Restricted Boltzmann Machine (RBM) is an importan- t generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vec- torized. This results in high-dimensional data and valu- able spatial information has got lost in vectorization. In this paper, a Matrix-Variate Restricted Boltzmann Machine (MVRBM) model is proposed by generalizing the classic RBM to explicitly model matrix data. In the new RBM model, both input and hidden variables are in matrix forms which are connected by bilinear transforms. The MVRBM has much less model parameters, resulting in a faster train- ing algorithm while retaining comparable performance as the classic RBM. The advantages of the MVRBM have been demonstrated on two real-world applications: Image super- resolution and handwritten digit recognition.
The Conditional Restricted Boltzmann Machine (CRBM) is a recently proposed model for time series that has a rich, distributed hidden state and permits simple, exact inference. We present a new model, based on the CRBM that preserves its most important computational properties and includes multiplicative three-way interactions that allow the effective interaction weight between two units to be modulated by the dynamic state of a third unit. We factor the three-way weight tensor implied by the multiplicative model, reducing the number of parameters from O(N3) to O(N2). The result is an efficient, compact model whose effectiveness we demonstrate by modeling human motion. Like the CRBM, our model can capture diverse styles of motion with a single set of parameters, and the three-way interactions greatly improve the model's ability to blend motion styles or to transition smoothly among them. In this paper a novel framework capable of both accurate predictions and classifications of dynamic images is introduced. The proposed technique makes of use of a novel combination of sparse coding, a feature extraction algorithm, and three-way weight tensor conditional restricted Boltzmann machines, a form of deep learning. Experiments performed on both the prediction and classification of various images show the efficiency, accuracy, and effectiveness of the proposed technique.