标题： 关于LexRank问题的$l_1$-鲁棒解的一些备注 显示英文标题

标题： Some Remarks on the $l_1$-Robust Solution of LexRank Problem

摘要： 基于图的排名方法，如LexRank，在自然语言处理（NLP）应用如文本摘要中是基础性的，因为它们衡量文本单元的相对重要性。 在最近排名方法用于增长和动态图的进展基础上，我们开发了一种稳健的LexRank变体，该变体在具有不确定和扩展结构的随机相似性图上运行。 我们的方法引入了一种基于$l_1$的公式，该公式捕捉了转移概率和图大小中的模糊性，同时保持稀疏性。 产生的非凸问题由一个线性规划上界，提供了一个可行且可解释的近似。 显示英文摘要

摘要： Graph-based ranking methods, such as LexRank, are fundamental in Natural Language Processing (NLP) applications like text summarization, as they measure the relative importance of textual units. Building on recent advances in ranking methods for growing and dynamic graphs, we develop a robust variant of LexRank that operates on stochastic similarity graphs with uncertain and expanding structure. Our approach introduces a novel $l_1$-based formulation that captures ambiguity in both transition probabilities and graph size, while maintaining sparsity. The resulting non-convex problem is upper-bounded by a linear program, providing a tractable and interpretable approximation.