Remote Sensing of Environment 164 (2015) 57–65
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Multi-method ensemble selection of spectral bands related to leaf biochemistry Hannes Feilhauer a,b,⁎, Gregory P. Asner b, Roberta E. Martin b a b
Institute of Geography, University of Erlangen-Nürnberg, Wetterkreuz 15, 91058 Erlangen, Germany Department of Global Ecology, Carnegie Institution for Science, 260 Panama Street, Stanford, CA 94305, USA
a r t i c l e
i n f o
Article history: Received 10 October 2014 Received in revised form 28 March 2015 Accepted 30 March 2015 Available online xxxx Keywords: Hyperspectral Imaging spectroscopy Partial Least Squares regression Random Forest regression Remote sensing Support Vector Machine regression
a b s t r a c t Multi-method ensembles are generally believed to return more reliable results than the application of one method alone. Here, we test if for the quantification of leaf traits an ensemble of regression models, consisting of Partial Least Squares (PLSR), Random Forest (RFR), and Support Vector Machine regression (SVMR) models, is able to improve the robustness of the spectral band selection process compared to the outcome of a single technique alone. The ensemble approach was tested using one artificial and five measured data sets of leaf level spectra and corresponding information on leaf chlorophyll, dry matter, and water content. PLSR models optimized for the goodness of fit, an established approach for band selection, were used to evaluate the performance of the ensemble. Although the fits of the models within the ensemble were poorer than the fits achieved with the reference approach, the ensemble was able to provide a band selection with higher consistency across all data sets. Due to the selection characteristics of the methods within the ensemble, the ensemble selection is moderately narrow and restrictive but in good agreement with known absorption features published in literature. We conclude that analyzing the range of agreement of different model types is an efficient way to select a robust set of spectral bands related to the foliar properties under investigation. This may help to deepen our understanding of the spectral response of biochemical and biophysical traits in foliage and canopies. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Spectroscopic data provide detailed information on the reflectance characteristics of vegetation across large areas of the solar electromagnetic spectrum quantified in several hundred wavelength bands. In many cases, the fidelity of the spectrum permits the entire signal to be used for the remote quantification of leaf biochemical and biophysical traits (e.g., Asner & Martin, 2008). In other cases, the flexibility provided by the high spectral resolution is used to select particular spectral regions or features that are most helpful to describe leaf or canopy properties under investigation. The aims behind such selection approaches are many, but are often related to one of the following benefits: (1) Utilizing carefully selected spectral bands helps to improve the fit of statistical models (Andersen & Bro, 2010; Genuer, Poggi, & Tuleau-Malot, 2010). Optimizing such models by considering only a subset of the full spectral information may clarify the relationship between the spectral information and leaf properties, thus improving the accuracy of the model. In addition, a simplified, consistent relationship may facilitate the assessment of leaf traits from
⁎ Corresponding author at: Institute of Geography, University of Erlangen-Nürnberg, Wetterkreuz 15, 91058 Erlangen, Germany. Tel.: +49 9131 85 26680. E-mail address:
[email protected] (H. Feilhauer).
http://dx.doi.org/10.1016/j.rse.2015.03.033 0034-4257/© 2015 Elsevier Inc. All rights reserved.
reflectance of different data sets (Kokaly & Clark, 1999), a task that otherwise requires an inversion of physical leaf-canopy reflectance models (Darvishzadeh, Atzberger, Skidmore, & Schlerf, 2011). (2) Utilizing the high fidelity of spectroscopic data may advance our ability to select meaningful spectral regions to improve indices already known to empirically relate to leaf traits (e.g., Blackburn, 1998b; Sims & Gamon, 2002). (3) Selecting specific spectral features and regions may allow clarification of the relationship of spectral signatures to the underlying molecular activity within the leaf (see Curran, 1989, for a review) while minimizing the signal from secondary responses (Andersen & Bro, 2010; Genuer et al., 2010). Spectral band selection is frequently implemented through regression techniques such as Stepwise Multiple Linear regression (Forina, Lanteri, Oliveros, & Millan, 2004; Hocking, 1976) or Partial Least Squares regression (PLSR; Wold, Sjöström, & Eriksson, 2001). Both methods originate from the field of chemometrics and have been optimized for band-selection analysis by using appropriate protocols (Andersen & Bro, 2010). These approaches have been successfully transferred to spectral data taken at the leaf or canopy level, and have been used to analyze the influence of distinct spectral bands or regions to describe the relation between biochemical and spectral properties (e.g., Hansen & Schjoerring, 2003; Johnson & Billow, 1996; Knox et al., 2010; Li, Cheng, Ustin, Hu, & Riaño, 2008; Peterson et al., 1988).
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Conclusions drawn from such analyses may be biased or blurred if the quantified relationship is affected by the challenges common to statistical models dealing with spectroscopic data. Remote sensing data sets are often sampled in a spatial context, contain highly intercorrelated spectral bands, and frequently create statistical problems due to small sample sizes compared to the large number of available spectral bands. These characteristics may lead to a violation of basic assumptions behind statistical models or may otherwise affect the model outcome. For example, both the spatial structures in the data and inter-correlated variables violate the assumption of independence (Fortin & Dale, 2005). Models fitted with such data sets are prone to over-fitting and their transferability may be limited. Naturally, these issues affect the prediction accuracy as well as the interpretability of the models. Available statistical modeling approaches further differ in their suitability for the identification and selection of spectral bands. This ability varies with the data. In general, no method can always be considered superior to others (Ustin et al., 2009). Technical characteristics of the modeling approach also affect the result of the analysis, and influence the conclusions that are drawn. Hence, regression techniques (in particular Stepwise Multiple Linear regression) have been criticized as unstable and providing unreliable band selections for biochemical traits (e.g., Curran, 1989; Grossman et al., 1996). Blackburn (2007), reviewing absorption features related to leaf chlorophyll content, reports little empirical agreement on an optimal set of wavelengths for the determination of this trait. Ustin et al. (2009) come to a similar conclusion and review possible sources of these uncertainties. It seems reasonable to assume that the reported instability of wavelengths is also at least partially a result of the variable performance of the applied method in the respective analysis. A multi-method ensemble, also sometimes referred to as decision fusion, may improve the definition of particular spectral regions as they relate to specific absorption features, improving the reliability of the results to generalizable associations, beyond what can be achieved with a single method. The idea to combine different methods to improve the robustness of results dates back to the 1960s (Bates & Granger, 1969). In more recent years, combinations of different methods have been used to increase the prediction accuracy in remote-sensing based studies (Du, Xia, Chanussot, & He, 2012a; Engler et al., 2013; Waske & van der Linden, 2008). Multi-method ensembles further offer the potential to achieve a good mapping accuracy without the need to elaborately identify the most suitable method for a mapping problem (Foody, Boyd, & Sanchez-Hernandez, 2007). Multi-method ensembles have, however, never been tested for their potential to provide a robust band selection. We thus address in this study the questions: (1) Do different regression methods within an ensemble agree on a consistent subset of spectral bands related to specified foliar traits? (2) Is the ensemble selection more robust than the selection by a well-established PLSR approach? 2. Model methods and data sets 2.1. Work flow of the analyses To address these questions, we used an ensemble of three different regression techniques to identify bands related to vegetation biochemical properties in different spectral data sets. For this ensemble, PLSR, Random Forest regression (RFR; Breiman, 2001), and Support Vector Machine regression (SVMR; Smola & Schölkopf, 2004) were used. We selected these methods for their ability to perform a band selection. Other methods with this ability, such as Gaussian Processes regression (Van Wittenberghe et al., 2014), could have been used likewise within the ensemble. We evaluated the spectral regions selected by the ensemble across the different data sets. Theses selections were compared to the selections from a PLSR model optimized for the goodness of fit, based on maximizing the R2 value with an iterative backward-selection of spectral bands (PLSRopt). Comparisons between ensemble results and corresponding PLSRopt results were made for
a) Ensemble
b) PLSRopt
c) Fig. 1. Work flow of the analyses. Each of the biochemical variables in a number of test data sets was modeled with the ensemble approach (a) as well as with the PLSRopt approach (b). The spectral bands selected via (a) and (b) were finally compared (c).
each biochemical trait and data set combination. The work-flow of the analyses is illustrated in Fig. 1.
2.2. The ensemble approach Within the ensemble, PLSR, RFR, and SVMR were used in parallel to quantify the relationship between a biochemical trait and the corresponding spectral signal measured at the leaf level. Each of the three models provided statistical values designating the spectral bands most important for a prediction of the respective leaf trait. These band importance values were merged and converted into an ensemble assessment (Fig. 1a). Bands with high influence in all three models gained a high ensemble importance and were considered important. PLSR is a parametric model type that has frequently been used to quantify relationships between biochemical and spectral properties (see Feilhauer, Asner, Martin, & Schmidtlein, 2010, for a review). To cope with the inter-correlation of spectral data and with data sets that feature a small number of samples in relation to a large number of variables, statistically independent latent vectors are generated as linear combinations of the original spectral bands. In their generation, both the information contents with respect to the spectral bands as well as their ability to explain the response variable (i.e., the biochemical trait) are equally considered. The latent vectors are subsequently regressed against the response variable using a cross-validated linear model. To minimize the risk of over-fitting, the number of latent vectors that result in the smallest root mean squared error in cross-validation is used for the model. Unfortunately, the determination of this number is often difficult and requires a subjective decision, e.g., if the model error does not show a unimodal development or is decreasing very slightly across several latent vectors. In this study, the fit of the model based on the selected number of latent vectors was quantified as R2 in 10-fold crossvalidation. Because the latent vectors are linear combinations of the original bands, band-related regression coefficients can be determined. These coefficients enable a straightforward interpretation of the model as well as a simple means to apply the quantified relationship onto additional data for prediction purposes. For standardized variables, the sign of the coefficients indicates a positive or negative relationship
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while the absolute value of the coefficients is a direct measure of variable importance (Wold et al., 2001). RFR was used as the second technique within the ensemble. The RFR approach provides several advantages. First, it is a simple and user-friendly approach that requires fewer decisions on the model parameterization than other methods (Pal, 2005). Second, the method legitimately handles data sets where there are more predictor variables than observations (Evans, Murphy, Holden, & Cushman, 2011). This is achieved through a combination of individual regression trees, each being based on a random subset of the available data set. In each tree, the samples not used for building the tree, termed the samples ‘out-of-the-bag’, are used to assess its fit. This approach allows for optimizing the RFR model towards an accurate but parsimonious and robust description of the relationship. The out-of-the-bag error, representing the model error across all runs, is used to describe the RFR model fit in terms of R2. However, due to the replacement some samples may have been chosen more frequently and thus have gained a higher influence in the assessment of the model error. This needs to be considered when the fit is compared to the results of other modeling techniques. Finally, RFR can be used as a powerful approach for the selection of spectral bands (e.g., Genuer et al., 2010; Menze et al., 2009). It provides a measure of band importance that is obtained by assessing the effect of removal of the respective band on the model error. If the removal of a band results in a pronounced increase of the model error, recorded as a high and positive change of the RMSE, the band is considered important. It is important to note that the band importance values from RFR differ considerably from the variable importance values generated from PLSR. For instance, no information can be inferred from this measure as to whether the selected band provides a positive or negative effect on the model relationship. Further, the RFR error statistics that are based on sampling with replacement while the statistics for PLSR and SVMR are determined without replacement. SVMR is another non-parametric modeling technique which, similar to RFR, does not contain assumptions regarding the data distribution. Axelsson, Skidmore, Schlerf, Fauzi, and Verhoef (2013), however, report the method to be prone to effects of collinearities in the spectral data. The method mathematically transfers the regression problem into a feature space of higher dimensionality than the original data space to facilitate a linear solution to an otherwise non-linear problem. In this space of higher dimensionality, the regression function is parameterized, aiming to find a solution for which none of the residuals exceeds a given threshold ε. Any residual below ε is accepted, the total of residuals exceeding ε represent the cost of the solution. In order to make this complex optimization computationally feasible, the method uses a kernel function for the transfer to higher dimensionality and considers only those samples close to the margin defined by ε, these becoming the support vectors. Application of this method requires several elaborate decisions with respect to the set up of the model, which diminishes its user-friendliness (Pal, 2005). The decisions include the selection of the kernel function, as well as the parameterization of the cost parameter C and the kernel parameter γ. In the present study, we used the ε-regression form of SVM and followed the recommendation of Hsu, Chang, and Lin (2010), using the radial basis function kernel in combination with a grid search for the optimization of C and γ. The C and γ parameterization resulting in the best model fit was selected for the model used in the ensemble. Model fit was assessed as R2 in 10-fold cross-validation. SVM does not offer direct measures of band importance. Several approaches to determine the importance of spectral regions within SVMR models have thus been developed (e.g., Krooshof, Üstün, Postma, & Buydens, 2010; Postma, Krooshof, & Buydens, 2011). Here, we used an importance measure proposed by Üstün et al. (2007) based on the inner product of the spectral bands and the α-vector incorporating the support vectors. These values can be interpreted similarly to regression coefficients (Axelsson et al., 2013). The sign of the coefficients indicates
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a positive or negative relation while the absolute value is the measure of variable importance. The importance measures from all three methods were multiplicatively aggregated. Prior to this aggregation, the importance measures were standardized to a standard deviation of 1 following Axelsson et al. (2013) and weighted by the explained variance of the selected model for each method according to Eq. (1): 2 ð1Þ I iw ¼ Ii R =σ I where Iiw is the weighted importance of band i, Ii is the raw measure of band importance of the method, R2 is the explained variance of the model in cross-validation or out-of-the-bag testing, and σ I is the standard deviation across the raw measures of importance of each model. The product of the three weighted importance values per band was taken as ensemble importance IE. A band was eliminated from the ensemble if any single method assigned the band an importance value of zero. A band was classified as important if the respective IE was more than one standard deviation greater than the mean of all IE. The ensemble approach was implemented in the R statistical environment (R Core Team, 2014) using the packages e1071 (Meyer, Dimitriadou, Hornik, Weingessel, & Leisch, 2014), pls (Mevik, Wehrens, & Liland, 2014), and randomForest (Liaw & Wiener, 2002). The related R code is available as supplementary material to this manuscript. 2.3. PLSR optimized for the goodness of fit To assess whether the ensemble method is more robust than a standard single-approach method (Question 2), we compared the ensemble results to the band selection obtained from a PLSR model optimized for its goodness of fit (PLSRopt, Fig. 1b). This established approach is a suitable benchmark for methodological studies since its performance characteristics are well known (Axelsson et al., 2013). The optimization is achieved through a jack-knifing approach (e.g., Andersen & Bro, 2010; Chen, Cai, & Shao, 2007; Forina et al., 2004) based on the Martens & Martens uncertainty test (Martens & Martens, 2000). This test evaluates the variability of the band-specific regression coefficients during crossvalidation. Bands that show a small variability of the coefficients during cross-validation are considered to feature a robust relationship to the response variable (Forina et al., 2004). The variability of the coefficients is expressed in terms of significance (0–1) of the respective bands. A user-defined threshold can be used to separate significant and thus important bands from non-significant bands. Here, we set this threshold to 0.1 based on an analysis of the distributions of the coefficients. The significant bands are subsequently passed to further PLSR models, iteratively refining the model fits and the set of selected bands in a backward selection (Fig. 1b). The PLSR model with the selected set of optimal bands was used for the comparison against the ensemble approach (Fig. 1c). In contrast, the PLSR models in the ensemble used all available spectral bands in a single analysis and the band regions were not further refined. 2.4. Datasets Six spectral data sets were used for the analyses. Each data set contained pairwise sample information of the leaf reflectance spectrum and the respective concentrations on a mass and area basis of chlorophyll, dry matter, and water content. These biochemical traits are well known to relate to specific spectral signatures apparent in leaf reflectance spectra (reviewed by Ollinger, 2011). Table 1 provides an overview of the sample sizes, concentrations, and the specific biochemical traits that were included in each test. The spectral data consisted of five leaf-level datasets collected using field spectroradiometers, and one set of modeled leaf spectra. Not all chemical traits were available for each data set (refer to Table 1 for details).
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Table 1 Summary of the data sets used for the comparison of the two approaches. Data set
Origin
n
Chlorophyll
Dry matter
Water
Reference
PROSPECT Tambopata Hawaii Jasper Ridge Douglas fir Big leaf Maple
PROSPECT 5 ASD (Boulder CO) custom spectrometer ASD (Boulder CO) custom spectrometer NIRSystems 6500 spectrometer NIRSystems 6500 spectrometer NIRSystems 6500 spectrometer
400 450 178 40 90 109
21.0–82.1 μg/cm2 1.64–13.3 mg/g 1.1–26.1 mg/g 1.2–18.6 mg/g 1.2–7.0 mg/g 2.9–17.3 mg/g
4.7–25.8 mg/cm2 3.4–21.6 mg/cm2 2.2–30.8 mg/cm2 3.1–25.6 mg/cm2 – –
7.3–53.9 mg/cm2 – 42.7–88.4% 5.3–55.2 mg/cm2 52.8–69.5% –
– Asner and Martin (2011) Asner et al. (2011a) Aber and Martin (1999) Aber and Martin (1999) Aber and Martin (1999)
For the synthetic data set, 400 artificial leaf level spectra were generated with the PROSPECT-5 model (Féret et al., 2008; Jacquemoud & Baret, 1990). The PROSPECT model simulates the leaf level reflectance based on the six biophysical and biochemical parameters: leaf structure parameter N, carotenoid content Car, brown pigment content Cbrown, as well as chlorophyll content per area Cab, water content Cw, and dry matter content Cm that were used to test the ensemble approach. The absorption coefficients of Cab, Car, Cbrown, Cw, and Cm are provided together with the PROSPECT model. For the generation of the data set, the model parameters were randomly assigned artificial values corresponding to the range of concentrations normally found in fresh leaves. Cbrown was set to a constant of 0 for all spectra. For the analyses, the chosen parameters were used as response variable. The simulated spectra were resampled to a resolution of 10 nm by averaging the reflectance values of neighboring bands, covering the range from 400 nm to 2500 nm in 210 bands. We used the PROSPECT absorption coefficients and spectral responses (Fig. 2) to test if the multi-method ensemble approach and the single-method approach were able to capture these features.
a) Chlorophyll
b) Dry matter
c) Water
We further expected that these regions will also be selected from the measured data. Although this comparison does not provide statistical validation of method performance, it does verify if the approaches are detecting regions of known signal. Similar approaches using synthetic data sets generated with the PROSPECT models have successfully been used for analyses of statistical relations between biochemical traits and reflectance before (see, Féret et al., 2011). The first measured data set (Tambopata) was sampled by the Carnegie Spectranomics project at the Tambopata site in the lowland Peruvian Amazon, and has been used in previous studies (Asner & Martin, 2011; Feilhauer et al., 2010). It consists of 450 pairs of reflectance spectra and biochemical measurements from a wide variety of evergreen tropical tree species. All leaf samples were taken from sunlit leaves from the upper canopy. The spectra cover the range from 405 nm to 2512 nm in 220 bands. Detailed technical information on the leaf spectral measurements is available from the Spectranomics web page (http://spectranomics.stanford.edu/). The second measured data set was sampled throughout the island of Hawaii (Asner et al., 2011a). This dataset contains leaf spectra and corresponding biochemical properties of 178 Hawaiian tree, palm, shrub, and vine species. The data were also taken by the Spectranomics project following the same sampling approach. The spectra cover the range from 380 nm to 2452 nm in 208 bands. Three additional data sets (Jasper Ridge, Douglas fir, and Big leaf maple; Aber & Martin, 1999) are part of the data collected in the Accelerated Canopy Chemistry Program (ACCP). These data were collected between 1991 and 1992 for a broad range of remote-sensing related investigations and are freely available from the ORNL DAAC portal (http://daac.ornl.gov). The data are from a number of temperate tree species, collected in the summer of 1992. The spectra were also resampled to a resolution of 10 nm and subsequently covered the spectral region from 400 nm to 2500 nm in 210 bands. All data sets were analyzed with both the ensemble approach and PLSRopt. The ensemble result was evaluated with respect to the consistency of the band selection. For this we tested whether the approach selected a similar set of bands across all tested data sets. Further, the results were compared to the outcome of the PLSRopt models to evaluate the performance of the ensemble approach. It was finally reviewed in the Discussion section regarding its agreement with the absorption coefficients of the PROSPECT model as shown in Fig. 2, and compared to published spectral features from the body of literature.
3. Results 3.1. Model fits
Fig. 2. Absorption coefficients of the PROSPECT model for a) chlorophyll, b) dry matter, and c) water content (Féret et al., 2008). The gray polygons illustrate spectral regions where the coefficients are obscured by other PROSPECT parameters.
Model fits achieved within the ensemble and for the PLSRopt models are shown in Fig. 3. PLSRopt models resulted frequently in the highest R2. Similar fits were, however, achieved for the SVMR models within the ensemble. PLSR and RFR models within the ensemble always showed a lower R2, with RFR generally featuring the lowest R2. Within the ensemble, the biochemical variables could be modeled with a mean R2 N 0.60 across all data sets with the exception of the RFR-based models for chlorophyll and water content.
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a) Chlorophyll
b) Dry matter
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c) Water
Fig. 3. Model fits quantified as R2 in 10-fold cross-validation (PLSR and SVMR) and in out-of-the-bag assessment (RFR) for the ensemble models and the PLSRopt models. Points indicate the median of the fits achieved for measured data sets while whiskers indicate the extremes.
3.2. Selection and consistency of spectral regions Fig. 4 illustrates the spectral bands that were selected by both approaches in the analyses. For chlorophyll in the modeled PROSPECT data, both the ensemble and PLSRopt models were able to identify spectral regions in which the absorption coefficients are not obscured
a) Chlorophyll
b) Dry matter
by other features (Figs. 2a, 4a). The ensemble selection, however, matched the pattern expected from Fig. 2a more closely than the PLSRopt selection that also included some bands in the near infrared (NIR) range. From the measured leaf level spectra, the ensemble approach consistently selected bands adjacent to the chlorophyll absorption peak at 675 nm, mostly within the range of 500 to 750 nm.
c) Water
Fig. 4. PLSR, RFR, and SVMR coefficients as measures of band importance within the ensemble, and bands selected by the ensemble and PLSRopt approach for the relation between reflectance and chlorophyll concentration (a), dry matter content (b), and water content (c). The color gradients illustrate the relative importance of the respective spectral band. The combination of PLSR, RFR, and SVMR coefficients determines the ensemble importance. The PLSRopt importances are used for comparison and evaluation purposes.
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The peak itself was not selected. For the field measured Hawaii, Tambopata, and Jasper Ridge data, this selection was accompanied by additional bands near 1400 nm and in the short wave infrared (SWIR) region near 2300 nm. The band selection based on PLSRopt similarly contained the bands adjacent to the chlorophyll absorption peak but in general showed a broad and ambiguous selection from the full spectrum. For the field measured Douglas fir and Big leaf maple data, the ensemble selection exactly matched the slopes of the chlorophyll absorption peak from 525 nm to 725 nm. The band selection for these data sets based on PLSRopt was also ambiguous and included bands from the full spectrum. Fig. 5 shows the frequency of selection of spectral regions by the ensemble and PLSRopt approaches. The ensemble for leaf chlorophyll consistently selected bands from the green peak and the red edge region (Fig. 5a). Across the six tested data sets, each of the wavelengths in these regions was selected four and five times, respectively. This selection from two spectral regions was extended only sporadically to additional bands in the NIR and SWIR regions. PLSRopt resulted in a broader selection for chlorophyll that included each wavelength of the full spectrum at least once. For dry matter (Fig. 4b), both approaches selected mostly bands near 1400 nm and 2300 nm from the PROSPECT data. These bands are in line with the regions in which the PROSPECT absorption coefficients are not completely obscured by absorption features of other biochemicals such as water (Fig. 2b). In the PLSRopt selection, the selected bands were further accompanied by bands in the regions from 1200 nm to 1400 nm
a) Chlorophyll
b) Dry matter
c) Water
and near 1700 nm. The bands that achieved the highest importance values are also the expected regions from Fig. 2b. In general, the ensemble approach consistently identified the bands adjacent to 2300 nm as the most important ones from all measured data sets (Fig. 5b). The PLSRopt resulted in a less clear selection that included most wavelengths indiscriminately in the SWIR regions multiple times. For leaf water, the ensemble approach mostly selected bands near 750 nm and 1920 nm from the PROSPECT data (Fig. 4c). This selection met the expected pattern (Fig. 2c). In comparison, the PLSRopt models resulted in a broad selection of bands throughout the NIR and SWIR regions. Due to the differences between the ensemble selection from the modeled PROSPECT and the measured data, the ensemble results for leaf water were less consistent than for chlorophyll and dry matter. An exploration of the source of these differences requires additional research. Still, the ensemble approach consistently selected the bands adjacent to 1400 nm from all measured data (Fig. 5c). In addition, sporadic bands from the VIS and NIR regions were included to the selection. The PLSRopt selection from the measured data sets was similar to the broad selection from the PROSPECT data, including various bands from the NIR and SWIR regions. 4. Discussion 4.1. Methodological considerations The use of multiple model ensembles to achieve more reliable results has been previously tested (see, Du et al., 2012b for a review of remote sensing applications and Araujo & New, 2007 for a review of ecological applications). Models can be aggregated in different ways, in parallel such that each model quantifies the relationship based on the original data and the results are merged (Foody et al., 2007; Smits, 2002) or concatenated so the result of one model is passed as input of the next (Rahman & Fairhurst, 1999). Multi-method ensembles have shown their ability to improve the results of remote sensing applications (Du et al., 2012a; Fauvel, Chanussot, & Benediktson, 2006). Benediktson, Chanussot, and Fauvel (2007) even name multi-method ensembles as a future key methodology in remote sensing. Although these methods are used to increase the model fit and prediction accuracy, the potential of a multiple method ensemble for the identification and selection of spectral bands has not been deeply evaluated. There were considerable differences in the band selection and model fits among the three methods in our ensemble. In general, the highest model fits were achieved with SVMR, while RFR resulted in the lowest fits (Fig. 3). At first glance, SVMR appears to have a greater influence on the ensemble selection than PLSR or RFR, based on the initial weighting calculation of the importance values within the ensemble. However, because a band must be considered important by all three methods to enter the ensemble, these outlying values do not achieve entrance. By utilizing the multiplicative aggregation of variable importance values for band selection, our approach balances the influence of singular strong and weak models. In addition to tempering the influence of strong models as described above, weaker models may eliminate bands by assigning low variable importance values. As seen in the individual spectral band/region selection, all the methods generally agree on known spectral regions (Fig. 2), but vary in the strength of importance and number of bands. Agreement among methods emphasizes the general importance of the region in its relation to the leaf trait and strips away extraneous information that might otherwise be included if only one method is considered such as shown with the comparison to the PLSRopt method. 4.2. Consistency of the selected bands across the data sets
Fig. 5. Frequency of the selected spectral regions for leaf chlorophyll (a), dry matter (b), and water (c) across the tested data sets. A typical reflectance spectrum of vegetation is shown to ease the interpretation of the selected spectral regions.
The ensemble selection is determined by the merged characteristics of various methods and their interactions. These characteristics are also responsible for the consistency of the selections across different data
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sets. In general, PLSR and SVMR resulted in a conservative and broad selection that conceded most bands at least some importance. The conservative characteristics of PLSR, aiming to preserve a maximum of the available information inherent to the spectral data as reported by Forina et al. (2004) naturally also apply to the PLSRopt models and are responsible for the often rather broad selection that included various bands across the full spectrum. The similarity of PLSR and SVMR is not surprising since linear combinations of bands are used in both methods as part of the determination of coefficients. In PLSR, this is part of the generation of latent vectors on which the regression model is based (Wold et al., 2001). In SVMR, linear combinations are used a priori to calculate coefficients based on the reflectance values corresponding to the support vectors (Üstün et al., 2007). The resemblance of PLSR and SVMR coefficients has previously been observed and used to establish SVMR as an alternative to PLSR in the field of chemometrics (Axelsson et al., 2013; Postma et al., 2011). In contrast, RFR-models frequently selected a narrow set of few neighboring bands that together gained a high importance. This pronounced and almost binary classification into important/ non-important bands is considered a major advantage of the RF-based band selection compared to other algorithms (Menze et al., 2009). The selection of narrow spectral regions with high importance is an outcome of efficiently pruned regression trees requiring just a small set of rules for a complete model based on simple trees. The emerging pattern is further influenced by the inter-correlation of bands (Genuer et al., 2010), which is most likely responsible for the selection of ranges instead of individual bands. This characteristic of the RF algorithm affects the ensemble insofar as a band considered important in the RF selection is almost certain to be included in the ensemble selection. Fig. 4a reveals that the distinct RF importance pattern in the chlorophyll ensembles is almost solely responsible for the good consistency of the selection across the data sets. In contrast, in the dry matter ensemble RF has an influence equal to the other methods. This is in agreement with the influence of dry matter on a wide range of the spectrum (Fig. 2b). The consistency of the selection across the data sets is mostly a result of the agreement between the three methods. For leaf water, the ensemble resulted in a consistent selection for the three measured data sets that is also determined by RF. The ensemble for the PROSPECT data, however, results in a different set of bands. A possible explanation for this inconsistency may be the influence of leaf structural properties, which have a major influence on the correlation of wavelengths with leaf water (Danson, Steven, Malthus, & Clark, 1992), and may have been not considered adequately in the parameterization of the PROSPECT model used in this study. In comparison to the PLSRopt results, the consistency of the ensemble selection across the tested data sets is high. Fig. 5 shows that the ensemble approach frequently selected bands located near spectral features such as the green peak, the red edge, the slope of the second SWIR peak, and the water absorption bands. In contrast, the selections resulting from the conservative PLSR opt approach were rather broad and often unspecific. An implementation of criteria towards a reduction of multicollinearity in the backward selection has the potential to improve the performance of PLSRopt (Chong & Jun, 2005; Schmidtlein, Feilhauer, & Bruelheide, 2012) and may lead to a more specific selection of bands. However, tests (not shown here) indicated that these criteria further decreased the consistency of the PLSRopt selection. Taken together, the narrow ensemble selections showed a higher consistency across all tested data sets than the rather broad and unspecific PLSRopt selections. This consistency indicates that the ensemble is more robust against individual characteristics of the tested data sets. We thus conclude that analyzing the range of agreement of different model types in an ensemble is an efficient way to select a consistent and thus robust set of spectral bands. This set of spectral bands can subsequently be used as pre-selection to build predictive models from new data sets.
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4.3. Agreement of the selection with known spectral features Apart from considerations regarding their robustness, a comparison of the selections with known spectral features is crucial for an evaluation of the performance of the ensemble approach. Therefore, in the following paragraphs we explain how spectral features published in the body of literature compare with our ensemble method results. For the analysis of total leaf chlorophyll, the ensemble approach identified well-known bands in the visible region between 500 nm and 750 nm as most important. PLSR and SVMR coefficients consistently indicated a negative relationship between chlorophyll concentration and the reflectance in these bands. The selection is in line with the PROSPECT coefficients (Féret et al., 2008) shown in Fig. 2. It further matches the results of Gitelson, Gritz, and Merzlyak (2003), who report the regions from 525 to 555 nm and from 695 to 725 nm as being strongly related to chlorophyll concentration. These regions correspond to the peaks indicating the most frequently selected bands in Fig. 5a. The bands between these two regions were mostly not selected by the ensemble. This is also in good agreement with Lichtenthaler, Gitelson, and Lang (1996) and Merzlyak, Solovchenko, and Gitelson (2003), who observed that the region adjacent to 678 nm becomes insensitive for reflectance data of samples with a high chlorophyll concentration. This particular wavelength exactly matched the minimum between the two peaks in Fig. 5a. This finding is substantiated by various studies using a band-wise correlation analysis based on reflectance spectra that observed a maximum correlation of chlorophyll content with these two spectral regions (e.g., Carter & Knapp, 2001; Datt, 1998; Lichtenthaler et al., 1996; Yoder & Pettigrew-Crosby, 1995). It is, however, interesting to note that the 678 nm region gains importance for a separate assessment of chlorophyll-a because in this wavelength the absorption feature is not obscured by effects of other pigments (Blackburn, 1998a, 1998b). In some of the present chlorophyll analyses, additional bands in the region of 1300 to 1400 nm and near 2300 nm were selected. These bands correspond to features related to the leaf dry matter content that is often correlated with the chlorophyll concentration and thus affects a spectral assessment of pigments (Serrano, Peñuelas, & Ustin, 2002). For dry matter, the ensemble selection included for all data sets bands near 2300 nm. This selection is in line with the regions in which the absorption coefficients of dry matter are not obscured by other absorption features such as water (Fig. 2b), a common problem in the spectral analysis of dry matter (Kokaly, Asner, Ollinger, Martin, & Wessman, 2009). The selected 2300 nm feature matches the regions identified by Cheng et al. (2014) using a wavelet analysis and by le Maire et al. (2008) as suitable for spectral indices targeting leaf dry mass per area. Further, Asner et al. (2011b) identified the spectral region from approximately 1900 nm to 2350 nm as most important for a leaf reflectance and transmittance based assessment of dry matter with PLSR. Within the ensemble for the PROSPECT data the sign of the PLSR and SVMR coefficients for the 2300 nm feature in the PROSPECT data are contradictory: according to the SVMR model the relationship between this feature and dry matter content is positive, the PLSR coefficients correctly describe the negative relationship. For the other data sets the coefficients of both models were unambiguously negative for this feature. The narrow and consistent ensemble selection, likely due to the selection characteristics of the RF models, was unexpected since other studies report that dry matter shows a broad correlation across the spectrum and only weak correlations to single wavelengths (Wang, Huang, & Lou, 2011). A remote assessment of leaf water content at the canopy level is often affected by atmospheric water vapor, making an analysis of water absorption bands a difficult task. At the leaf level, these effects are not present. However, leaf water is considered a major source of uncertainty in the assessment of other biochemical traits due to its pronounced influence on large areas of the reflectance spectrum (Kokaly & Clark, 1999). Simultaneously, leaf structural properties and
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dry matter content affect the statistical relationship between spectral regions and leaf water (Danson et al., 1992). It is thus challenging to identify spectral regions that can be attributed to leaf water alone with regression approaches (Ustin, Riaño, & Hunt, 2012). Some water absorption features have been found suitable for estimation of water content even at the canopy scale. For example, Clevers, Kooistra, and Schaepman (2008, 2010) found the 970 nm, 1200 nm, and 1015–1050 nm features successfully predicted canopy water content from derivative spectra. However, these bands were not selected by the ensemble and were related in only two out of four data sets by PLSRopt. At the leaf level, Carter (1993) observed maximum leaf-water induced changes of reflectance in the wavelengths 1412 nm, 1978 nm, 2004 nm, and 2401 nm. The 1412 nm band was selected by the ensemble in all but the PROSPECT data set. In the modeled data set, the 1978 nm and 2004 nm bands were selected instead. None of these bands were selected by the PLSRopt approach. A laboratory study by Danson et al. (1992) found the spectral wavelengths of 1450 nm, 1650 nm, and 2250 nm of reflectance spectra were significantly correlated with leaf water content as well as a few additional bands with the derivatives of these spectra. None of these wavelengths were selected by the ensemble or PLSRopt methods. The observed differences in the band selections for the measured and modeled PROSPECT data may also indicate uncertainties in modeling leaf water content. Taking this together, we consider leaf water to be the most challenging trait addressed in this study. 4.4. Future research needs Various studies show that transformed spectra result in a more distinct band selection in association with many traits compared to un-transformed spectra (Schlerf et al., 2010). Advanced pre-processing techniques are thus promising tools which ease and improve the selection of bands related to leaf biochemistry and help to fully exploit the spectral signal. Among these techniques are the use of first or higher order derivative spectra (Danson et al., 1992; Sims & Gamon, 2002), wavelet filtering (Blackburn & Ferwerda, 2008; Cheng et al., 2014), continuum removal approaches (Kokaly & Clark, 1999), and water removal for protein absorption features (Schlerf et al., 2010). However, these techniques require a very high spectral resolution that may be beyond the capabilities of most imaging spectrometers (Asner & Martin, 2008). In this study, we did not use such processing techniques for the sake of simplicity and tested the ensemble approach with un-transformed reflectance spectra. It stands to reason that a combination of advanced processing techniques with multi-method ensemble approaches offers additional benefits and may boost the selection of meaningful bands. Further research is needed to test and explore the opportunities of such a combination. Yet, the consistent results achieved in this study for un-transformed reflectance spectra raises the hope that ensemble selection is a versatile and flexible approach capable to analyze spectra not suitable for advanced spectral transformations. The three methods used in this study provide information on the importance of individual bands for a regression problem. Although providing this information on a per-band basis is convenient for technical purposes, it hampers the interpretation of the quantified relationships. In a causal sense, biochemical traits determine spectral features. These features are dispersed across multiple neighboring bands that need to be considered collectively. Further work is thus needed to bridge the gap between individual bands and spectral features towards a comprehensive understanding of the underlying processes. The biochemical traits addressed in this study strongly influence the spectral reflectance signal, and our tests were implemented only at the leaf level. Most remote sensing data are, however, taken at the canopy level and therefore incorporate an additional level of canopy complexity. This complexity is due to the fact that the relationship between leaf biochemistry and spectral response is influenced by effects of structural traits such as leaf area and orientation, the atmosphere, and the signals
of the soil as well as of non-leaf or dead plant parts (Kumar, Schmidt, Dury, & Skidmore, 2001). Identifying spectral bands related to leaf biochemical properties at the canopy scale is thus more difficult than at the leaf level, and quantified relationships are often not transferable (Asner, 1998; Kokaly & Clark, 1999). Similarly, the identification of spectral bands related to biochemicals that feature a less prominent optical response (e.g., leaf nitrogen, phosphorus, lignin, and cellulose) is a more difficult task than the analyses implemented in this study. Additional tests are thus required to test whether a multi-method ensemble is able to cope with these challenges. 5. Conclusions The results of this study show that a multi-method ensemble provides a robust and consistent selection of spectral bands related to biochemical traits. The selections from measured and simulated leaf-level data are mostly in line with known absorption features of the tested biochemicals. In a direct comparison, the ensemble approach further outperformed the established technique of a band selection by PLSR models optimized for the goodness of fit. We conclude that ensemble modeling is a promising approach for the quantitative analysis of spectral signals in relation to biochemical traits. The spectral bands selected by the ensemble can subsequently be used as pre-selection to build predictive models from new data sets. Further testing of the ensemble approach is needed, particularly with respect to applications at the canopy level or for biochemicals that are less definitively expressed in the spectral signal. Acknowledgments HF's contribution to this study was financially supported by the German Research Foundation (DFG) through research grant FE 1331/2-1. Funding for the Spectranomics project is provided by the John D. and Catherine T. MacArthur Foundation and the Carnegie Institution for Science. The authors thank the Accelerated Canopy Chemistry Program for making available the spectral data sets used in this study as well as Jennifer Dungan and two anonymous reviewers for their helpful comments on this manuscript. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.rse.2015.03.033. References Aber, J. D., & Martin, M. E. (1999). Leaf chemistry, 1992–1993 (ACCP). Retrieved from http://www. daac.ornl.gov (accessed 2014/03/11) Andersen, C. M., & Bro, R. (2010). Variable selection in regression—A tutorial. Journal of Chemometrics, 24, 728–737. Araujo, M. B., & New, M. (2007). Ensemble forecasting of species distributions. Trends in Ecology & Evolution, 22, 42–47. Asner, G. P. (1998). Biophysical and biochemical sources of variability in canopy reflectance. Remote Sensing of Environment, 64, 234–253. Asner, G. P., & Martin, R. E. (2008). Spectral and chemical analysis of tropical forests: Scaling from leaf to canopy levels. Remote Sensing of Environment, 112, 3958–3970. Asner, G. P., & Martin, R. E. (2011). Canopy phylogenetic, chemical and spectral assembly in a lowland Amazonian forest. New Phytologist, 189, 999–1012. Asner, G. P., Martin, R. E., Knapp, D. E., Tupayachi, R., Anderson, C., Carranza, L., et al. (2011a). Spectroscopy of canopy chemicals in humid tropical forests. Remote Sensing of Environment, 115, 3587–3598. Asner, G. P., Martin, R. E., Tupayachi, R., Emerson, R., Martinez, P., Sinca, F., et al. (2011b). Taxonomy and remote sensing of leaf mass per area (LMA) in humid tropical forests. Ecological Applications, 21, 85–98. Axelsson, C., Skidmore, A. K., Schlerf, M., Fauzi, A., & Verhoef, W. (2013). Hyperspectral analysis of mangrove foliar chemistry using PLSR and support vector regression. International Journal of Remote Sensing, 34, 1724–1743. Bates, J. M., & Granger, C. W. J. (1969). The combination of forecasts. Operational Research Quarterly, 20, 451–468. Benediktson, J. A., Chanussot, J., & Fauvel, M. (2007). Multiple classifier systems in remote sensing: From basics to recent developments. In M. Haindl, J. Kittler, & F. Roli (Eds.), Multiple classifier systems. Lecture Notes in Computer Science, 4472. (pp. 501–512).
H. Feilhauer et al. / Remote Sensing of Environment 164 (2015) 57–65 Blackburn, G. A. (1998a). Quantifying chlorophylls and carotenoids at leaf and canopy scales: An evaluation of some hyperspectral approaches. Remote Sensing of Environment, 66, 273–285. Blackburn, G. A. (1998b). Spectral indices for estimating photosynthetic pigment concentrations: A test using senescent tree leaves. International Journal of Remote Sensing, 19, 657–675. Blackburn, G. A. (2007). Hyperspectral remote sensing of plant pigments. Journal of Experimental Botany, 58, 855–867. Blackburn, G., & Ferwerda, J. (2008). Retrieval of chlorophyll concentration from leaf reflectance spectra using wavelet analysis. Remote Sensing of Environment, 112, 1614–1632. Breiman, L. (2001). Random forests. Machine Learning, 45, 5–32. Carter, G. A. (1993). Responses of leaf spectral reflectance to plant stress. American Journal of Botany, 80, 239–243. Carter, G. A., & Knapp, A. K. (2001). Leaf optical properties in higher plants: Linking spectral characteristics to stress and chlorophyll concentration. American Journal of Botany, 88, 677–684. Chen, D., Cai, W., & Shao, X. (2007). Removing uncertain variables based on ensemble partial least squares. Analytica Chimica Acta, 598(1), 19–26. Cheng, T., Rivard, B., Sánchez-Azofeifa, A. G., Féret, J. -B., Jacquemoud, S., & Ustin, S. L. (2014). Deriving leaf mass per area (LMA) from foliar reflectance across a variety of plant species using continuous wavelet analysis. ISPRS Journal of Photogrammetry and Remote Sensing, 87, 28–38. Chong, I. -G., & Jun, C. -H. (2005). Performance of some variable selection methods when multicollinearity is present. Chemometrics and Intelligent Laboratory Systems, 78, 103–112. Clevers, J. G. P. W., Kooistra, L., & Schaepman, M. E. (2008). Using spectral information from the NIR water absorption features for the retrieval of canopy water content. International Journal of Applied Earth Observation and Geoinformation, 10, 388–397. Clevers, J. G. P. W., Kooistra, L., & Schaepman, M. E. (2010). Estimating canopy water content using hyperspectral remote sensing data. International Journal of Applied Earth Observation and Geoinformation, 12, 119–125. Curran, P. J. (1989). Remote sensing of foliar chemistry. Remote Sensing of Environment, 30, 271–278. Danson, F. M., Steven, M. D., Malthus, T. J., & Clark, J. A. (1992). High-spectral resolution data for determining leaf water content. International Journal of Remote Sensing, 13, 461–470. Darvishzadeh, R., Atzberger, C., Skidmore, A., & Schlerf, M. (2011). Mapping grassland leaf area index with airborne hyperspectral imagery: A comparison study of statistical approaches and inversion of radiative transfer models. ISPRS Journal of Photogrammetry and Remote Sensing, 66, 894–906. Datt, B. (1998). Remote sensing of chlorophyll a, chlorophyll b, chlorophyll a + b, and total carotenoid content in Eucalyptus leaves. Remote Sensing of Environment, 66, 111–121. Du, P., Xia, J., Chanussot, J., & He, X. (2012a). Hyperspectral remote sensing image classification based on the integration of Support Vector Machine and Random Forest. Proceedings of the 2012 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Munich (pp. 174–177). Du, P., Xia, J., Zhang, W., Tan, K., Liu, Y., & Liu, S. (2012b). Multiple classifier system for remote sensing image classification: A review. Sensors, 12, 4764–4792. Engler, R., Waser, L. T., Zimmermann, N. E., Schaub, M., Berdos, S., Ginzler, C., et al. (2013). Combining ensemble modeling and remote sensing for mapping individual tree species at high resolution. Forest Ecology and Management, 310, 64–73. Evans, J., Murphy, M., Holden, Z., & Cushman, S. (2011). Modeling species distribution and change using Random Forest. In C. A. Drew, Y. F. Wiersma, & F. Huettmann (Eds.), Predictive species and habitat modeling in landscape ecology (pp. 139–159). Springer. Fauvel, M., Chanussot, J., & Benediktson, J. A. (2006). Decision fusion for the classification of urban remote sensing images. IEEE Transactions on Geoscience and Remote Sensing, 44, 2828–2838. Feilhauer, H., Asner, G. P., Martin, R. E., & Schmidtlein, S. (2010). Brightness-normalized partial least squares regression for hyperspectral data. Journal of Quantitative Spectroscopy and Radiative Transfer, 111, 1947–1957. Féret, J. B., Francois, C., Asner, G. P., Gitelson, A. A., Martin, R. E., Bidel, L. P. R., et al. (2008). PROSPECT-4 and 5: Advances in the leaf optical properties model separating photosynthetic pigments. Remote Sensing of Environment, 112, 3030–3043. Féret, J. -B., François, C., Gitelson, A., Asner, G. P., Barry, K. M., Panigada, C., et al. (2011). Optimizing spectral indices and chemometric analysis of leaf chemical properties using radiative transfer modeling. Remote Sensing of Environment, 115, 2742–2750. Foody, G. M., Boyd, D. S., & Sanchez-Hernandez, C. (2007). Mapping a specific class with an ensemble of classifiers. International Journal of Remote Sensing, 28, 1733–1746. Forina, M., Lanteri, S., Oliveros, M. C. C., & Millan, C. P. (2004). Selection of useful predictors in multivariate calibration. Analytical and Bioanalytical Chemistry, 380, 397–418. Fortin, M. J., & Dale, M. (2005). Spatial analysis: A guide for ecologists. Cambridge, N.Y.: Cambridge University Press. Genuer, R., Poggi, J. -M., & Tuleau-Malot, C. (2010). Variable selection using random forests. Pattern Recognition Letters, 31, 2225–2236. Gitelson, A. A., Gritz, Y., & Merzlyak, M. N. (2003). Relationships between leaf chlorophyll content and spectral reflectance and algorithms for non-destructive chlorophyll assessment in higher plant leaves. Journal of Plant Physiology, 160, 271–282. Grossman, Y. L., Ustin, S. L., Jacquemoud, S., Sanderson, E. W., Schmuck, G., & Verdebout, J. (1996). Critique of stepwise multiple linear regression for the extraction of leaf biochemistry information from leaf reflectance data. Remote Sensing of Environment, 56, 182–193. Hansen, P. M., & Schjoerring, J. K. (2003). Reflectance measurement of canopy biomass and nitrogen status in wheat crops using normalized difference vegetation indices and partial least squares regression. Remote Sensing of Environment, 86, 542–553. Hocking, R. R. (1976). A biometrics invited paper. The analysis and selection of variables in linear regression. Biometrics, 32, 1–49. Hsu, C., Chang, C., & Lin, C. (2010). A practical guide to support vector classification. Retrieved from http://www.csie.ntu.edu.tw/~cjlin Jacquemoud, S., & Baret, F. (1990). PROSPECT: A model of leaf optical properties spectra. Remote Sensing of Environment, 34, 75–91. Johnson, L. F., & Billow, C. R. (1996). Spectrometry estimation of total nitrogen concentration in Douglas-fir foliage. International Journal of Remote Sensing, 17, 489–500. Knox, N. M., Skidmore, A. K., Schlerf, M., de Boer, W. F., van Wieren, S. E., van der Waal, C., et al. (2010). Nitrogen prediction in grasses: Effect of bandwidth and plant material state on absorption feature selection. International Journal of Remote Sensing, 31, 691–704.
65
Kokaly, R. F., Asner, G. P., Ollinger, S. V., Martin, M. E., & Wessman, C. A. (2009). Characterizing canopy biochemistry from imaging spectroscopy and its application to ecosystem studies. Remote Sensing of Environment, 113, S78–S91. Kokaly, R. F., & Clark, R. N. (1999). Spectroscopic determination of leaf biochemistry using banddepth analysis of absorption features and Stepwise Multiple Linear Regression. Remote Sensing of Environment, 67, 267–287. Krooshof, P. W. T., Üstün, B., Postma, G. J., & Buydens, L. M. C. (2010). Visualization and recovery of the (bio)chemical interesting variables in data analysis with Support Vector Machine Classification. Analytical Chemistry, 82, 7000–7007. Kumar, L., Schmidt, K., Dury, S., & Skidmore, A. (2001). Imaging spectrometry and vegetation science. In F. D. van der Meer, & S. M. de Jong (Eds.), Imaging spectroscopy. Basic principles and prospective applications (pp. 111–155). Dordrecht: Kluwer Academic Publishers. le Maire, G., Francois, C., Soudani, K., Berveiller, D., Pontailler, J., Breda, N., et al. (2008). Calibration and validation of hyperspectral indices for the estimation of broadleaved forest leaf chlorophyll content, leaf mass per area, leaf area index and leaf canopy biomass. Remote Sensing of Environment, 112, 3846–3864. Li, L., Cheng, Y. -B., Ustin, S., Hu, X. -T., & Riaño, D. (2008). Retrieval of vegetation equivalent water thickness from reflectance using genetic algorithm (GA)-partial least squares (PLS) regression. Advances in Space Research, 41, 1755–1763. Liaw, A., & Wiener, M. (2002). Classification and regression by randomForest. R News, 2, 18–22. Lichtenthaler, H. K., Gitelson, A., & Lang, M. (1996). Non-destructive determination of chlorophyll content of leaves of a green and an aurea mutant of tobacco by reflectance measurements. Journal of Plant Physiology, 148, 483–493. Martens, H., & Martens, M. (2000). Modified Jack-knife estimation of parameter uncertainty in bilinear modelling by partial least squares regression (PLSR). Food Quality and Preference, 11, 5–16. Menze, B. H., Kelm, B. M., Masuch, R., Himmelreich, U., Bachert, P., Petrich, W., et al. (2009). A comparison of random forest and its Gini importance with standard chemometric methods for the feature selection and classification of spectral data. BMC Bioinformatics, 10, 213. Merzlyak, M. N., Solovchenko, A. E., & Gitelson, A. A. (2003). Reflectance spectral features and non-destructive estimation of chlorophyll, carotenoid and anthocyanin content in apple fruit. Postharvest Biology and Technology, 27, 197–211. Mevik, B. H., Wehrens, R., & Liland, K. H. (2014). pls: Partial least squares and principal component regression. R package version 2.4-3. Retrieved from http://CRAN.R-project.org/ package=pls Meyer, D., Dimitriadou, E., Hornik, K., Weingessel, A., & Leisch, F. (2014). e1071: Misc functions of the department of statistics (e1071), TU Wien. R package version 1.6-3. Retrieved from http://CRAN.R-project.org/package=e1071 Ollinger, S. V. (2011). Tansley review. Sources of variability in canopy reflectance and the convergent properties of plants. New Phytologist, 189, 375–394. Pal, M. (2005). Random forest classifier for remote sensing classification. International Journal of Remote Sensing, 26, 217–222. Peterson, D. L., Aber, J. D., Matson, P. A., Card, D. H., Swanberg, N., Wessman, C., et al. (1988). Remote sensing of forest canopy and leaf biochemical contents. Remote Sensing of Environment, 24, 85–108. Postma, G. J., Krooshof, P. W. T., & Buydens, L. M. C. (2011). Opening the kernel of kernel partial least squares and support vector machines. Analytica Chimica Acta, 705, 123–134. R Core Team (2014). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing (Retrieved from http://r-project.org.). Rahman, A. F. R., & Fairhurst, M. C. (1999). Serial combination of multiple experts: A unified evaluation. Pattern Analysis and Applications, 2, 292–311. Schlerf, M., Atzberger, C., Hill, J., Buddenbaum, H., Werner, W., & Schüler, G. (2010). Retrieval of chloropyhll and nitrogen in Norway spruce (Picea abies L. Karst.) using imaging spectroscopy. International Journal of Applied Earth Observation and Geoinformation, 12, 17–26. Schmidtlein, S., Feilhauer, H., & Bruelheide, H. (2012). Mapping plant strategy types using remote sensing. Journal of Vegetation Science, 23, 395–405. Serrano, L., Peñuelas, J., & Ustin, S. L. (2002). Remote sensing of nitrogen and lignin in Mediterranean vegetation from AVIRIS data. Remote Sensing of Environment, 81, 355–364. Sims, D. A., & Gamon, J. A. (2002). Relationships between leaf pigment content and spectral reflectance across a wide range of species, leaf strutures and developmental stages. Remote Sensing of Environment, 81, 337–354. Smits, P. C. (2002). Multiple classifier systems for supervised remote sensing image classification based on dynamic classifier selection. IEEE Transactions on Geoscience and Remote Sensing, 40, 801–813. Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing, 14, 199–222. Ustin, S. L., Gitelson, A. A., Jacquemoud, S., Schaepman, M., Asner, G. P., Gamon, J. A., et al. (2009). Retrieval of foliar information about plant pigment systems from high resolution spectroscopy. Remote Sensing of Environment, 113, S67–S77. Ustin, S. L., Riaño, D., & Hunt, E. R. (2012). Estimating canopy water content from spectroscopy. Israel Journal of Plant Sciences, 60, 9–23. Üstün, B., Melssen, W. J., & Buydens, L. M. C. (2007). Visualisation and interpretation of support vector regression models. Analytica Chimica Acta, 595, 299–309. Van Wittenberghe, S., Verrelst, J., Rivera, J. P., Alonso, J., Moreno, J., & Samson, R. (2014). Gaussian processes retrieval of leaf parameters from a multi-species reflectance, absorbance and flourescence dataset. Journal of Photochemistry and Photobiology B: Biology, 134, 37–48. Wang, F., Huang, J., & Lou, Z. (2011). A comparison of three methods for estimating leaf area index of paddy rice from optimal hyperspectral bands. Precision Agriculture, 12, 439–447. Waske, B., & van der Linden, S. (2008). Classifying multilevel imagery from SAR and optical sensors by decision fusion. IEEE Transactions on Geoscience and Remote Sensing, 46, 1457–1466. Wold, S., Sjöström, M., & Eriksson, L. (2001). PLS-regression: A basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems, 58, 109–130. Yoder, B. J., & Pettigrew-Crosby, R. E. (1995). Predicting nitrogen and chlorophyll content and concentrations from reflectance spectra (400–2500 nm) at leaf and canopy scales. Remote Sensing of Environment, 53, 199–211.
