A fundamental problem in business and other applications is ranking items with respect to some notion of profit based on historical transactions. The difficulty is that the profit of one item not only comes from its own sales, but also from its influence on the sales of other items, i.e., the "cross-selling effect". In this paper, we draw an analogy between this influence and the mutual reinforcement of hub/authority web pages. Based on this analogy, we present a novel approach to the item ranking problem.We apply this ranking approach to solve two selection problems. In size-constrained selection, the maximum number of items that can be selected is fixed. In cost-constrained selection, there is no maximum number of items to be selected, but there is some cost associated with the selection of each item. In both cases, the question is what items should be selected to maximize the profit. Empirically, we show that this method finds profitable items in the presence of cross-selling effect.
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