Bayesian Robust Principal Component Analysis
Bayesian Robust Principal Component Analysis
复制标题
贝叶斯稳健主成分分析
DOI：
10.1109/tip.2011.2156801
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发表时间：
2011-12-01
影响因子：
10.6
通讯作者：
Carin, Lawrence
中科院分区：
文献类型：
--
作者：
Ding, Xinghao;He, Lihan;Carin, Lawrence
一个层次贝叶斯模型被认为是一个矩阵分解成低秩和稀疏的组件，假设观察到的矩阵是一个叠加的两个。该矩阵被假设为噪声，具有未知的和可能非平稳的噪声统计。贝叶斯框架推断出噪声统计的近似表示，同时推断出低秩和稀疏离群值的贡献;该模型对广泛的噪声水平具有鲁棒性，而无需改变模型超参数设置。此外，贝叶斯框架允许利用矩阵中的附加结构。例如，在视频应用中，每行（或列）对应于一个视频帧，并且我们在矩阵中的连续行（对应于视频中的连续帧）之间引入马尔可夫依赖性。该马尔可夫过程的性质也推断基于观察矩阵，同时去噪和恢复的低秩和稀疏成分。我们将贝叶斯模型与最先进的基于优化的鲁棒PCA实现进行比较;考虑几个例子，我们证明了所提出的模型的竞争性能。
A hierarchical Bayesian model is considered for decomposing a matrix into low-rank and sparse components, assuming the observed matrix is a superposition of the two. The matrix is assumed noisy, with unknown and possibly non-stationary noise statistics. The Bayesian framework infers an approximate representation for the noise statistics while simultaneously inferring the low-rank and sparse-outlier contributions; the model is robust to a broad range of noise levels, without having to change model hyperparameter settings. In addition, the Bayesian framework allows exploitation of additional structure in the matrix. For example, in video applications each row (or column) corresponds to a video frame, and we introduce a Markov dependency between consecutive rows in the matrix (corresponding to consecutive frames in the video). The properties of this Markov process are also inferred based on the observed matrix, while simultaneously denoising and recovering the low-rank and sparse components. We compare the Bayesian model to a state-of-the-art optimization-based implementation of robust PCA; considering several examples, we demonstrate competitive performance of the proposed model.