In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k-dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random walks on simplicial complexes in the context of a semi-supervised learning problem. Specifically, we consider a label propagation algorithm on oriented edges, which applies to a generalization of the partially labelled classification problem on graphs. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 379-405, 2016.

中文翻译：

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随机游走于简单复数和谐波。

在本文中，我们介绍了一类具有单纯形复合体吸收状态的随机游动。给定维数为d的单纯复形，定义了具有吸收状态的随机游走，该游走与k维拉普拉斯算子在1≤k≤d时的谱有关。我们研究了在半监督学习问题的背景下，对单纯形复合体进行随机游动的示例。具体来说，我们考虑在定向边缘上的标签传播算法，该算法适用于图上部分标记的分类问题的一般化。©2016 Wiley Periodicals，Inc.随机结构。Alg。，49，379-405，2016。