;
    6 1;
    3 2];

Now the elements in each row are there because they have some relationship with each other. For example here, in row 1, there is element 1 and element 2, which means that element 1 and element 2 are related with each other, somehow. Similarly row 2 suggests that element 2 is also related with element 6 and row 3 suggests that element 6 is also related with element 1, and finally row 4 suggests that element 2 is also related with element 3. Since from the first three rows we can deduce that elements 1 2 and 6 are related with each other, so that should be grouped together. Element 3 is only related with 2, but not with 1 and 6 and hence can't be grouped with them. So my outcome should be A1=[1 2 6;3 2]; Please note that I have to apply the same logic on a big matrix, with hundreds of rows. The matrices I am working with have sizes (n*2), n=number of rows and 2 columns. Help would be appreciated.

Thank you!

[Image Analyst]

Can you not be so secretive and share the bigger picture? For example, like the first column is the age of the male child in the family and the second column is the age of the female child, or whatever. What does "related" mean? in the larger context? I see that you mean it to mean if any number is "connected to" the other number, regardless of what row that connection/pairing happens on, but I'd still like to know the big picture. For example, maybe you could use the gray level cooccurrence matrix, or region growing, or connected components labeling, or something, but I don't really know enough to know if an efficient higher level function like that would work or not. Or another possibility I see is making a graph (node network) out of it and trying to see how many unconnected graphs there are.

Answer 1

[Walter Roberson]

s = max(A(:));
B = sparse(A(:,1), A(:,2), 1, s, s);
B = max(B, B.');  %make it symmetric

relates = arrayfun(@(COL) find(B(:,COL)), 1:s, 'Uniform', 0);

[AAQIB PEERZADA]

Thank you for replying. I tried these lines of code, but it seems it also groups element 3 with elements 1,2 and 6. I realize its a cell array, but it should group only elements 1,2 and 6, which I can then extract as a single group. Element 3 should be a separate cell element, not grouped with any other element.

Thanks

[Image Analyst]

I'm thinking graph() might somehow be involved. So your requirement for a separate graph is that every node is connected to every single other node, but since your 3 is only connected to 2, it should not be part of the same graph even though 2 is connected to 1 and 6. I'm not real knowledgeable on nodes, tree, graphs, networks, topology, etc. but I think the solution might come from that field.

[Walter Roberson]

Okay, so grab https://www.mathworks.com/matlabcentral/fileexchange/47524-find-maximal-cliques-for-large---sparse-network and use

   cliques = ELSclique(B);

Each column of the result masks out one complete subgraph. For example, a column containing [1; 1; 0; 0; 0; 1] indicates that nodes 1, 2, and 6 form a complete graph, all "relating" to each other.

[AAQIB PEERZADA]

Ok I used the function but its not giving me what I need. after using cliques=ElSclique(B);, on this examople matrix I get a something like this

[Walter Roberson]

relates = arrayfun(@(COL) find(cliques(:,COL)), 1:size(cliques,2), 'Uniform', 0);

[AAQIB PEERZADA]

Thank you very much. This works. I appreciate your help.

[Image Analyst]

This is why Walter is the awesome master of MATLAB. He seems to know everything. You can also vote for his answer to give him double points for helping you.

[AAQIB PEERZADA]

I did vote for his answer. He sure is. I want his help again. Walter your code works fine but now i need to modify it a little bit. I need to update the "relates" array in a loop and get the related groups at every iteration. for example

    for h=1:1:10
z = max(Clusters(:));
B = sparse(Clusters(:,1), Clusters(:,2), 1, z, z);
B = max(B, B.');
cliques = ELSclique(B);
relates = arrayfun(@(COL) find(cliques(:,COL)), 1:size(cliques,2), 'Uniform', 0); 
 end

I am updating my "Clusters" matrix at every iteration and I need to get the "relates" array at each iteration also. Basically what I did previously was just at one instant with my "Clusters" matrix constant. Now my "Clusters" matrix updates itself at each iteration and I need to get the maximal cliques at each iteration. Can you help me in modifying this code? Thanks