Integer linear programming for transforming pairwise based results to the original ratings

Many pairwise models are proposed for ranking problems in the field of information retrieval. Classification problems in the field of data mining also use pairwise comparison. However, conventionally, these pairwise approaches are evaluated based evaluation metrics. The original rating for a single document or instance is not explained faithfully, which makes these algorithms cannot be evaluated by standard evaluation metrics, such as Mean Average Precision and Normalized Discounted Cumulative Gain for ranking models. In this research, the focus is on how to transform pairwise based results to the original ratings. Particularly, an integer linear programming model is formulated for this problem. In this algorithm, the objective is to minimize the number of conflicts for the predicted pairwise based relationship between instances by the assignment of rating values. An example is presented in order to clarify the proposed integer linear programming method. It validates the possibility to transform pairwise based results to the original ratings, which make them to be evaluated by standard evaluation metrics.