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Probabilistic Interpretations and Extensions for a Family of 2D PCA-style Algorithms

Recently there have been several 2D or higher-order PCAstyle dimensionality reduction algorithms, but they mostly lack probabilistic interpretations and are difficult to apply with, e.g., incomplete data. We propose a probabilistic framework to better understand the 2D and higher-order PCA-style algorithms, and show that it takes several existing algorithms as its (non-probabilistic) special cases. Efficient learning algorithms are proposed, and the stationary points are theoretically analyzed. Empirical studies on several benchmark data and real-world cardiac ultrasound images demonstrate the strength of this framework.