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Additional info for Artificial neural networks - methodological advances and biomedical applications
The application of an additional mR criterion with the existing MR criterion leads to mRMR selection criteria, where input variables are evaluated with the dual consideration of relevance, with respect to the output variable; and independence (dissimilarity), with respect to the other candidate variables (Ding & Peng, 2005). Embedded IVS considers regularisation (reducing the size or number) of the weights of a regression to minimise the complexity, while maintaining predictive performance. This involves the formulation of a training algorithm that simultaneously finds the minimum model error and model complexity, somewhat analogous to finding the optimum the AIC.
IVS algorithms can be broadly classified into three main classes: wrapper, embedded or filter algorithms (Blum & Langley, 1997; Guyon & Elisseeff, 2003; Kohavi & John, 1997), as shown in Figure 1. These different conceptual approaches to IVS algorithm design are illustrated in Figure 2. Wrapper algorithms, as shown in Figure 2(a), approach the IVS task as part of the optimisation of model architecture. The optimisation searches through the set, or a subset, of all possible combinations of input variables, and selects the set that yields the optimal generalisation performance of the trained ANN.
In filter designs, the single most relevant candidate variable is selected first, and then forward selection proceeds by iteratively identifying the next most relevant candidate and evaluating whether the variable should be selected, until the optimality criterion is satisfied. The approach is computationally efficient overall, and tends to result in the selection of relatively small input variable sets, since it considers the smallest possible models, and trials increasingly larger input variable sets until the optimal set is reached.