How to set the number of hidden-units [12-6-1-6-12] ?
How to control the flexibility of a curve: from almost linear components (under-fitting) to very complex curves (over-fitting)? Several ways are used to control neural network complexity: number of hidden nodes, number of iterations (early stopping), etc. In nonlinear PCA the most important parameter is weight-decay. Hidden units are not good for controlling the complexity because of the discrete scale: 2 or 3 nodes is a big difference, there is no option between. Best to have a reasonable large (or even too large) number of hidden units and control complexity by using weight-decay only. If not specified by 'units_per_layer', hidden units are set automatically to fit best the data dimension. Number of hidden units gives the potential of non-linearity and weight-decay is for controlling it! You can test different weight-decay values to check and avoid over-fitting. [pc,net,network]=nlpca(data,1,'weight_decay_coefficient',0.01)Low or zero means no restriction of complexity which can lead to over-fitting. A very high value (max 1) leads to under-fitting with the effect that we get only a linear component as in standard PCA. The optimum is somewhere between, from experience a good choose and default is 0.01 Inverse NLPCA and hierarchical order also have important impacts on controlling curve complexity. see Section 5.5.1 (page 51) of my PhD theses: http://opus.kobv.de/ubp/volltexte/2006/783/pdf/scholz_diss.pdf |
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