Criteria Comparison for Classifying Peatland Vegetation Types Using In Situ Hyperspectral Measurements

This study aims to evaluate three classes of methods to discriminate between 13 peatland vegetation types using reflectance data. These vegetation types were empirically defined according to their composition, strata and biodiversity richness. On one hand, it is assumed that the same vegetation type spectral signatures have similarities. Consequently, they can be compared to a reference spectral database. To catch those similarities, several similarities criteria (related to distances (Euclidean distance, Manhattan distance, Canberra distance) or spectral shapes (Spectral Angle Mapper) or probabilistic behaviour (Spectral Information Divergence)) and several mathematical transformations of spectral signatures enhancing absorption features (such as the first derivative or the second derivative, the normalized spectral signature, the continuum removal, the continuum removal derivative reflectance, the log transformation) were investigated. Furthermore, those similarity measures were applied on spectral ranges which characterize specific biophysical properties. On the other hand, we suppose that specific biophysical properties/components may help to discriminate between vegetation types applying supervised classification such as Random Forest (RF), Support Vector Machines (SVM), Regularized Logistic Regression (RLR), Partial Least Squares-Discriminant Analysis (PLS-DA). Biophysical components can be used in a local way considering vegetation spectral indices or in a global way considering spectral ranges and transformed spectral signatures, as explained above. RLR classifier applied on spectral vegetation indices (training size = 25%) was able to achieve 77.21% overall accuracy in discriminating peatland vegetation types. It was also able to discriminate between 83.95% vegetation types considering specific spectral range [350–1350 nm], first derivative of spectral signatures and training size = 25%. Conversely, similarity criterion was able to achieve 81.70% overall accuracy using the Canberra distance computed on the full spectral range [350–2500 nm]. The results of this study suggest that RLR classifier and similarity criteria are promising to map the different vegetation types with high ecological values despite vegetation heterogeneity and mixture.


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Peatlands represent a diverse array of wetlands that accumulate partially decomposed organic material. 24 Whilst they may only cover a small proportion (∼ 3 %) of the Earth's land surface, these ecosystems are highly where L sam is the measured radiance from the sample plot and L ref is the measured radiance from the white 141 reference.

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The sensor was positioned approximatively 1 m over the target with a 10 • field of view. Consequently 143 the ground spatial resolution is 0.18 m. The ASD was configured to collect 20 samples and automatically 144 average in order to provide a single mean spectral measurement. Then a total of 7 to 53 field spectroradiometer 145 measurements, i.e. spectral signatures, depending on vegetation type was taken.
146 Some spectral bands (1350 nm to 1450 nm, 1810 nm to 1940 nm and 2400 nm to 2500 nm) have been removed 148 due to a small signal-to-noise ratio resulting from strong atmospheric absorption mainly due to the presence of 149 water vapour. More precisely, if the atmospheric transmittance value of the U.S. Standard profile was lower than 150 0.8 for a given wavelength, this wavelength was not taken into account in the analyse. Thus, each measured 151 spectrum has been smoothed using a Savitzky-Golay filter [32] for reducing the noise. Figure 2 155 The flowchart to evaluate the potential of hyperspectral data to discriminate and classify wetland vegetation 156 types is given in Figure 3. More precisely, three classes of methods have been investigated and compared: • similarity measures calculated on spectral reflectance, 158 • supervised classification based on "local" information (spectral vegetation indices), 159 • supervised classification based on "global" information (spectral ranges). 160 Indeed, spectral matching can be used to discriminate different vegetation types, because it is assumed 161 that the spectral signatures of a given vegetation type must have similarities. To catch those similarities, 162 several mathematical transformations -enhancing absorption features are applied on spectral signatures -163 (Section 3.1) and several similarity criteria -related to distances or spectral shapes or probabilistic behaviour -164 (Section 3.2) are investigated. Furthermore those similarity measures are applied on several spectral ranges 165 which characterize specific biophysical properties (Section 3.5) and compared to a reference spectral database 166 using relative spectral discriminatory probability (Section 3.3). 167 On the other hand as it may be difficult to have a spectral reference database, different supervised 168 classifiers are used (Section 3.6). Besides, we assume that specific biophysical properties/components may 169 help discriminating vegetation types. Biophysical components can be used in a local way considering spectral 170 vegetation indices (Section 3.4) or in a global way considering spectral ranges and transformed spectral 171 signatures as explained above. 172 To evaluate performance of similarity measures and supervised classification, the overall accuracy and 173 F1-score are used (Section 3.7).  (Table 3). Brightness-normalized spectral signature and second 177 derivative are relatively insensible to variations in illumination intensity causes by changes in sun angle [33,34]. 178 Other transformations (first derivative, second derivative, log transformation, Continuum Removal, Continuum
[35] L is the number of wavelengths.

Similarity measures 182
Let ρ i be a spectral signature, ρ i,λ its reflectance at wavelength λ and [1, ..., L] its spectral range. Several 183 criteria have been used (Table 4). Some criteria characterize the difference between reflectance levels (like the 184 distances) and other ones are related to the difference of the spectral shape (e.g. SAM) and other ones are related 185 to probabilistic behaviour (e.g. SID, ...).
It is a weighted version of the Manhattan distance Since the angle between two vectors is invariant with respect to the length of the vectors, this technique is relatively insensitive to illumination and albedo effects It calculates the probabilistic behaviour between spectral signatures [45] where It is a combination of probability and geometry spaces that improves discrimination ability Low value of SSV means high similarity and vice versa [48] Spectral Correlation Angle (SCA) It is an improvement of SAM derivated from PCC that has been shown to be able to distinguish between positive and negative correlations and to yield better estimates in some experiments [49,50] Spectral Gradient Angle (SGA) It is invariant to illumination conditions [51] 3.3. Relative spectral discriminatory probability

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To determine if a spectral signature belongs to a class, the method proposed by [45] is used. Let {ρ j } J j=1 J spectral signatures in ∆ an existing spectral reference database and τ be a target signature to be identified using ∆. Let m(·, ·) be a given hyperspectral measure, the spectral discriminatory probabilities of all ρ j in ∆ with respect to τ as is defined as follows: where J ∑ j=1 m(τ, ρ j ) is a normalization constant determined by τ and ∆. The resulting probability vector is defined (3) Using Equation (3), the target signature can be identified by selecting the one with the smallest spectral 189 discriminatory probability because τ and the selected one have the minimum spectral discrimination.

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Spectral reference database

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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: where N is the number of spectra for a plant species. Similarly, spectra of median reflectance is defined as the 192 median of reflectances for each wavelength λ. Median spectra is defined as the "closest" spectrum of the median 193 reflectance considering a vegetation type. In other words, giving a spectrum of median reflectance, the spectrum 194 that minimize the Minkowski distance between them is considered as the median spectrum ( Figure 4 shows 195 differences between the median reflectances spectrum which is an theoretic spectral signature and the different 196 median spectra which were investigated       significant difference between the median spectral index value between pairs of plant species.

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The null hypothesis for N = 13 vegetation types and I = 129 spectral vegetation indices per reflectance measurements is: where η n is the median spectral index value for vegetation type number n = 0, ..., N, and i = 1, ..., I the spectral In order to discriminate the 78 pairs of vegetation types, the Hellinger distance, which is introduced further,

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is computed for each vegetation spectral index (Table 5). Then indices are ordered by frequency discrimination.

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A first subset of indices is composed of ones that can discriminate pairs of vegetation types and that are not

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For a better understanding of the feature selection method, an example is given. We consider 4 vegetation 229 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 230 spectral vegetation index can discriminate neither V 1 from V 3 nor V 2 from V 4 nor V 3 from V 4 . But different 231 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: We obtain the first subset S 1 = {I 1 , I 2 , I 3 }. To discriminate V 1 from V 3 , V 2 from V 4 and V 3 from V 4 , we are 234 looking among the following combinations: by frequency discrimination: [I 3 , I 2 , I 1 , I 4 , I 5 ]. We suppose that {I 3 − I 1 } can discriminate V 1 from V 3 and V 2 236 from V 4 but there is still no index that can discriminate V 3 from V 4 . For the latter case, possible combinations Whatever a combination of spectral vegetation 238 indices can be found to discriminate or not those plant species, the process will stop in our case.

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The Bhattacharyya coefficient and the Hellinger distance

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For two arbitrary discrete probability distributions p and q, the amount of overlap between those distributions can be measured using the Bhattacharyya coefficient: 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: = 1 − C(p, q).
The Hellinger distance defined in Equation (8)  • if H(p, q) < 0.85 the separation is poor.     surface in a way that the margin of separation between two classes is maximized. To do this, the original 270 feature space is mapped into a space with a higher dimensionality, where classes can be modelled to be linearly 271 separable. This transformation is implicitly performed by applying kernel functions to the original data.

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The learning of the classifier is performed using a constrained optimization process that is associated with a 273 complex cost function. For problems that involve identification of multiple classes, adjustments are made to 274 the simple SVM binary classifier to operate as a multi-class classifier using methods such as one-against-all, 275 one-against-others.

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For this study, two kernels are retained: a linear kernel (SVM linear) and a Gaussian kernel (SVM RBF).  For this study, the 1 -norm and 2 -norm regularization term are investigated. To evaluate the classifier precision overall accuracy and F1-score are used. Overall accuracy computes number of correct spectra over all spectra, whereas F1-score is given by: where PA (Producer's Accuracy) is the fraction of retrieved classes that are relevant whereas UA (User's 296 Accuracy) is the fraction of relevant classes that are retrieved.  (Table 7). Indeed, the Canberra distance gives the higher overall accuracy because it is sensitive to a 302 small change when both coordinates are closed to zero [140,141].

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Because of the high variability of some vegetation types (Appendix B), spectral reference database built 304 from median spectra, that are real spectra, gave worse results than spectral reference database built from median 305 and mean spectra, that are theoretical spectra not representative of a in situ measured vegetation type (Table 7).

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There is a need to collect more spectral signatures to build a consistent spectral database.

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As spectral signatures can be considered as high dimensional vectors, a specific distance is needed to 308 compare them. It is well known that Euclidean distance is not good when comparing high dimension data 309 [142]. Table 8 shows that the Canberra distance always outperforms other distances, including SAM, which is 310 commonly used in remote sensing, when considering the whole spectral range (1823 wavelengths).  components which will be discussed in details in Section 4.2. Furthermore, Table 9 shows that the whole 315 spectral range gives the best results. Although spectral ranges are related to specific biophysical components 316 ( Considering classification accuracy for each vegetation type, Table 10 shows that best F1-score is obtained user's accuracy is higher than 85 %. Indeed these vegetation types are less mixed than others: rather than the low number of spectra: PING has 8 spectra whereas AQ_B has 7 spectra.   Boochs2 index, they can be discriminated thanks to a water index (right side of Figure 8 shows that those  x * : index selected on first step. x * * : index selected on second step.

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x * * * : index selected on third step.         (Table 13). Unlike an index related to water content (Figure 9), 380 an index related to the chlorophyll will discriminate SPHA from AQ_A. Indeed, the right side of Figure 9 shows 381 that some AQ_A plant species can not be distinguished from SPHA because it is a dry moss and the left side of 382 Figure 9 shows that SPHA and non discerned AQ_A have the same spectral signature shape. The right side of 383 Figure 10 shows that these two vegetation species can clearly be separated despite the class variability of AQ_A.

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A complex biophysical component such as F_WP will differentiate SPHA from CAVU (left side of Figure 11) 385 shows that different spectral shapes between those vegetation types can be exploited on the [1220-1280 nm] 386 domain. The right side of Figure 10 shows that the wavelengths corresponding to the maximum of the first 387 derivatives can clearly discern these two vegetation types even if these vegetation types can be mixed. In most case, a single biophysical component is sufficient to class a vegetation type from the others (except 389 for CA_HV), but a pair of biophysical components is needed to discriminate more specifically some vegetation 390 types (Table 12), apart from some particular cases where a pair of biophysical components is needed CA_HV 391 ( Figure 12) type. The advent of a third index only improves significantly their discrimination ( Figure 13).      (Table 15). Moreover, these selected indices are robust because no significant 402 difference between classifiers score (except for RF) regardless of the training size is noted ( Figure 14). As types due to their plant species composition. Indeed, SVM aims to find the best hyperplane that can separate 408 data, whereas RLR aims to find a probability (according to a logistic function) to separate them.

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Considering RLR-2 some vegetation types are not easily discriminated whatever the indices.          to better understand the link between those classifiers and improve the choice of the parameters. Figure 16 453

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This study aimed at inventorying and evaluating the performance of discrimination techniques for peatland 484 habitats based on in situ hyperspectral measurements with a high spectral resolution and high signal-to-noise 485 ratio. To evaluate the potential of hyperspectral data to separate and classify those habitats, three classes of 486 methods were investigated and compared:

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• similarity measures calculated on spectral reflectance,

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This study demonstrated that peatland vegetation types could be discriminated using the Canberra distance