Zhao Jianhua, Ma Xuan, Shi Lei, Wang Zhen
IEEE Trans Neural Netw Learn Syst. 2023 Dec;34(12):10683-10697. doi: 10.1109/TNNLS.2022.3170797. Epub 2023 Nov 30.
The bilinear probabilistic principal component analysis (BPPCA) was introduced recently as a model-based dimension reduction technique on matrix data. However, BPPCA is based on the Gaussian assumption and hence is vulnerable to potential outlying matrix-valued observations. In this article, we present a new robust extension of BPPCA, called BPPCA using a matrix variate t distribution ( t BPPCA), that is built upon a matrix variate t distribution. Like the multivariate t , this distribution offers an additional robustness tuning parameter, which can downweight outliers. By introducing a Gamma distributed latent weight variable, this distribution can be represented hierarchically. With this representation, two efficient accelerated expectation-maximization (EM)-like algorithms for parameter estimation are developed. Experiments on a number of synthetic and real datasets are conducted to understand t BPPCA and compare with several closely related competitors, including its vector-based counterpart. The results reveal that t BPPCA is generally more robust and accurate in the presence of outliers. Moreover, the expected latent weights under t BPPCA can be effectively used for outliers' detection, which is much more reliable than its vector-based counterpart due to its better robustness.
双线性概率主成分分析（BPPCA）是最近作为一种基于模型的矩阵数据降维技术被引入的。然而，BPPCA基于高斯假设，因此容易受到潜在的异常矩阵值观测的影响。在本文中，我们提出了一种新的BPPCA的稳健扩展方法，称为使用矩阵变量t分布的BPPCA（t BPPCA），它基于矩阵变量t分布构建。与多元t分布一样，这种分布提供了一个额外的稳健性调整参数，可以降低异常值的权重。通过引入一个伽马分布的潜在权重变量，这种分布可以分层表示。基于这种表示，开发了两种用于参数估计的高效加速期望最大化（EM）类算法。在一些合成数据集和真实数据集上进行了实验，以了解t BPPCA并与几个密切相关的竞争对手进行比较，包括其基于向量的对应方法。结果表明，在存在异常值的情况下，t BPPCA通常更稳健、更准确。此外，t BPPCA下的期望潜在权重可以有效地用于异常值检测，由于其更好的稳健性，比其基于向量的对应方法更可靠。
