Materials and Methods

Declaration 2: Publications

5.2 Materials and Methods

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80 5.2.3 Separability analysis

The evaluation and quantification of the spectral separability of bracken fern and other land cover classes at four phenological stages were performed using the Transformed Divergence Spectral Index (TDSI) statistical test. The TDSI separability test determines how similar or different the distributions of two groups of pixels are using the class means and the distribution of the values. The TDSI statistical measure has values that range between 0 –2, with values close to 0 indicating non-separability and values close to 2 indicating high separability (Chemura and Mutanga, 2017). The TDSI was formulated as:

𝑇𝐷𝑆𝐼 = [1 − exp (−𝐷 8)]

𝐷 = ¹

2 𝑡𝑟 [(𝐶₁− 𝐶₂)(𝐶₂⁻¹− 𝐶₂⁻¹)] + ¹₂𝑡𝑟 [(𝐶₁⁻¹− 𝐶₂⁻¹)(µ₁− µ₂) 𝑇]

Equation 5.1 Where C1 represents the covariance matrix of class1, µ1 is regarded as the mean vector of class 1, tr is the matrix trace function and T is the matrix transposition function.

5.2.4 Optimized spectral vegetation indices

Spectral vegetation indices were chosen based on their utility in vegetation mapping and their ability to increase the dimensionality of remotely sensed data (Kiala et al., 2020). The original TDVI was developed by Bannari et al. (2002) for vegetation cover mapping. The TDVI was designed to reduce the effects of bare soil during land cover classification. Bannari et al. (2002) reported that the TDVI does not saturate like NDVI or SAVI and it revealed good linearity as a function of the rate of vegetation cover and shows the same sensitivity as the SAVI to the optical proprieties of bare soil. However, the TDVI remains limited in terms of differentiating vegetation covers that have similar spectral reflectance. To remedy this, the current study proposes the optimization of the TDVI based on the spectral separability tests for the land cover classes under investigation. In the process of optimizing the TDVI, the mathematical formulation of the TDVI was maintained (Equation 5.1), only spectral bands were changed based on their capability to separate bracken fern from other land cover classes at various phenological stages. The NDVI was chosen as a reference index to compare the accuracy and sensitivity of the optimized indices to the ground measured LAI. The computation of TDVI was performed as follows;

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𝑇𝐷𝑉𝐼 = 1.5 ∗ [(𝑁𝐼𝑅 − 𝑅𝑒𝑑)/√𝑁𝐼𝑅²+ 𝑅 + 0.5] Equation 5.2

5.2.5 Validation of the optimized indices

The validation of newly developed or optimized spectral vegetation indices includes the computation of statistical tests of correlations between the vegetation indices and in situ measurements of vegetation characteristics such as vegetation cover, biomass and LAI. A direct application of NDVI is to characterize canopy growth; therefore, many scientists have compared it with the LAI (Fan et al., 2009, Kang et al., 2016, Towers et al., 2019). Similarly, the TDVI also characterizes canopy growth while it minimizes the effects of soil background effects, hence this study adopted the use of LAI to validate OTDVI for bracken fern phenology mapping. The bracken fern sampled locations were used to extract values from the optimized vegetation indices maps for correlation analysis with bracken LAI. To quantify the statistical relationships between optimized vegetation indices and ground measured bracken fern LAI, the coefficient of determination was computed. The optimized indices were used as a dependent variable while LAI measurements were used as the independent variable.

5.2.6 Bracken fern phenology mapping 5.2.6.1 Random Forest

Random forest, an ensemble decision-based classification algorithm (Chan and Paelinckx, 2008) was used to test the effectiveness of the optimized spectral vegetation indices in mapping bracken fern at its four phenological stages. Random forest is designed as a machine learning algorithm governed by decision trees, where each learning contributes one vote for the most frequent class to classify an input vector (Kiala et al., 2020). However, RF heavily relies on the fine tuning of the input hyper-parameters, and if not adjusted sufficiently could negatively influence the classification accuracy. Consequently, the current study adopts the Improved Grid Search Optimization Random Forest (IGSO-RF) for mapping bracken fern at its four phenological stages. The detailed technical workflow process of the IGSO-RF algorithm can be found in (Xu et al., 2021). To test the performance of the optimized indices in mapping bracken fern phenology, three data sets were used in the first part of the analysis as detailed in Table 5.1. The first stage of the classification process was performed using the default IGSO- RF parameters. The data set which yielded the highest overall accuracy was used to select the best features for mapping bracken fern based on the sequential forward selection (SFS) method.

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Table 5.1: Combination of variables tested in mapping bracken fern

Data set Variable combinations Total number of variables i) B2, B3, B4, B5, B6, B7, B8, B8A,

B11, B12 + NDVI + TDVI

12 ii) B2, B3, B4, B5, B6, B7, B8, B8A,

B11, B12 + OTDVI1-5

16 iii) B2, B3, B4, B5, B6, B7, B8, B8A,

B11, B12 + OTDVI1-5 + NDVI + TDVI

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5.2.6.2 Feature selection

Feature selection is a preprocessing method that is used for improving model performance and predictive accuracy (Li et al., 2017). The feature selection process reduces the effect of dimensionality which has a negative impact on the classification accuracy (Kiala et al., 2019).

Furthermore, feature selection eliminates redundant or noisy variables by choosing one feature amongst the highly correlated features (Chandrashekar and Sahin, 2014). The sequential forward selection (SFS) was used to select the best features for mapping bracken fern. To assemble the best set of features, the SFS search begins on an empty set and features are added one by one until the required subset is reached (Pudil et al., 1994).

5.2.6.3 Accuracy assessment

To evaluate the mapping capability of the proposed optimized spectral indices in mapping bracken fern at four phenological stages, the overall, producer and user accuracy metrics were computed. The estimated land cover classes were cross-tabulated against the ground-sampled land cover classes for the corresponding pixels in a confusion matrix. Ten-fold cross validation model selection criterion was used to validate the IGSO-RF model at each phenological stage.

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