To demonstrate the ecological application of the MLP, we use brown trout redd data set. Sampling was done at 29 stations, distributed on six rivers, and subdivided into 205 morphodynamic units. Each unit corresponds to an area where depth, current, and gradient are homogeneous. They indicate the conditions met by the trout during its reproduction. Ten physical habitat variables (river width, area with suitable spawning gravel for trout per linear meter of river, surface velocity, water gradient, flow/width, depth, standard deviation of depth, bottom velocity, standard deviation of bottom velocity, and velocity/depth) were measured and used to predict density of trout redds per linear meter of streambed.
The variables have different ranges of values and different units. If a variable has relatively high values, it might dominate or paralyze the model. In this case, data transformation is recommended. In this example, input data were transformed by variance normalization. The data set consisting of 305 samples was divided into three sub-data-sets for training (103), validation (101), and testing (101).
The model was stabilized through the training of 280 iterations. Sum of square errors (SSEs; i.e., differences) between desired target values and estimated model outputs for training, validation, and testing is given in Figure 5.
Figure 5 shows relations between observed output values and calculated values by the trained MLP model, displaying regression determination coefficients (R ) 0.54, 0.67, and 0.49 for training, validation, and test, respectively
Training SSE Validation SSE Testing SSE
101 151 Iteration
Figure 5 Changes of SSEs during the training process of the MLP model.
(Figure 6). Their residuals, which are differences between observed values and estimated values, are also provided, showing relations between with estimated values (Figure 6). In all the three cases, residuals are scattered around zero lines.
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