A Fast Augmented Lagrangian Algorithm for Learning Low-Rank Matrices
A Fast Augmented Lagrangian Algorithm for Learning Low-Rank Matrices
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发表时间：
2010-06
影响因子：
4
通讯作者：
Ryota Tomioka;Taiji Suzuki;Masashi Sugiyama;H. Kashima
中科院分区：
文献类型：
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作者：
Ryota Tomioka;Taiji Suzuki;Masashi Sugiyama;H. Kashima
本文提出了一种通用的、有效的低秩矩阵学习算法。该算法具有超线性收敛性，并且可以保持学习矩阵的紧凑分解表示，而无需事先指定秩。此外，我们表明，该框架可以很容易地推广到学习多个矩阵和一般谱正则化的问题。从经验上讲，我们可以在大约5分钟内从120万个观测值中恢复10，000 × 10，000矩阵。此外，我们表明，在一个脑机接口问题，该方法可以加快优化两个数量级对传统的投影梯度法，并产生更可靠的解决方案。
We propose a general and efficient algorithm for learning low-rank matrices. The proposed algorithm converges super-linearly and can keep the matrix to be learned in a compact factorized representation without the need of specifying the rank beforehand. Moreover, we show that the framework can be easily generalized to the problem of learning multiple matrices and general spectral regularization. Empirically we show that we can recover a 10,000×10,000 matrix from 1.2 million observations in about 5 minutes. Furthermore, we show that in a brain-computer interface problem, the proposed method can speed-up the optimization by two orders of magnitude against the conventional projected gradient method and produces more reliable solutions.