Artificial neural networks - methodological advances and by Kenji Suzuki, editor

By Kenji Suzuki, editor

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By applying penalty terms to avoid large weights, or by using a model sparsity term within the objective function, the optimisation can effectively determine the optimum trade-off between model error and model complexity during training (Tikka, 2008). 34 Artificial Neural Networks - Methodological Advances and Biomedical Applications IVS is embedded within the EANN approach, since the optimisation will implicitly exclude input variables by setting the input connection weight values close to, or equal to zero.

In this case, the termination criterion is based upon the distribution of the error in PMI estimation, which is numerically approximated by a bootstrap approach (Sharma, 2000). The significance of the most relevant candidate is determined by direct comparison to the upper confidence bound on the estimation error. , 2009a): 1: Let X → φ (Initialisation) 2: While C = φ (Forward selection) 3: ˆ Y (X) Construct kernel regression estimator m 4: ˆ Y (X) Calculate residual output u = Y − m 5: 6: 7: 8: 9: 10: For each c ∈ C ˆ c (X) Construct kernel regression estimator m ˆ c (X) Calculate residual candidate v = c − m Estimate I (v; u) Find candidate cs (and vs ) that maximises I (v; u) For b = 1 to B (Bootstrap) 11: Randomly shuffle vs to obtain v∗s 12: Estimate Ib = I (v∗s ; u) 13: Find confidence bound Ib 14: If I (vs , u) > Ib 15: 16: 17: (95) (95) (Selection/termination) Move cs to X Else Break 18: Return selected input set X.

V. Rank the eigenvectors according to their eigenvalues. vi. Select the d PCs according to their eigenvalues. Selection of PCs is based on examining the eigenvalues of each PC, which correspond to the amount of variance explained by each PC, and thereby including only the significant PCs as input features. A common selection method is to rank the PCs and select all PCs whose eigenvalues exceed some threshold λ0 , or generate a plot of the cumulative eigenvalue as a function of the number of PCs, k, to ensure the selected components explain the desired Review of Input Variable Selection Methods for Artificial Neural Networks 31 amount of variance of Y.

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