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Speedup Matrix Completion with Side Information: Application to Multi-Label Learning
Miao Xu · Rong Jin · Zhi-Hua Zhou

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor #None
In standard matrix completion theory, it is required to have at least $O(n\ln^2 n)$ observed entries to perfectly recover a low-rank matrix $M$ of size $n\times n$, leading to a large number of observations when $n$ is large. In many real tasks, side information in addition to the observed entries is often available. In this work, we develop a novel theory of matrix completion that explicitly explore the side information to reduce the requirement on the number of observed entries. We show that, under appropriate conditions, with the assistance of side information matrices, the number of observed entries needed for a perfect recovery of matrix $M$ can be dramatically reduced to $O(\ln n)$. We demonstrate the effectiveness of the proposed approach for matrix completion in transductive incomplete multi-label learning.

Author Information

Miao Xu (Nanjing University)
Rong Jin (Michigan State University (MSU))
Zhi-Hua Zhou (Nanjing University)

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