We will show here that the principal eigenvector of a matrix is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison consistent or near consistent matrix. A positive reciprocal n by n consistent matrix W = (wij) satisfies the relation wik = wij wjk . If the principal eigenvector of W is w=(w1 , ... ,wn ) the entries of W may be written as wij = wi ...

Statistical estimation using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this article, we propose a general framework model the mutual interactions in network, which enjoys ample flexibility terms of parameterization. Under setup, show that maximum likelihood estimator for latent score vector subjects uniformly consistent under near-minimal con...

A tournament is a binary dominance relation on a set of alternatives. Tournaments arise in many contexts that are relevant to AI, most notably in voting (as a method to aggregate the preferences of agents). There are many works that deal with choice rules that select a desirable alternative from a tournament, but very few of them deal directly with incentive issues, despite the fact that gameth...

The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity dichotomy for Distinct Vectors based on the maximum (H) and the minimum (h) pairwise Hamming distance between matrix rows: Distinct Vectors can be solved in polyno...

Low-rank matrix completion (MC) has achieved great success in many real-world data applications. A latent feature model formulation is usually employed and, to improve prediction performance, the similarities between latent variables can be exploited by pairwise learning, e.g., the graph regularized matrix factorization (GRMF) method. However, existing GRMF approaches often use a squared L2 nor...

This study presents theoretical proof and empirical evidence of the reduction algorithm convergence for the distance-based inconsistency in pairwise comparisons. Our empirical research shows that the convergence very quick. It usually takes less than 10 reductions to bring the inconsistency of the pairwise comparisons matrix below the assumed threshold of 1/3 (sufficient for most applications)....

The pairwise-error probability upper bounds of space–time codes (STCs) in independent Rician fading channels are derived in this letter. Based on the performance analysis, novel code design criteria for slow and fast Rayleigh fading channels are developed. It is found that in fading channels, STC design criterion depends on the value of the possible diversity gain of the system. In slow fading ...

Motivation: Equipped with sophisticated biochemical measurement techniques we generate a massive amount of biomedical data that needs to be analyzed computationally. One long-standing challenge in automatic knowledge extraction is clustering. We seek to partition a set of objects into groups such that the objects within the clusters share common traits. Usually, we have given a similarity matri...