Spectral Reference Database

To build the spectral reference database, spectra of mean reflectance, spectra of median reflectance and median spectra are used. Spectra of mean reflectance is defined as the mean of reflectances for each wavelength *λ*:

$$\overline{\rho\_{\lambda}} = \frac{1}{N} \sum\_{i=1}^{N} \rho\_{i,\lambda\prime} \,\forall \lambda \in [1, \dots, L]\_{\prime} \tag{4}$$

where *N* is the number of spectra for a plant species. Similarly, spectra of median reflectance is defined as the median of reflectances for each wavelength *λ*. Median spectra is defined as the "closest" spectrum of the median reflectance considering a vegetation type. In other words, giving a spectrum of median reflectance, the spectrum that minimize the Minkowski distance between them is considered as the median spectrum (Figure 4 shows differences between the median reflectances spectrum which is an theoretic spectral signature and the different median spectra which were investigated). As distances are not equivalent considering high-dimensional data, three Minkowski distances are investigated for this study: the Euclidean distance, the Canberra distance and the City Block or Manhattan distance (which are reminded in Section 3.1).

**Figure 4.** Median spectra, spectrum of mean reflectances, spectrum of median reflectances of *Eleocharis quinqueflora* (ELQU).

#### *3.4. Feature Selection of Spectral Indices*

#### 3.4.1. Spectral Index Description

Spectral indices are combinations of surface reflectance (or the derivated reflectance) at two or more wavelengths or narrow spectral bands. Lots of spectral indices can be found in literature (Table 5) to characterize some biochemical components of plant species such as chlorophyll, nitrogen, lignin, cellulose, water. Although these indices have never been selected in the literature to characterize wetlands plant species, we assume that some of them can still be useful to classify them.

#### **Table 5.** Spectral vegetation indices.


#### **Index Name Formulation Vegetation Properties String Type Highlighted by the Index** EGFR (Edge-Green First derivative Ratio) dRE dG Chlorophyll, nitrogen [69] EGFN (Edge-Green first Derivative Normalized difference) dRE − dG dRE + dG Chlorophyll, nitrogen GEMI (Global Environment Monitoring Index) *η*(<sup>1</sup> − 0.25*η*) − *R*660 − 0.25 1 − *R*660 , [70] where *η* = 2 *R*2830 − *R*2660 + 1.5*R*830 + 0.5*R*660 *R*830 + *R*660 + 0.5 GI (Greeness Index) *R*554 *R*677 Chlorophyll [71] Gitelson 1 *R*700 Chlorophyll [72] Gitelson2 *R*750 − *R*800 *R*965 − *R*740 − 1 Chlorophyll [59] GMI (Gitelson and Merzlyak Index) *R*750 *R*550 Chlorophyll [73] Green NDVI *R*800 − *R*550 *R*800 + *R*550 Chlorophyll [74] Maccioni *R*780 − *R*710 *R*780 − *R*680 Chlorophyll [75] MARI (Modified Anthocyanin Reflectance Index) *R*800 1*R*550 − 1*R*700 Anthocyanin [76,77] MCARI[700,670] (Modified Chlorophyll Absorption Index) (*<sup>R</sup>*700 − *<sup>R</sup>*670) − 0.2(*<sup>R</sup>*700 − *<sup>R</sup>*550) *R*700 *R*670 Chlorophyll, Leaf Area Index [78] MCARI[750,705] (*<sup>R</sup>*750 − *<sup>R</sup>*705) − 0.2(*<sup>R</sup>*750 − *<sup>R</sup>*550) *R*750 *R*705 Chlorophyll [79] MCARI[700,670]/OSAVI[800,670] (*<sup>R</sup>*700 − *<sup>R</sup>*670) − 0.2(*<sup>R</sup>*700 − *<sup>R</sup>*550) *<sup>R</sup>*700 *<sup>R</sup>*670 (1 + 0.16) *<sup>R</sup>*800−*R*<sup>670</sup> *<sup>R</sup>*800+*R*670+0.16 Chlorophyll [80] MCARI[750,705]/OSAVI[750,705] *<sup>R</sup>*750 − *<sup>R</sup>*705) − 0.2(*<sup>R</sup>*750 − *<sup>R</sup>*550) *<sup>R</sup>*750 *<sup>R</sup>*705 (1 + 0.16) *<sup>R</sup>*750−*R*<sup>705</sup> *<sup>R</sup>*750 + *<sup>R</sup>*705 + 0.16 Chlorophyll [79] MCARI[750,705]/MTVI2[750] MCARI[750,705] MTVI2[750] Nitrogen [81] MNDVI[800,680] (Modified NDVI) *R*800 − *R*680 *R*800 + *R*680 − 2*R*445 Chlorophyll [82] MNDVI[750,705] *R*750 − *R*705 *R*750 + *R*705 − 2*R*445 Chlorophyll MSAVI (Modified Soil Adjusted Vegetation Index) 0.52*R*800 + 1 − '(2*R*800 + 1)<sup>2</sup> − <sup>8</sup>(*<sup>R</sup>*800 − *<sup>R</sup>*670) Chlorophyll [83] MSI (Moisture Stress Index) *R*1599 *R*819 Water stress [84] MSR[800,680] (modified Simple Ratio) *R*800 − *R*445 *R*680 − *R*445 Chlorophyll [82] MSR[750,705] *R*750 − *R*445 *R*705 − *R*445 Chlorophyll MSR2 *R*750 *R*705 − 1 *<sup>R</sup>*750 *<sup>R</sup>*705 + 1 Chlorophyll, Leaf Area Index [85] MTCI (MERIS 1 Terrestrial Chlorophyll Index) *R*754 − *R*709 *R*709 − *R*681 Chlorophyll [86] MTVI[800] (Modified Triangular Vegetation Index) 1.51.2(*<sup>R</sup>*800 − *<sup>R</sup>*550) − 2.5(*<sup>R</sup>*670 − *<sup>R</sup>*550) Leaf Area Index [87] MTVI[750] 1.51.2(*<sup>R</sup>*750 − *<sup>R</sup>*550) − 2.5(*<sup>R</sup>*670 − *<sup>R</sup>*550) Leaf Area Index [87] MTVI2 [800] 1.51.2(*<sup>R</sup>*800 − *<sup>R</sup>*550) − 2.5(*<sup>R</sup>*670 − *<sup>R</sup>*550) (2*R*800 + 1)<sup>2</sup> − (6*R*800 − <sup>5</sup>√*<sup>R</sup>*670) − 0.5 Leaf Area Index [87] MTVI2 [750] 1.51.2(*<sup>R</sup>*750 − *<sup>R</sup>*550) − 2.5(*<sup>R</sup>*670 − *<sup>R</sup>*550) (2*R*750 + 1)<sup>2</sup> − (6*R*750 − <sup>5</sup>√*<sup>R</sup>*670) − 0.5 [87] NDII (Normalized Difference Infrared Index) *R*850 − *R*1650 *R*850 + *R*1650 Water status [88] *R*819 − *R*1649 *R*819+*R*1649

#### **Table 5.** *Cont*.

#### **Table 5.** *Cont*.



#### **Table 5.** *Cont*.

*R*x represents reflectance at wavelength x nm. *D*x represents the derivative of the reflectance spectrum at wavelength x nm. w., c., s., l = water, cellulose, starch, lignin.

#### 3.4.2. Classical Feature Selection Method—The Kruskal-Wallis H-Test

As some spectra per vegetation types were quite small (8 spectra for *Pinguicula* sp. (PING), 7 spectra for Aquatic type b (AQ\_B)), usual ANOVA [118] test or Mann-Whitney U-test [119] can not be used. That is the reason why Kruskal-Wallis H-test [120], a non-parametric test is proposed. Moreover this test is adapted to not independent data and not normally distributed data. The H-test is used to test the hypothesis that there was no significant difference between the median spectral index value between pairs of plant species.

The null hypothesis for *N* = 13 vegetation types and *I* = 129 spectral vegetation indices per reflectance measurements is:

$$H\_0: \eta\_n(i) = \eta\_{n+1}(i),\tag{5}$$

where *ηn* is the median spectral index value for vegetation type number *n* = 0, ..., *N*, and *i* = 1, ..., *I* the spectral index. The maximum frequency for this study is 13 2 = 13 × (<sup>13</sup>−<sup>1</sup>) 2 = 78. The hypothesis was therefore tested 78 times for all possible combinations of the 13 plant species at the adjusted Bonferroni significance level of *α* = 0.05 78= 6.410−4.

#### 3.4.3. Principle of the Applied Feature Selection Method

In order to discriminate between the 78 pairs of vegetation types, the Hellinger distance, which is introduced further, is computed for each vegetation spectral index (Table 5). Then indices are ordered by frequency discrimination. A first subset of indices is composed of ones that can discriminate between pairs of vegetation types and that are not redundant. If there is no discrimination between a pair of vegetation types, the Hellinger distance is computed for a pair of vegetation indices composed of the single most discriminating one and the other ones ordered by frequency distribution amongs<sup>t</sup> previous selected. Then, a second subset of pairs of indices is composed by ordering those pairs of indices by frequency discrimination. To stop the process, a maximum number of subsets is then defined. In our case, the maximum subset consists of not more than three indices. Indeed, the longer the tuple length is, the more difficult it is to explained why such combinations of indices or such biophysical components combination can discriminate between such pairs. Finally, selected vegetation indices come from each subset and single spectral vegetation indices or spectral index combinations are retained.

For a better understanding of the feature selection method, an example is given. We consider four vegetation types named: *V*1, *V*2, *V*3, *V*4 and 5 spectral vegetation indices named: *I*1, *I*2, *I*3, *I*4, *I*5. We suppose that no single spectral vegetation index can discriminate between neither *V*1 and *V*3 nor *V*2 and *V*4 nor *V*3 and *V*4. But different single indices can separate *V*1 from *V*2, *V*1 from *V*4 and *V*2 from *V*3.This is summarized in the following table:

$$\begin{array}{c|c|c|c} & V\_2 & V\_3 & V\_4 \\ \text{line } V\_1 & I\_1, I\_3 & & \mathcal{O} & \\ V\_2 & \text{ } & \text{ } & I\_2, I\_3 & \\ V\_3 & \text{ } & \text{ } & \text{ } & \mathcal{O} \end{array}$$

We obtain the first subset *S*1 = {*<sup>I</sup>*1, *I*2, *<sup>I</sup>*3}. To discriminate between *V*1 and *V*3, *V*2 and *V*4, and *V*3 and *V*4, we are looking among the following combinations: {*<sup>I</sup>*3 − *<sup>I</sup>*2}, {*<sup>I</sup>*3 − *<sup>I</sup>*1}, {*<sup>I</sup>*3 − *<sup>I</sup>*4}, {*<sup>I</sup>*3 − *<sup>I</sup>*5} because indices are ordered by frequency discrimination: [*I*3, *I*2, *I*1, *I*4, *I*5]. We suppose that {*<sup>I</sup>*3 − *<sup>I</sup>*1} can discriminate between *V*1 and *V*3, and *V*2 and *V*4 but there is still no index that can discriminate between *V*3 and *V*4. For the latter case, possible combinations are looking among {*<sup>I</sup>*3 − *I*1 − *<sup>I</sup>*2}, {*<sup>I</sup>*3 − *I*1 − *<sup>I</sup>*4}, {*<sup>I</sup>*3 − *I*1 − *<sup>I</sup>*5}. Whatever a combination of spectral vegetation indices can be found to discriminate between those plant species or not, the process will stop in our case.

#### 3.4.4. The Bhattacharyya Coefficient and the Hellinger Distance

For two arbitrary discrete probability distributions **p** and **q**, the amount of overlap between those distributions can be measured using the Bhattacharyya coefficient:

$$\mathcal{C}(\mathbf{p}, \mathbf{q}) = \sum\_{i=1}^{n} \sqrt{p\_i q\_i} \,\mathrm{s} \tag{6}$$

where *n* is the partition number. To measure the similarity between two statistical distributions in remote sensing the Hellinger distance (also known as the Matusita distance) is commonly used. It is defined as:

$$H(\mathbf{p}, \mathbf{q}) = \sqrt{\frac{1}{2} \sum\_{i=1}^{n} \left(\sqrt{p\_i} - \sqrt{q\_i}\right)^2},\tag{7}$$

$$=\sqrt{1-\mathcal{C}(\mathbf{p},\mathbf{q})}.\tag{8}$$

The Hellinger distance defined in Equation (8) has upper bound equal to 1, indicating the total separability of the class pairs characterized by their distribution. As a general rule adapted from [121],

