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Matrix Variate Restricted Boltzmann Machine (MVRBM) model could maintain valuable spatial information using much fewer model parameters than the classic RBM, thus it has been used in image analysis, pattern recognition and machine learning for data analysis. This paper introduces two extensions of MVRBM: Matrix Variate Deep Belief Network (MVDBN) and Multimodal MVRBM (MMVRBM), both of them are composed of two or more MVRBMs whose input and latent variables are in matrix form. The MVDBN and MMVRBM have much fewer model parameters and deeper layer with better features to avoid overfitting and more accurate model easier to be learned. We test their efficiency on two real-world applications: image super-resolution and handwritten digit recognition. The experiments show the feasibility and superiority of the proposed models.

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