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1 function [Y, Loss] = separationOracleAUC(q, D, pos, neg, k)
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2 %
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3 % [Y,Loss] = separationOracleAUC(q, D, pos, neg, k)
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4 %
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5 % q = index of the query point
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6 % D = the current distance matrix
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7 % pos = indices of relevant results for q
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8 % neg = indices of irrelevant results for q
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9 % k = length of the list to consider (unused in AUC)
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10 %
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11 % Y is a permutation 1:n corresponding to the maximally
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12 % violated constraint
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13 %
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14 % Loss is the loss for Y, in this case, 1-AUC(Y)
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15
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16
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17 % First, sort the documents in descending order of W'Phi(q,x)
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18 % Phi = - (X(q) - X(x)) * (X(q) - X(x))'
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19
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20 % Sort the positive documents
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21 ScorePos = - D(pos,q);
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22 [Vpos, Ipos] = sort(full(ScorePos'), 'descend');
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23 Ipos = pos(Ipos);
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24
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25 % Sort the negative documents
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26 ScoreNeg = - D(neg,q);
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27 [Vneg, Ineg] = sort(full(ScoreNeg'), 'descend');
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28 Ineg = neg(Ineg);
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29
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30
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31 % How many pos and neg documents are we using here?
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32 numPos = length(pos);
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33 numNeg = length(neg);
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34 n = numPos + numNeg;
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35
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36
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37 NegsBefore = sum(bsxfun(@lt, Vpos, Vneg' + 0.5),1);
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38
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39 % Construct Y from NegsBefore
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40 Y = nan * ones(n,1);
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41 Y((1:numPos) + NegsBefore) = Ipos;
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42 Y(isnan(Y)) = Ineg;
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43
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44 % Compute AUC loss for this ranking
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45 Loss = 1 - sum(NegsBefore) / (numPos * numNeg * 2);
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46 end
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47
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