Reading a 1-dimensional Matlab array built on pairwise interactions - matlab

Question

Let's say I have a bunch of data with labels [0-9]. I want to gather information based on all the pairwise interactions of these data. To avoid redundancy, I do something like this:
a = zeros(45, 1);
pair = 1;
for i = 1:9
for j = (i+1):10
a(pair) = i * j;
pair = pair + 1;
end
end
If I want to examine everything in a I can loop through it in a 2-dimensional way using the pair, i, j structure. That's fine. But what if I want to programmatically examine only certain pairs? Is there some logic by which I can do something analogous to a(i,j), where a(i,j) is actually "the coefficients from the model that was trained on data classes i and j"?
Running Matlab_R2018b. For the curious, I'm doing this as part of a DAGSVM implementation.

Answer 1

You can store the input information along side the resulting vector.
a = zeros(45, 1);
pair = 1;
I = a;
J = a;
for i = 1:9
for j = (i+1):10
I(pair) = i;
J(pair) =j;
a(pair) = i * j;
pair = pair + 1;
end
end
res=[a,I,J];
Then using a function match the input values to a given pair using a tolerance for floating point values.
function Val = findVal(res,pair)
#pair = [i,j]
pairs = res(:,2:3);
ind = sum(abs(pairs-pair)<1e-6,2)==2;
if sum(ind) == 0
disp('No match found')
Val = NaN
else
Val = res(ind,1);
disp('pair')
disp(pair)
disp('value')
disp(Val)
end
endfunction
Now I generate two pairs, one that is in the set and the other that is not to show the usage of the function.
testpair = res(8,2:3)
badpair = [20,20]
findVal(res,testpair)
findVal(res,badpair)

Answer 2

You shouldn't need loops for this.
If i spans the range [1:I] and j spans the range [1:J], then you have K = I*J possible interactions half of which are redundant/permutations (A(i,j) = A(j,i)).
j = mod(pair, J); % "row"
i = floor((pair-1) / J) + 1; % "col"
pair = j + i * J; % linear index
To access only certain combinations you can just use this basic linear indexing.
a(pair) = a(j,i) = a(i,j) = i * j;
It sounds like you'd like to avoid self interaction & redundancy so only choose pairs where either i > j xor j > i which is equivalent to just creating either the upper triangular or lower triangular (as in your code above) matrix.