Neural network implementation

Modelling inputs:

Three inputs were generated to model the forage nutrients:

1. The full range - The three ancillary data layers and the 68 layers from the continuum-removed CAO spectral dataset were stacked to create a 71 node input layer.

Chapter 6. Savanna forage quality mapped in the dry season

2. The reduced range - the 68 band, continuum-removed CAO Alpha spectral dataset was run through a principal component analysis. Us- ing a combination of the eigenvalues and eigenvectors, the first five principal component layers were selected. These layers accounted for 98% of the variation within the CAO Alpha data. Visualisation of the principal components also showed that above the fifth component traces of the cross-track illumination were evident. This gave further support to the inclusion of only the first five components. Together with the ancillary data a stack of 8 nodes was created for this input layer

3. The causal range - A literature study revealed that, within this spec- tral range, there were absorption features associated with variations in nitrogen concentration (see Knox et al. [2010]). Wavelengths lo- cated at 422, 432, 460, 639, 715, 724, 913 and 1016 nm [Curran, 1989; Mutanga et al., 2004c] were identified and these were used in com- bination with the three ancillary data layers as input for a nitrogen prediction model, creating 11 nodes for the input dataset.

Given no causal absorption features were identified for phosphorus and fibre within the CAO Alpha spectral range, network modelling was applied using only the full and reduced spectrum range data as input for modelling.

Model training and selection:

A 3-layer back propagation perceptron network, based on the algorithm of Rumelhart et al. [1986] was implemented (programmed in ENVI\IDLr). Unlike widely used linear empirical methods (e.g. stepwise regression), the implementation of neural networks is stochastic and requires an iterative process to select the best models. Networks are prone to over-learning, resulting in over-fitted models and models that are unable to generalise to new datasets [Chen et al., 2007; Skidmore et al., 1997], therefore the use of a test and training set for model evaluation is essential. The most challenging aspect to applying neural networks is to determine the models that are best suited to predicting the item of interest. Using a similar procedure applied by Mutanga and Skidmore [2004a] and Skidmore et al. [1997], we trained and tested our models. This procedure for training the models is outlined in figure 6.3.

6.3.

Data

Analysis

Figure 6.3: The procedure implemented for training and saving the best individual network parameters. For each nutrient, the model outcomes were evaluated per input data type, the model that produced the lowest average test RMSE value was selected as the best-input model. These different best-input models were compared and the model with the

Chapter 6. Savanna forage quality mapped in the dry season

Once all the individual components of the network architecture had been trained and tested, the network with the lowest average RMSE value ob- tained for the test and training dataset, for each nutrient, and each input data model was selected. Given the stochastic nature of neural networks, model selection is a compromise between several factors (network architec- ture and the training and test results) [Skidmore et al., 1997]. Taking this property into consideration, if two outputs had the same lowest average RMSE value, then the network with the least number of epochs required for training the models was selected. For each nutrient the different se- lected models were compared, and the model with the lowest test RMSE value was selected as the model for inversion.

Model inversion and validation:

The selected model for each nutrient was inverted and used to create an output map. The network architecture, training set size and training time (epochs) are all factors that contribute to the ability of a network to inter- polate and extrapolate on new data-sets [Atkinson and Tatnall, 1997]. As stated earlier this study focused only on the grazing resource, network train- ing was therefore limited to grass samples. The pixels selected for training the models were limited to pixels containing grass spectra. The savanna environment is however a combination of trees, grass and bare ground. To limit extrapolation beyond the values used to train the model, a check was performed prior to inversion. Inversion was performed on a pixel by pixel basis. It was first verified if each layer within a pixel fell within the same spectral range used to train the models, only if this was the case, for all of the layers, was model inversion applied. Each output map was recalculated to the percentage value of the nutrient, by inverting the linear contrast normalisation.

Using the 24 pixels set aside for validation, the output images were vali- dated, the root mean square error (RMSE) and R2_adj of these images are presented.

6.4. Results

Table 6.1: Summary of the chemical analysis of the 52 plant samples collected in the field.

Nutrient mean (% DM) Range (% DM) Nitrogen 0.53 0.31–0.91 Phosphorus 0.17 0.04–0.36

Fibre 44.7 40.9–48.5

6.4

Results

The results from the chemical analysis performed on the sampled plants is presented in table 6.1. The range of nitrogen and phosphorus is in agree- ment with findings reported by Grant and Scholes [2006]. The findings of Grant and Scholes [2006] and Treydte et al. [2009] indicated that nitrogen and phosphorus, in this region, during the dry season, fell below mainte- nance levels required by herbivores. Of particular interest is that the mean nitrogen and phosphorus levels were already, so early in the dry season, below levels identified for maintenance for wild herbivores. Nitrogen main- tenance levels for wild herbivores has been calculated as 1% N on a dry matter basis [Prins and Beekman, 1989], and phosphorus maintenance lev- els have been calculated for wild equids to be 0.24% P on a dry matter basis [Duncan, 1992].

The quantity of standing biomass contributes to a pixel’s signal [Asner, 2004]. To ensure predictions were related to the nutrient content and not standing biomass, they were compared with leaf area index measurements (LAI). LAI measurements were collected in a separate study (unpublished data4), and those measurements confirmed that the forage nutrient val- ues and LAI values were uncorrelated (r-values below 0.01 for the three nutrients).