A Fuzzy Deep Model Based on Fuzzy Restricted Boltzmann Machines for High-dimensional Data Classification

We establish a fuzzy deep model called the fuzzy deep belief net (FDBN) based on fuzzy restricted Boltzmann machines (FRBMs) due to their excellent generative and discriminative properties. The learning procedure of an FDBN is divided into a pretraining phase and a subsequent fine-tuning phase. In the pretraining phase, a group of FRBMs is trained in a greedy layerwise way: the first FRBM is trained by original samples, and the average values of the left and right probabilities produced by its hidden units are treated as the training data for subsequent FRBMs. The resulting FDBN is either a generative or a discriminative model depending on the choice of training a generative or a discriminative type of FRBM on top. Then, a hybrid learning approach is proposed to fine-tune this novel fuzzy deep model: the well pretrained fuzzy parameters are first defuzzified, and the FDBN with defuzzified parameters is fine-tuned by the wake-sleep or stochastic gradient descent algorithm. This hybrid strategy not only avoids learning an intractable fuzzy neural network, but also greatly improves the classification capability of the FDBN. The experimental results on MNIST, NORB, and 15 Scene databases indicate that the FDBN with the hybrid learning approach can handle high-dimensional raw images directly. It inherits the fine nature of the FRBM and outperforms some state-of-the-art discriminative models in classification accuracy. Moreover, it shows better capability of robustness than a deep belief net when encountering noisy data.