Automatic Relevance Determination in Nonnegative Matrix Factorization with the β-Divergence
Automatic Relevance Determination in Nonnegative Matrix Factorization with the β-Divergence
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DOI：
10.1109/tpami.2012.240
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发表时间：
2013-07-01
影响因子：
23.6
通讯作者：
Fevotte, Cedric
中科院分区：
文献类型：
--
作者：
Tan, Vincent Y. F.;Fevotte, Cedric
本文研究了非负矩阵分解（NMF）中潜在维数的估计。散度是一组代价函数，它包括欧氏距离的平方、Kullback-Leibler （KL）和Itakura-Saito （is）散度作为特例。学习模型顺序很重要，因为它对于在数据保真度和过拟合之间取得适当的平衡是必要的。我们提出了一种基于自动相关性确定（ARD）的贝叶斯模型，其中字典矩阵的列和激活矩阵的行通过其先验中的公共尺度参数绑定在一起。针对最大后验估计问题，提出了一组优化最小化算法。在推理过程中，尺度参数的子集被驱动到一个小的下界，具有修剪相应的杂散分量的效果。通过对合成数据、游泳者数据集、音乐分解示例和股票价格预测任务进行大量实验，我们证明了算法的有效性和鲁棒性。
This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the beta-divergence. The beta-divergence is a family of cost functions that includes the squared euclidean distance, Kullback-Leibler (KL) and Itakura-Saito (IS) divergences as special cases. Learning the model order is important as it is necessary to strike the right balance between data fidelity and overfitting. We propose a Bayesian model based on automatic relevance determination (ARD) in which the columns of the dictionary matrix and the rows of the activation matrix are tied together through a common scale parameter in their prior. A family of majorization-minimization (MM) algorithms is proposed for maximum a posteriori (MAP) estimation. A subset of scale parameters is driven to a small lower bound in the course of inference, with the effect of pruning the corresponding spurious components. We demonstrate the efficacy and robustness of our algorithms by performing extensive experiments on synthetic data, the swimmer dataset, a music decomposition example, and a stock price prediction task.