IEEE Trans Neural Netw Learn Syst. 2012 Mar;23(3):492-503. doi: 10.1109/TNNLS.2012.2183006.
Probabilistic principal component analysis (PPCA) is a popular linear latent variable model for performing dimension reduction on 1-D data in a probabilistic manner. However, when used on 2-D data such as images, PPCA suffers from the curse of dimensionality due to the subsequently large number of model parameters. To overcome this problem, we propose in this paper a novel probabilistic model on 2-D data called bilinear PPCA (BPPCA). This allows the establishment of a closer tie between BPPCA and its nonprobabilistic counterpart. Moreover, two efficient parameter estimation algorithms for fitting BPPCA are also developed. Experiments on a number of 2-D synthetic and real-world data sets show that BPPCA is more accurate than existing probabilistic and nonprobabilistic dimension reduction methods.
概率主成分分析（PPCA）是一种流行的线性潜在变量模型，用于以概率的方式对 1-D 数据进行降维。然而，当用于 2-D 数据（如图像）时，PPCA 由于模型参数数量随后变得很大而受到维度灾难的影响。为了克服这个问题，我们在本文中提出了一种用于 2-D 数据的新的概率模型，称为双线性 PPCA（BPPCA）。这允许在 BPPCA 与其非概率对应物之间建立更紧密的联系。此外，还开发了两种用于拟合 BPPCA 的有效参数估计算法。对许多 2-D 合成和真实世界数据集的实验表明，BPPCA 比现有的概率和非概率降维方法更准确。
