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224    CHAPTER 11 Deep Learning Approaches to Electrophysiological

























                         FIGURE 11.2
                         Deep belief network (DBN) architecture composed by stacked restricted Boltzmann
                         machines (RBMs). Each RBM consists of a visible layer v and a single hidden layer h n .
                         RBM 1 is trained using the input data as visible units. The hidden layer h 2 of RBM 2 is trained
                         using the output of the previous trained layer h 1 of the RBM 1 . The output of h 2 is the input of
                         the next RBM 3 and so on. The trained layers h 1 , h 2 . h n form the stacked architecture.
                         Finally, the whole DBN is fine-tuned with standard back propagation algorithm.


                         3.2 STACKED AUTOENCODERS
                         The stacked autoencoders architecture is similar to DBNs, where the main compo-
                         nent is the autoencoder (Fig. 11.3) [6]. An autoencoder (AE) is an NN trained with
                         unsupervised learning whose attempt is to reproduce at its output the same config-
                         uration of input. A single hidden layer with the same number of inputs and outputs
                         implements it. AE consists of two main stages: compression of the input space into a
                         lower dimension space (encoding) and reconstruction of the input data from the
                         compressed representation (decoding). In a stacked architecture, the encoded pattern
                         is used as input for training the successive AEs. The SAE ends with an output layer
                         trained with supervised criterion. As DBN, the whole network can be fine-tuned to
                         improve classification performance.

                         3.3 CONVOLUTIONAL NEURAL NETWORKS
                         Convolutional Neural Networks (CNN) are an alternative type of DNN that allow to
                         model both time and space correlations in multivariate signals. They are attractive as
                         they explicitly consider and take advantage of input topology. In SAE, for example,
                         the inputs can be organized in any order without affecting the performance of the
                         model. In biomedical signal processing, however, spectral and time-frequency
                         representations of the original signals show strong correlations: modeling local
                         correlations is easy with CNNs through weight sharing. CNNs are inspired from
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