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Furthermore, the deep structure of DNNs allows for a more efficient representation of many nonlinear transformations due to many layers of simple nonlinear processing.
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Since DNNs are powerful in transforming features through many layers of nonlinear transformations, it is common to splice the input features with a long context window to learn the temporal dynamic information automatically.
In the case of nonlinear transformations, the transformed model equations can be deduced following the same procedure.
To achieve a better performance on finding the most discriminative biomarkers or identifying infected subjects from the control group, in many neuroimaging applications, nonlinear transformation of the original tensor data should be considered.
Input x is processed through many layers of nonlinear transformation before posterior probabilities p(s|x) for CD states s are obtained from DNN output vector y by applying the softmax function element-wise to activations a at output layer L mathbf{y}^{(L)} = frac{1}{Z} exp(mathbf{a}^{(L }), (1).
The homotopy perturbation method is also combined with the well-known Laplace transformation method and the variational iteration method to produce a highly effective technique (homotopy perturbation transform method) for handling many nonlinear problems [51].
Neural networks construct a hierarchical representation where inputs are transformed into (potentially) nonlinear features that can undergo further nonlinear transformations.
"This is one of the many nonlinear methods known to produce quantum states of light," he said.
In particular, Newton's approach to the solution plays a fundamental role in many nonlinear algorithms.
The advantage of a DNN over one-hidden-layer NN is that the deep structure of the DNN allows much more efficient representation of many nonlinear transformations/functions [22].
PLSDA-softmax could overcome the class overlapping by nonlinear transformations.
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