An Iterative Algorithm to Derive Priority From Large-Scale Sparse Pairwise Comparison Matrix

Abstract

Pairwise comparison matrix (PCM) is an important tool to rank items by deriving priorities and has been used in various applications. Though large-scale sparse PCMs appear frequently in today’s big data environment, it is hard for existing prioritization methods to handle large-scale sparse PCMs efficiently due to the curse of dimensionality. The goal of this article is to propose a new algorithm, bipartite graph iterative method (BGIM), to derive priorities from large-scale sparse PCMs. We first extended graph representations of PCMs to bipartite graphs. A transition matrix was induced by resource allocation on the bipartite graph. Finally, an iterative algorithm was designed to calculate priorities. The theoretical properties of the BGIM were analyzed to show its ability to derive priorities from large-scale sparse PCMs. Two experiments were conducted to validate the proposed approach. The numerical examples indicated that the BGIM can deal with traditional decision problems and derive reliable priorities with minimum Euclidean distance (ED) and minimum violation (MV) among the tested methods. The simulation examples suggested that the BGIM can not only derive reliable priorities from large-scale sparse PCMs but also require the least computation time compared with eight prioritization approaches. To demonstrate its applicability to real-world large-scale problems, we applied the BGIM to rank movies using MovieLens dataset with more than 100 000 ratings for 9125 movies. The results showed that the BGIM was the fastest approach and obtained the best ranking among the average ratings and the five prioritization methods.