A quadratic programming approach in estimating similarity relations

The problem of estimating how similar N objects are when they are compared with each other is investigated, using comparative judgments of all possible pairs of the N objects as data. The pairwise comparisons focus on the similarity relations instead of the relative importance of each object. A quadratic programming model is also proposed. It processes the similarity-based pairwise comparisons and determines the similarity relations among the N objects. The model has linear constraints; therefore it can be solved easily by transferring it into a system of linear equations