The bipartite graph is a ubiquitous data structure that can model the
relationship between two entity types: for instance, users and items, queries
and webpages. In this paper, we study the problem of ranking vertices of a
bipartite graph, based on the graph's link structure as well as prior
information about vertices (which we term a query vector). We present a new
solution, BiRank, which iteratively assigns scores to vertices and finally
converges to a unique stationary ranking. In contrast to the traditional random
walk-based methods, BiRank iterates towards optimizing a regularization
function, which smooths the graph under the guidance of the query vector.
Importantly, we establish how BiRank relates to the Bayesian methodology,
enabling the future extension in a probabilistic way. To show the rationale and
extendability of the ranking methodology, we further extend it to rank for the
more generic n-partite graphs. BiRank's generic modeling of both the graph
structure and vertex features enables it to model various ranking hypotheses
flexibly. To illustrate its functionality, we apply the BiRank and TriRank
(ranking for tripartite graphs) algorithms to two real-world applications: a
general ranking scenario that predicts the future popularity of items, and a
personalized ranking scenario that recommends items of interest to users.
Extensive experiments on both synthetic and real-world datasets demonstrate
BiRank's soundness (fast convergence), efficiency (linear in the number of
graph edges) and effectiveness (achieving state-of-the-art in the two
real-world tasks).

本文研究了基于图的连接结构和先前的节点信息（我们称之为查询向量）来排名双分图顶点的问题，并介绍了一种新的解决方案 BiRank，该方案通过迭代分配分数，最终收敛为唯一的静态排序，并且展示了其在实际应用上的灵活性和实用性。