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How to group connected pairs

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Genevieve 2014년 8월 11일
댓글: Genevieve 2014년 8월 11일
Hi, I have a serie of recording instruments and I compute the correlation between the measurements of each instrument pair. This gives a square upper-triangular matrix of correlation coefficients (call it "cc"). I want to select the instruments that corresponds to correlation coefficients over some threshold "T".
This gives the row and column index of all the pairs of instrument that satisfy my condition. However, I want to add a consistency constraint, namely, I want to identify only the "connected pairs". For example, if I have the pairs (1,2), (2,3), (5,8),(8,10),(8,11),(11,6), (14,15), then I have the following groups of connected instruments: [1,2,3], [5,6,8,10,11] and [14,15].
I tried something like this, as a start:
for ip1=1:size(pp,1)-1
for ip2=ip1+1:size(pp,1)
if ~isempty(intersect(pp(ip1,:),pp(ip2,:)))
However, if I have more than 1 group with more than 2 connected instruments, then I would need to set ccpairs(ip1,ip2) to a different index so I can identify the groups. This double for loop is also very slow for the number of pairs I usually get (>100).
Does anybody have an idea of how to do this efficiently?

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Kelly Kearney
Kelly Kearney 2014년 8월 11일
There are several graph theory-related entries on the FEX that provide connected components algorithms. This one is a nice, self-contained version that I've used before.
% Example data
sub = [1 2; 2 3; 5 8; 8 10; 8 11; 11 6; 14 15];
ir = sub(:,1);
ic = sub(:,2);
% Find the connected components
nval = length(ir);
nnode = max([ir; ic]);
adj = sparse(ir, ic, ones(nval,1), nnode, nnode);
lbl = graph_connected_components(adj);
grp = accumarray(lbl', (1:nnode)', [max(lbl) 1], @(x) {x});
  댓글 수: 1
Genevieve 2014년 8월 11일
Elegant solution. It does exactly what I need. Thank you very much!

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