HodgeRank is the limit of Perron Rank
arXiv:1201.46323 citationsh-index: 12
Originality Incremental advance
AI Analysis
Provides a theoretical connection between two ranking methods for researchers in pairwise comparison ranking.
The paper proves that HodgeRank is the limit of Perron Rank as a parameter k tends to 0, establishing a mathematical link between two pairwise ranking methods.
We study the map which takes an elementwise positive matrix to the k-th root of the principal eigenvector of its k-th Hadamard power. We show that as $k$ tends to 0 one recovers the row geometric mean vector and discuss the geometric significance of this convergence. In the context of pairwise comparison ranking, our result states that HodgeRank is the limit of Perron Rank, thereby providing a novel mathematical link between two important pairwise ranking methods.