dataesr/scientific-paragraphs-categorization huggingface dataset:
The TLS point cloud was collected with an angular resolution of 0. 04 ˝(vertically and horizontally) from one station. More than 10. 6 million points were recorded over the study area (Figure  4 ); however, the point cloud density is heterogeneous. The TLS dataset was georeferenced indirectly, using 12 reflective targets. The absolute position of these targets was measured by post-processed RTK GPS, while their relative position in the point cloud was obtained with the TLS by semi-automatic detection and re-scanning at very fine spatial resolution. A least squares algorithm was applied to compute the transformation providing the best fit between absolute and relative positions of the targets. The residual error of this georeferencing process is about 5 cm for the targets. Such uncertainties result in errors up to 32 cm at a range of 300 m from the TLS position (e.
The user can also specify the maximum number of polygons in the final mesh. In our study, this parameter is set to "High" (i. e. , 1/5 of the number of points in the previously generated dense point cloud) to optimize the level of detail of the mesh. 4. The reconstructed mesh can be textured following different mapping modes. In this study, we used the default "Generic" mode. The intermediate results can be checked and saved at every step. At the end of the process, a DSM and an orthophotograph are exported in GeoTiff format, without any additional post-processing (optimization, filtering, etc. ). This format implies that datasets are converted to 2. 5D.
4. The reconstructed mesh can be textured following different mapping modes. In this study, we used the default "Generic" mode. The intermediate results can be checked and saved at every step. At the end of the process, a DSM and an orthophotograph are exported in GeoTiff format, without any additional post-processing (optimization, filtering, etc. ). This format implies that datasets are converted to 2. 5D. Such a conversion may have an effect on the reconstruction of complex structures. However, as there are almost no overhanging elements in the study area, the impact of the 2. 5D conversion remains limited and is therefore neglected in this study, considering that photos are acquired from a nadir point of view and that both PhotoScan and MicMac DSM are affected in the same way by this conversion.
MicMac Overview MicMac (acronym for "Multi-Images Correspondances, Méthodes Automatiques de Corrélation") is an open-source photogrammetric software suite developed by IGN ® for computing 3D models from sets of images  [22, 23]. Micmac ® chain is very open and most of the parameters can be finely tuned. In this study, we use the version v. 5348 for Linux. The standard "pipeline" for transforming a set of aerial images in a 3D model and generating an orthophoto with MicMac consists of four steps.
2. External orientation and intrinsic calibration: the Apero tool generates external and internal orientations of the camera. The relative orientations were computed with the Tapas tool in two steps: first on a small set of images and then by using the calibration obtained as an initial value for the global orientation of all images. The distortion model used in this module is a Fraser's radial model with decentric and affine parameters and 12 degrees of freedom. Recently, Tournadre et al. (2015) published a study  [25]  presenting the last evolutions of MicMac's bundle adjustment and some additional camera distortion models specifically designed to address issues arising with UAV linear photogrammetry. Indeed, UAV surveys along a linear trajectory may be problematic for 3D reconstruction, as they tend to induce "bowl effects"  [25, 26]  due to a poor estimation of the camera's internal parameters.
Processing Scenarios Surface reconstruction is performed on the one hand using PhotoScan, and using MicMac on the other. Both SfM photogrammetric processes are computed with the same set of images and the same set of GCPs. GCPs are manually tagged on the images. Four scenarios are tested: ‚ Scenario 1: the process is performed with the automatic selection of 121 photographs (Selection #1), using full-resolution images, i. e. , 4256 ˆ2832 pixels (12 Mpix), and 12 GCPs. ‚ Scenario 2: the process is performed with the manual selection of 109 photographs (Selection #2), using full-resolution images and 12 GCPs. ‚ Scenario 3: the process is performed with the set of 109 selected photographs, using reduced-quality images, i. e. , 2128 ˆ1416 pixels (3 Mpix), and 12 GCPs. The images of the datasets were down-sampled from 12 Megapixels (Mpix) to 3 Mpix, selecting one line and one sample out of two without modifying the color content of the pixels (nearest-neighbor approach).
2016, 8, 465 9 of 17 • Scenario 2: the process is performed with the manual selection of 109 photographs (Selection #2), using full-resolution images and 12 GCPs. • Scenario 3: the process is performed with the set of 109 selected photographs, using reduced-quality images, i. e. , 2128 × 1416 pixels (3 Mpix), and 12 GCPs. The images of the datasets were down-sampled from 12 Megapixels (Mpix) to 3 Mpix, selecting one line and one sample out of two without modifying the color content of the pixels (nearest-neighbor approach). • Scenario 4: the process is performed with the set of 109 selected photographs using full-resolution images and only six GCPs: GCP 1, GCP 2, GCP 6, GCP 7, GCP 8 and GCP 9. The goal of this scenario is to test the impact of the number of GCPs and their distribution within the control region.
Effects of the Refined Distortion Model on MicMac Processing Chain Outside of the control region, the images are acquired on two quasi-parallel lines of flight. Linear sequences of images have been shown to yield warped 3D models due to a drift in bundle adjustment  [25, 26]. Before processing data with MicMac based on the different scenarios, the MicMac module for UAV linear photogrammetry  [25]  has been put to the test. These additional distortion models integrated into MicMac have been developed for long linear surveys, especially for riverbed monitoring over several kilometers. Even if the study area is more "compact" here, the refined distortion models are tested to find out whether, in our case, they improve the accuracy of the solution. Scenario 1 has been implemented on one hand with a basic radial distortion model (Fraser's radial model) and, on the other hand, with a refined radial distortion model (Four 15 ˆ2) with a polynomial correction of degree 7, referred in the following as "MicMac-rdm".
The accuracy of the resulting reconstructions is assessed using eight reference targets (Table  1 ). With MicMac, the vertical Root Mean Square Error (RMSE) is 8. 0 cm, while it is 60% lower with Micmac-rdm. As the targets are not covering the entire surveyed area, further comparisons are carried out to assess the uncertainty of the reconstructed DSM outside of the control region. A Digital Elevation Model (DEM) of Difference between MicMac-rdm and MicMac is computed (Figure  7a ) and altitude profiles are extracted (Figure  7b ). The profile extracted from TLS data can be used as a reference, although (i) it is fragmented because of no-data zones induced by occlusions and (ii) the TLS dataset is also subject to greater uncertainty outside of the control region. The profile extracted from the PhotoScan DSM is also displayed for relative comparisons.
It appears that the MicMac-rdm DSM and the MicMac DSM are nearly similar over the control region (Figure  7a ) where the GCPs are located. In contrast, in the external part of the area, the MicMac-rdm DSM shows higher mean elevations than the MicMac DSM, which is affected by bowl effects. The refined distortion model increases the altitude of the external parts of the DEM up to 50 cm in the Western part of the study area, and up to 3 m in the Eastern part. The altitude profiles (Figure  7b ) highlight that the stereophotogrammetric DSMs are below TLS data. MicMac-rdm appears more efficient than MicMac with basic distortion model since the altitude profile derived from the DSM computed using MicMac-rdm is very similar to the PhotoScan profile and closer to TLS data than the profile obtained from MicMac.
Quality Assessment of PhotoScan and MicMac within the Control Region Using Ground-Truth Reference Points For each scenario, the horizontal Root Mean Square Error (RMSE) is calculated from the differences between the x-y positions of the nine "ground-truth" reference points (the blue reference targets) measured by RTK DGPS and their x-y positions pointed out on the georeferenced PhotoScan/MicMac orthophoto. The vertical RMSE is calculated from the differences between the z positions of the blue targets measured by RTK DGPS and their altitude on the PhotoScan/MicMac reconstructed DSM. These errors are thus computed independently of the estimation made by both software packages. The results are presented in Table  2. Horizontal and vertical RMSE are calculated on the nine blue reference targets.
Quality Assessment of PhotoScan and MicMac within the Control Region Using Ground-Truth Reference Points For each scenario, the horizontal Root Mean Square Error (RMSE) is calculated from the differences between the x-y positions of the nine "ground-truth" reference points (the blue reference targets) measured by RTK DGPS and their x-y positions pointed out on the georeferenced PhotoScan/MicMac orthophoto. The vertical RMSE is calculated from the differences between the z positions of the blue targets measured by RTK DGPS and their altitude on the PhotoScan/MicMac reconstructed DSM. These errors are thus computed independently of the estimation made by both software packages. Th results are presented in Table  2. In scenario 1, the horizontal RMSE is 4. 5 cm with PhotoScan and 3. 5 cm with Micmac; the vertical RMSE are 3.
Relative Quality Assessment of PhotoScan and MicMac with Respect to the TLS Point Cloud over the Whole Study Area At the same time as the UAV survey, the 3D positions of 10. 6 million points were measured by TLS. As the TLS point cloud is acquired from a terrestrial point of view, the point cloud is very dense on the vertical scanned surfaces. However, because of the complex topography causing occlusion effects, the TLS point cloud presents some areas without data. As expected, given the poor GPS reception typical in a mountainous context, the accuracy of the TLS dataset is low. The TLS dataset is also subject to greater uncertainties outside of the control region. Nevertheless, it can be used as a point of comparison to analyze in which way the results of the photogrammetric chains drift where there is no GCP.
Thus, the TLS dataset serves as a reference DTM, but it is not considered as ground truth. To avoid interpolations effects from meshing the sparse TLS point cloud, this dataset is kept in XYZ point cloud format. Both PhotoScan and MicMac DSMs are thus directly compared to the georeferenced TLS point cloud, using the FlederMaus ® CrossCheck tool. For each point of the TLS point cloud, Z TLS is compared to the z value of the corresponding xy-coordinates cell in the photogrammetric DSM raster. The results of the comparison (Z TLS -DSM) are presented in Figure  8  and Table  3. In Figure  8 , the light yellow areas depict areas where the altitude of TLS point cloud is equal or close to the altitude of the DSM computed by SfM photogrammetry. In red areas, the TLS point cloud is above the photogrammetric DSM.
It appears that the mean differences to the TLS DSM are higher with MicMac than with PhotoScan (Table  3 ). With MicMac, the errors assessed by comparison to the TLS point cloud (Table  3 ) are also higher than the errors assessed using ground truth reference points (Table  2 ). Such an increase in the error may be partly due to greater uncertainties on TLS dataset than on the ground truth reference points, as well as discrepancies on the reconstruction of sharp-relief zones. Indeed, the gaps on the southern and northern edges of the TLS point cloud coincide with the terraces fronts (Figure  4 ), which are challenging to compute by aerial photogrammetry. Moreover, such poor reconstructions largely contribute to increasing the error. Indeed, first, a horizontal shift of some centimeters in such complex environments may generate important vertical offsets in DSM differencing, implying errors in volume budgets.
Such an increase in the error may be partly due to greater uncertainties on TLS dataset than on the ground truth reference points, as well as discrepancies on the reconstruction of sharp-relief zones. Indeed, the gaps on the southern and northern edges of the TLS point cloud coincide with the terraces fronts (Figure  4 ), which are challenging to compute by aerial photogrammetry. Moreover, such poor reconstructions largely contribute to increasing the error. Indeed, first, a horizontal shift of some centimeters in such complex environments may generate important vertical offsets in DSM differencing, implying errors in volume budgets. Second, as the sections of the TLS point cloud corresponding to quasi-vertical terraces fronts are generally very dense, the relative weight of these areas in the error calculation is very large.
Using oblique imagery may limit such artefacts; nevertheless, it would increase occlusions and shadowing. With MicMac, sharp relief variations also appear on the 10 m-long vertical profile extracted along a set of rocky blocks (Figure  10 ). The surface reconstructed with PhotoScan is smoother. However, the Root Mean Square (RMS) offset between both photogrammetric DSMs is only 6 cm, and 17 cm with the TLS dataset. With MicMac, sharp relief variations also appear on the 10 m-long vertical profile extracted along a set of rocky blocks (Figure  10 ). The surface reconstructed with PhotoScan is smoother. However, the Root Mean Square (RMS) offset between both photogrammetric DSMs is only 6 cm, and 17 cm with the TLS dataset. Even if these offsets due to spatial high-frequencies reconstruction remain low at the scale of the topographic variations, they may have an impact on sediment budgets in diachronic DSM differencing  [29, 30].
Conclusions This study aims at comparing the reconstruction of the DSM and orthophotograph obtained with two software packages for SfM photogrammetry. AgiSoft ® PhotoScan Pro, a commercial solution, and MicMac, an open-source solution proposed by IGN © , are tested with UAV images collected in challenging conditions. The sensitivity of each software tool to different parameters Even if these offsets due to spatial high-frequencies reconstruction remain low at the scale of the topographic variations, they may have an impact on sediment budgets in diachronic DSM differencing  [29, 30]. In such complex environments, a horizontal shift of a few centimeters may create large shifts in the vertical direction due to highly sloping surfaces. These offsets partly explain the differences previously observed in the comparisons with the TLS point cloud (Figure  8 ).
Conclusions This study aims at comparing the reconstruction of the DSM and orthophotograph obtained with two software packages for SfM photogrammetry. AgiSoft ® PhotoScan Pro, a commercial solution, and MicMac, an open-source solution proposed by IGN © , are tested with UAV images collected in challenging conditions. The sensitivity of each software tool to different parameters (images selection, images resolution, position and number of GCPs) has been analyzed. The MicMac-rdm package recently developed for linear surveys greatly improves the quality of the results compared to the basic distortion model. Nevertheless, Brown's distortion model implemented in PhotoScan still seems more appropriate than the refined radial model implemented in MicMac in this particular context of rugged terrain.
The results are analyzed in two ways: (i) using ground truth reference targets (distinct from the GCPs, but located in the same area) within the control region; and (ii) by comparison with a TLS point cloud (at the scale of the entire surveyed area). To limit the impact of GPS uncertainties in the comparison, we consider precision rather than accuracy. Within the control region, both software packages provide satisfying results, with an achievable precision of 3-4 cm. Outside of the control region, the comparison with TLS dataset shows that both reconstructed DSMs tend to deviate in the Eastern part because of "bowl's effects" in the absence of GCPs. Nevertheless, PhotoScan seems to provide better results than MicMac thanks to a more relevant distortion model (limiting deviations in the DSM) and a better reconstruction of the terrace front.
We develop a new robust stopping criterion for partial least squares regression (PLSR) component construction, characterized by a high level of stability. This new criterion is universal since it is suitable both for PLSR and extensions to generalized linear regression (PLSGLR). The criterion is based on a non-parametric bootstrap technique and must be computed algorithmically. It allows the testing of each successive component at a preset significance level α. In order to assess its performance and robustness with respect to various noise levels, we perform dataset simulations in which there is a preset and known number of components. These simulations are carried out for datasets characterized both by n > p, with n the number of subjects and p the number of covariates, as well as for n < p.
Introduction Modeling relationships using traditional statistical methods like ordinary least squares regression (OLSR), between a univariate response and highly correlated covariates, is rarely recommended, and for datasets including more covariates than subjects, is not even possible. However, with recent technological and computing advances, providing consistent analysis of such datasets has become a major challenge, particularly in domains such as medicine, biology and chemometrics. For such reasons, statistical methods have been developed, including partial least squares regression (PLSR), introduced by  Wold et al. (1983)  and described in detail by  Höskuldsson (1988) , amongst others. PLSR has become a standard tool in chemometrics  (Wold et al. 2001 ) and for dealing with genomic datasets  (Boulesteix and Strimmer 2007).
This led to further research and developments related to the field  (Nguyen and Rocke 2002; Boulesteix 2004; Ding and Gentleman 2005). Note that in this case, y is naturally not centered or scaled to unit variance. In this paper, the process developed by  Bastien et al. (2005)  and implemented in the R package plsRglm  (Bertrand et al. 2014 ) is used. In this context, the regression model is the following: g(θ ) = K k=1 c k ⎛ ⎝ p j=1 w * jk x j ⎞ ⎠ , ( 9 ) with θ the conditional expected value of y for a continuous distribution, or the probability vector of a discrete distribution with a finite support. The link function g depends on the distribution of y. As mentioned above, both PLSR and its extension to generalized models rely on determining a tuning parameter: the number of components.
Second, this new criterion has to avoid CV methodology and related issues such as instability. Therefore, we develop a new bootstrap-based criterion to select the number of PLS components. The originality of the approach is due to the fact that it tests directly both the Xand y-loadings. To do this, the establishment of bootstrapbased confidence intervals (CI) is achieved. By focusing on the unknown distribution of the regression coefficients rather than predictive error-based statistics as previously proposed, we open up the possibility of directly testing the significance of successive components, which is pertinent for both the PLSR and PLSGLR frameworks. This method avoids the use of CV techniques and related issues. In this article, we first explain the context and give theoretical details, before introducing the new algorithmic bootstrap-based criterion as pseudo-code in Sect.
2. In Sect. 3, we present existing criteria that have been chosen for comparison purposes, and then describe the simulation set-up we use to make comparisons. In Sect. 4, we analyze results obtained in the PLSR framework, followed by PLS-GLR results for logistic regression (PLS-LR) and Poisson regression (PLS-PR) in Sect. 5. In Sect. 6, we focus on some real datasets and compare our new criterion to relevant existing ones. Using a real allelotyping dataset, we also compare the robustness of our new bootstrap-based criterion through resampling, approximating the distribution of the extracted number of components. Lastly, in Sect. 7, we discuss the observed advantages and disadvantages of each criterion.
Bootstrapping pairs in PLSR Let Z = (z 1 ,. , z n ) T = (y, X) ∈ M n, p+1 (R), i. e. , z i = y i , x i1 ,. , x i p , 1 i n. The so-called bootstrapping pairs method was introduced by  Freedman (1981)  and consists of building R new datasets by re-sampling with replacement in Z in order to mimic the generation of the original data. This leads to an empirical approximation of the distribution linked to a statistic S (Z). This technique only relies on the assumption that the originals pairs (y i , x i• ), where x i• represents the ith row of X, are randomly sampled from some unknown ( p + 1)-dimensional distribution. It was developed to treat so-called correlation models, in which covariates are considered as random, and may be related to them. In this way, it is appropriate to "estimate the regression plane for a certain population on the basis of a simple random sample"  (Freedman 1981 (Freedman , p.
Our goal is to test particular PLS components based on the original dataset, since these latent variables are built and used for modeling specifically these original data. In other words, a method able to test the significance of these particular random latent variables, defined as specific linear combinations obtained through the PLSR processed on the original dataset, is to be looked for. As a concrete example, let t ori 1 = p j=1 w ori j1 x j be the first PLS component based on the original data. By bootstrapping pairs (y i , x i• ) and applying the PLS process to a bootstrap sample (y, X) b , the obtained weights w b 1 are naturally different from w ori 1 , so the uncertainty of the specific random variable p j=1 w ori j1 x j is not tested by this ill-adapted process, but rather uncertainty about the construction of this first component.
Existing criteria used for comparison To perform our benchmarking study, several existing criteria were used. In the PLSR framework, the Q 2 criterion was selected since it represents a standard criterion, implemented notably in both the R package plsRglm  (Bertrand et al. 2014 ) and the SIMCA-P software  (Umetrics 2005). This criterion is based on q-fold CV methods  (Breiman et al. 1984)  and was computed for both q = n, leading to the universal standard CV method called leave-one-out CV  (Gómez-Carracedo et al. 2007) , and q = 5 (5-CV) following recommendations of  Kohavi (1995)  and  Hastie et al. (2009) , so as to reduce variability in the CV method. The BIC criteria, corrected with the estimated degrees of freedom (DoF) by  Krämer and Sugiyama (2011) , was also included since to the best of our knowledge, no published study has analyzed its performance.
In the PLSGLR framework, there are a limited number of relevant criteria available; we thus present only two here: the number of misclassified values  (Meyer et al. 2010) , and a criterion introduced by  Bastien et al. (2005). Both are available in the R package plsRglm. The usual AIC and BIC criteria were also included. -In PLSR: 1 Q 2. For each new component t k , the following statistic is evaluated: Q 2 k = 1 - PRESS k RSS k-1 , where RSS k-1 represents the Residual Sum of Squares when the number of components is k-1, and PRESS k the PRESS when the number of components is equal to k. Tenenhaus (1998)  considers that a new component t k improves significantly the prediction of y if: PRESS k 0. 95 RSS k-1 ⇐⇒ Q 2 k 0. 0975. Results linked to this criterion using both leave-oneout and q = 5 CV are referred to in the text and plots by Q2lv1o and Q2K5 respectively.