I was reading an article called "Ensemble learning in recommender systems: combining multiple user interactions for ranking personalization" where they explain a method they use called "BPR Optimization Criterion" to develop their own algorithm, and also they explain that BPR's authors apply a technique to calculate the order of relative item-item relevance for the same user to obtain a personalized ranking.
Basically, the first matrix contains only positive interaction of the user and the item, '?' is used for unknown interaction that may be positive, negative or not interaction at all. Then they compare each pair of items for each user, so if the user has interaction with the item i and has not interacted with the item j, then the user prefer i over j. But when they express that on the secondary matrix, it's all the opposite, it appears a minus sign for interaction i1,j2 and i1,j3.
So I wonder if the image is wrong or I'm missing something. Thanks.