Centre for Quantum Computation and Intelligent Systems, the Faculty of Engineering and Information Technology, University of Technology, Sydney, Ultimo, NSW 2007, Australia.
IEEE Trans Image Process. 2012 Dec;21(12):4830-43. doi: 10.1109/TIP.2012.2211372. Epub 2012 Aug 2.
Principal component analysis (PCA) computes a succinct data representation by converting the data to a few new variables while retaining maximum variation. However, the new variables are difficult to interpret, because each one is combined with all of the original input variables and has obscure semantics. Under the umbrella of Bayesian data analysis, this paper presents a new prior to explicitly regularize combinations of input variables. In particular, the prior penalizes pair-wise products of the coefficients of PCA and encourages a sparse model. Compared to the commonly used l1regularizer, the proposed prior encourages the sparsity pattern in the resultant coefficients to be consistent with the intrinsic groups in the original input variables. Moreover, the proposed prior can be explained as recovering a robust estimation of the covariance matrix for PCA. The proposed model is suited for analyzing visual data, where it encourages the output variables to correspond to meaningful parts in the data. We demonstrate the characteristics and effectiveness of the proposed technique through experiments on both synthetic and real data.
主成分分析 (PCA) 通过将数据转换为少数几个新变量来计算简洁的数据表示，同时保留最大变化。然而，新变量难以解释，因为每个变量都与所有原始输入变量相结合，并且语义模糊。在贝叶斯数据分析的保护伞下，本文提出了一种新的先验方法来明确正则化输入变量的组合。具体来说，该先验惩罚 PCA 系数的两两乘积，并鼓励稀疏模型。与常用的 l1 正则化相比，所提出的先验鼓励在原始输入变量中具有内在组的结果系数中的稀疏模式保持一致。此外，所提出的先验可以解释为恢复 PCA 的协方差矩阵的稳健估计。所提出的模型适合于分析视觉数据，其中它鼓励输出变量与数据中的有意义部分相对应。我们通过对合成数据和真实数据的实验证明了所提出的技术的特点和有效性。
