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Learning with Partially Absorbing Random Walks
Xiao-Ming Wu · Zhenguo Li · Shih-Fu Chang · John Wright · Anthony Man-Cho So

Tue Dec 04 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor #None
We propose a novel stochastic process that is with probability $\alpha_i$ being absorbed at current state $i$, and with probability $1-\alpha_i$ follows a random edge out of it. We analyze its properties and show its potential for exploring graph structures. We prove that under proper absorption rates, a random walk starting from a set $\mathcal{S}$ of low conductance will be mostly absorbed in $\mathcal{S}$. Moreover, the absorption probabilities vary slowly inside $\mathcal{S}$, while dropping sharply outside $\mathcal{S}$, thus implementing the desirable cluster assumption for graph-based learning. Remarkably, the partially absorbing process unifies many popular models arising in a variety of contexts, provides new insights into them, and makes it possible for transferring findings from one paradigm to another. Simulation results demonstrate its promising applications in graph-based learning.

Author Information

Xiao-Ming Wu (Columbia University)
Zhenguo Li (Huawei Noah's Ark Lab, Hong Kong)
Shih-Fu Chang (Columbia University)
John Wright (Columbia University)
Anthony Man-Cho So (CUHK)

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