dataesr/scientific-paragraphs-categorization huggingface dataset:
For both training and testing, reads of length L = 200 are extracted from the genomes. The validation datasets are built by extracting fragments such that their coverage -the average number of times each nucleotide is present -is 1. This amounts to a total of 134, 319 validation samples for the small database, and ∼ 3. 5M samples for the large database. The machine learning-based models are trained on reads sampled from the reference genomes and their known taxonomic labels, while alignment-based methods simply align validation reads to the training reference genomes. To account for the fact that DNA is double-stranded and that when a read is sequenced it can come from any of the two strands, which are reverse-complement to each other, we systematically add the reverse-complement of each read with the same label at training time.
Reference methods We compare our method, which we call fastDNA in the rest of the text, to two other strategies. One is the BWA-MEM sequence aligner  [13]  and the other is the linear SVM classifier on the k-spectral representation, implemented using the Vowpal Wabbit software in  [22]. We name the latter method VW in the rest of the paper. We follow exactly the same configurations as  [22]  for both methods.
Large dataset We report the classification performance, measured by average species-level recall and precision of fastDNA on the validation sets described in 3. 1. The influence of the training noise is shown in figure  3. As could be expected, greater levels of sequencing noise in the validation sets lead to degraded performances. Adding random mutations to the training reads curbs this effect. The greater the mutation rate is, the more robust the model becomes to higher levels of sequencing noise. Somewhat more surprisingly, a certain range of mutation rates also increases the performance on the validation reads with no sequencing noise. The regularization induced by these artificial errors is therefore beneficial for both sequencing noise and intra-species heterogeneity. We found that the best rates of mutation were between 2 and 5%.
Due to the large values of 4 k , this can make up a significant portion of the total time. Moreover, we observe in practice a longer memory access time for larger vectors. These are the two reasons for the time gap observed between classification with models of same embedding dimension d but different k. The total time complexity for predicting a dataset with n samples is therefore O(n(dL + dT ) + dN ). With reads of constant length, fastDNA and VW classify reads indiscriminately of their content, and therefore yield equal classification times across the validation sets. On the other hand, BWA's speed degrades with the sequencing noise, which is easily explained. BWA searches iteratively on the number of mismatches z and stops once it gets a hit. It will therefore be slower if there are more mismatches between the testing and reference data.
We show in figure  5  the classification speeds measured for the large dataset. The values reported are for a single CPU (Intel Xeon E5-2450 v2 -2. 5GHz). We show fastDNA for d = 100 and k = 12, 13 and VW. fastDNA and VW have similar classification times of ∼ 6, 7 • 10 3 reads per minute. As remarked in  [22] , compositional approaches offer systematically better prediction times than BWA, with improvements of 2 -9×. This speed improvement increases with the mismatch between predicted sequences and reference genomes, therefore with both sequencing noise and intra-species variations. We demonstrated that learning a low-dimensional representation of DNA reads based on their k-mer composition is feasible, and outperforms state-of-the-art compositional approaches that work directly on the high-dimensional, k-spectral representation of DNA sequences.
Numerical experiments In this section, numerical experiments are conducted to evaluate the performance of proposed algorithms. Both of PST heuristic and GA are programmed in Matlab 2014a and executed on a personal computer (Intel Core i5 with 4 GB RAM) with Microsoft Windows 7 operating system. Commercial solver CPLEX 12. 6 is used and called in Matlab 2014a to solve the MIP model. The computational time of CPLEX is limited by 7200 seconds (two hours in CPU time) since large computational time is unacceptable for terminal practice.
g. characterised by multi-layer structures, such as vegetated areas  [3]  or urban canyons  [4] , or by intimate sandlike mixtures  [5]. The interested reader is invited to consult  [6] [7] [8]  for comprehensive discussions on both classes of models. Most of the unmixing strategies are based on two-step procedures. Firstly, the spectral signatures associated with the endmembers are extracted from the whole set of image pixels. Secondly, in an inversion step, the abundances are estimated in each pixel based on the estimated endmembers and the adopted LMM or NLMM. Popular endmember extraction algorithm includes N-FINDR  [9]  and simplex growing algorithm (SGA)  [10]  which search for a simplex with the maximum volume inscribed in the dataset. Similarly, pixel purity index (PPI)  [11]  and vertex component analysis (VCA)  [12]  recovers this simplex through geometrical projections.
When dealing with non-linear mixtures, dedicated unmixing techniques should be considered. Some of them proposed in the literature rely on parametric formulations of the non-linearities that may occur during the mixing process. When these non-linearities result from multiple scattering effects, various bilinear mixing models have been designed  [15]  for which specific unmixing techniques have been developed  [4, 16, 17]. Conversely, nonparametric model-based unmixing strategies have been derived to address a larger variety of non-linear mixtures. When the nonlinearities are considered as additional contributions of the LMM, robust models allow these non-linear terms to remain unspecified  [18, 19]. Additionally, some significant contributions exploit the versatility of the machine learning framework to handle the variety of non-linear effects, in particular when training dataset are available to learn the non-linear mapping from the abundances to the measured pixel spectra.
g. K-means), which are topologically organised on a lattice structure. According to the general framework of kernel SOM described in  [30] , all prototypes are written as convex combinations of the input data in the feature space ∀m ∈ ℳ, p m = ∑ p = 1 P γ mp ϕ(x p ) (9) The proposed MK-SOM unmixing algorithm consists of two main steps. First, the training step recovers the pure pixels to obtain the weight map. Then, the testing step computes the abundance vector for each pixel in the image. These two steps are briefly recalled in what follows.
Experimental results To validate the proposed MK-SOM-based unmixing algorithm, its performance has been compared to those obtained by the linear unmixing methods FCLS  [13]  and SUNSAL  [14]  and the nonlinear unmixing methods PPNM  [16] , rLMM  [18] , K-Hype and its generalised counterpart (SK-Hype)  [41]. The experimental datasets consist of synthetic and real images described in what follows.
Datasets Firstly, to assess the performance of the unmixing procedures, we consider a hyperspectral image of size 100 × 100 pixels and composed of nine endmembers representative of minerals which have been extracted from the U. S. Geological Survey (USGS) spectral library  [42]. The abundance maps have been choosing as freely available dataset referred to as Fractal 1 and available online  [43]  has been used. They have been generated according to fractal patterns to ensure realistic distribution of the materials other the scene. In particular, it is constructed such that the pixels nearby the region centres are more spectrally pure than the pixels in the transition areas  [44]. Based on these endmembers and abundance maps, the mixed pixels have been generated according to the nonlinear model, namely the so-called Fan bilinear model introduced in  [45].
An additive white Gaussian noise has been considered with a corresponding signal-to-noise ratio chosen as SNR=40 dB. To illustrate Fig. 3  depicts the synthetic image in a band #1. Secondly, the real so-called Cuprite dataset acquired by the airborne visible/infrared imaging spectrometer (AVIRIS) has been considered  [46]. It consists of a 614 × 512 pixel image and 224 bands with a spectral range of 0. 4 -2. 5 μm. A set of 33 bands have been removed prior to analysis since they correspond to water absorption band or low SNR. Fig. 4  shows the Cuprite image observed in band #10.
Quality metrics For the synthetic dataset for which ground-truth (i. e. in terms of actual abundance maps) is available, the performances of the unmixing procedures are evaluated through the mean square error of the abundances  [47] MSE A = 1 NK ∑ n = 1 N ∥ a ^n -a n ∥ 2 2 ( 13 ) where a n and a ^n are the actual and estimated abundance vectors associated with the pixel #n (n ∈ 1, …, N ), respectively, and K is the number of endmembers used during the unmixing process. For the real datasets for which no ground-truth is available, the reconstruction error between the original and recovered pixel signatures  [47] RE Y = 1 LN ∑ n = 1 N ∥ y ^n -y n ∥ 2 2 ( 14 ) where y n and y ^n are the measured and reconstructed spectra associated with the pixel #n (n ∈ 1, …, N ) and L is the number of spectral bands.
0625) is obtained by MK-SOM for a number of epochs equals to T epoch = 500. When the number of endmembers is equal to K = 9, the MK-SOM consistently performs better than all other methods. The best MSE value (0. 0123) is reached when MK-SOM is run with the number of epochs equal to T epoch = 500. To illustrate, the corresponding estimated abundance maps for a synthetic image are depicted in Fig. 5  for K = 4. As complementary results, Figs. 6 and 7 report the reconstruction errors for different levels of noise for K = 4 and a different number of endmembers for SNR = 40, respectively. Similarly, Table  3  shows the performance of compared algorithms when applied to the real AVIRIS Cuprite dataset for a number of endmembers equal to K = 9. The proposed MK-SOM consistently outperforms the concurrent methods and, in particular, provides the lowest error for a number of epochs equal to T epoch = 20.
Parallel implementation of the MK-SOM algorithm This section presents a parallel implementation of the MK-SOM algorithm described in Section 2. This implementation is developed on a GPU using a CUDA programming language. The experiments are conducted on an NVidia Tesla N2090 architecture and show that the parallelisation provides a significant speedup of the required computational time. Per se, MK-SOM learning is a highly parallelised problem as it is based on an SOM learning approach. The complexity of the calculation is greatly affected by the SOM map size and number of features (number of bands in the   considered unmixing problem). A simple SOM learning can be summarised as Algorithm 3 (see Fig. 9 ). The most computationally intensive steps are Steps 3 and 4 of Algorithm 3 (Fig. 9 ) described below: • Computing the Euclidean distance between the selected training sample and the SOM map, then obtaining the best matching unit (BMU) which correspond to the minimum distance, • Updating the SOM map weights according to the distance between the selected training sample and BMU yet updates are limited to only the BMU neighbours.
The degree of parallelism of Step 3 is limited to the dimension of the training set (number of features). On the other hand, the complexity of the MK-SOM testing step (see Section 2. 3 and Algorithm 2 (Fig. 2 )) mainly depends on the image size, the SOM map size and the number of endmembers. Therefore, for a given image, the expected parallelisation speedup directly increases with the SOM map size. As an illustrative example of the possible computational gain, the implemented CUDA version has been evaluated in the real AVIRIS Cuprite Image of size 512 × 614 × 189 with different SOM map sizes. The resulting computational times, compared to those obtained on crude (i. e. serial) or multi-threading MATLAB implementations, are reported in Table  4. These results show a significant speedup ranging from × 185 to × 6252 with respect to its MATLAB counterpart.
Conclusion This paper introduced a new unmixing method based on simple MKL with SOM as a solver. The proposed non-linear unmixing approach succeeded in reducing the estimation error when applied to synthetic and real hyperspectral images. Moreover, it seemed to be robust with respect to the choice of the parameters required by   the training stage. At the price of a slightly more computationally intensive complexity, the proposed MK-SOM framework appears as a relevant alternative of state-of-the-art non-linear unmixing methods. Finally, this paper showed that a parallel implementation of the proposed algorithm was possible. This parallelisation was implemented using a graphics processing unit and the resulting computational gain was shown to be highly significant when compared to serial and multi-threaded MATLAB implementations.
, 2013 (Young et al. , , 2016;; Kim et al. , 2018). To date, the radiometric calibration of space-based elastic backscatter lidar measurements has always been accomplished by calculating timevarying scale factors that provide the best near-instantaneous match between the measured data and the theoretically expected backscatter signals derived for some stable, wellcharacterized calibration target. The choice of calibration target depends critically on target availability and the signalto-noise ratio (SNR) of the target measurements. By far the most common target is the Earth's atmosphere, which at very high altitudes is essentially free of aerosol contamination, and hence the expected molecular backscatter can be well-characterized using the temperature and pressure profiles provided by atmospheric model data (e.
Through the course of three major data releases spanning ∼ 8 years of on-orbit operations, the CALIOP 1064 nm calibration scheme remained relatively unchanged. The theoretical basis of the original algorithm is given in  Hostetler et al. (2005). Vaughan et al. (2010)  provide details on some procedural modifications that were incorporated for the version 3 (V3) data release. In contrast to these V3 updates, the version 4. 1 (V4) release is a comprehensive upgrade that features major changes to all of the primary components of the 1064 nm calibration algorithm. In particular, we (a) defined a detailed set of sharply focused criteria to identify a much more homogeneous population of clouds used in the calibration procedure; (b) implemented a wholly new data averaging scheme that reduces uncertainties while simultaneously preserving intra-orbit variations in the calibration coefficients; and (c) augmented the lidar level 1 (L1) data products with substantially more robust estimates of calibration uncertainties.
The fundamentals of the CALIOP 532 molecular normalization technique are given in  Hostetler et al. (2005)  (hereafter H05) and  Powell et al. (2009) (hereafter, P09). Initial development of CALIOP's 1064 nm cirrus cloud calibration scheme and the mathematical development of the error propagation is given in H05, with postlaunch updates provided in  Vaughan et al. (2010)  (hereafter V10). The paper is organized as follows. Section 2 reviews the fundamental assumptions and equations that are used in the CALIOP 1064 nm calibration scheme. Section 3 provides a brief review of the specific techniques used for the V3 data release and highlights the shortcomings that motivated the development of the V4 scheme. Details of the V4 approach, including the physical basis for selecting "calibration quality" cirrus clouds and the constraints involved in developing a multi-orbit data averaging scheme, are given in Sect.
1. The 1064 nm daytime calibration coefficients are derived from the 532 nm daytime calibration coefficients, which in turn are derived from the 532 nm nighttime calibration coefficients  (Getzewich et al. , 2018). The uncertainties for the daytime 1064 nm calibration coefficients thus contain contributions from both the daytime and nighttime 532 nm calibrations. 3 Motivation for change: the V3 calibration algorithms Effective use of the 1064 nm calibration equation implicitly requires two critically important subroutines: 1. an algorithm to identify cirrus clouds appropriate for use in the calibration calculation and 2. a data averaging scheme to reduce the random noise in the calibration coefficients without simultaneously introducing biases. In this section we review the methods used for these tasks in the CALIOP V3 calibration scheme and point out the shortcomings that led to the subsequent development of revised techniques for V4.
The third type of bias occasioned by the V3 calibration routine is the risk of differential attenuation of the 532 and 1064 nm signals. While X 532 and X 1064 are both corrected for wavelength-dependent attenuation effects due to molecular and ozone two-way transmittances, at this initial stage of the lidar data analysis, no correction is possible for as-yet undetected particulates (i. e. , cloud or aerosol layers) lying between the lidar and the top of the calibration cloud. A more rigorous expansion of Eq. (2) would explicitly include these terms; i. e. , F V3 = χ -1 cirrus T 2 p,1064 0, r z top X 1064 r z top , r (z base ) T 2 p,532 0, r z top X 532 r z top , r (z base ) , (9) where T 2 p,λ 0, r z top represents the particulate two-way transmittance between the lidar (at range = 0) and the top of the calibration cloud (at range = z top ), and the mean signals are now explicitly calculated over the range from z top to z base.
The V3 calibration averaging scheme Although individual estimates of F V3 use high SNR measurements (i. e. , R 532 (z) > 50), the uncertainties for these estimates are still large, and thus obtaining reliable values requires some amount of signal averaging. To maximize the number of F V3 samples averaged, the V3 scheme computes mean values of F V3 , denoted as F V3 , over each granule of the CALIOP data record (H05, V10). CALIOP data granules extend from one terminator to the next, thus dividing each orbit into separate daytime and nighttime segments. This averaging scheme implicitly assumes that the pattern of thermally driven intra-orbit changes observed in the 532 nm calibration coefficients (P09) is reproduced more or less identically in the 1064 nm calibration coefficients, and hence F V3 can be considered constant with respect to the elapsed time throughout the individual daytime and nighttime segments of any orbit.
Calculating profiles of V3 attenuated backscatter coefficients Once F V3 has been computed for a granule, the V3 1064 nm calibration coefficients are computed for each profile in the granule using Eq. (  1 ). The altitude-resolved profiles of 1064 nm attenuated backscatter, β 1064 (z), reported in  the CALIPSO lidar level 1 data products are then derived as follows (H05): β 1064 (z)= r(z) 2 P 1064 (z) -P 1064,bkg G 1064 E 1064 C 1064 (10) = β 1064,m (z) + β 1064,p (z) T 2 λ,m (z) T 2 λ,O 3 (z) T 2 η λ,p (z) , where P 1064 (z) is the backscattered signal from altitude z measured aboard the satellite in the 1064 nm receiver (units: digitizer counts), P 1064,bkg is the background signal measured aboard the satellite for each profile, and r(z) is the range (units: km) from the lidar to altitude z.
The version calibration algorithms To correct the shortcomings discovered in the V3 calibration scheme, CALIOP's V4 algorithm differs from its predecessors in three fundamental aspects: cirrus cloud selection, data averaging, and the characterization of uncertainties. Each of these will be addressed in the following subsections. Ad- G λ = base top X λ (r) dr -dG λ , where dG λ = 1 2 z top -z base X λ (z base ) + X λ z top , (11) (e. g. , as derived in Eqs. 18-20 in V10), and thus F V4 = χ -1 cirrus G 1064 G 532. ( 12 ) The dG λ terms represent corrections for the molecular scattering contributions to the signals measured within the cloud boundaries. As explained in detail in Sect. 4. 1, the V4 cirrus cloud selection method no longer enforces the large scattering ratio requirement (R 532 > 50) that allowed us to neglect these contributions in V3, and thus corrections for molecular scattering are essential in the V4 calibration algorithm.
Characterizing intra-orbit changes using multi-granule data averaging The primary motivation for the complete redesign of the CALIOP 1064 nm calibration scheme is to accurately characterize the time-varying behavior of the calibration scale factors. As illustrated in Fig. 5 , these changes occur on multiple timescales, from intra-orbit to seasonal. Designing an effective data averaging scheme thus becomes a question of balancing requirements in two time dimensions: along track within a single granule and again across multiple granules. Specifically, we need to accumulate a sample size large enough to minimize the random uncertainty in our estimates of F V4 , while at the same time (a) limiting the extent of the along-track averaging in order to reliably capture the dependence of scale factors with respect to granule elapsed time and (b) limiting the duration of our multi-granule averaging window to prevent smearing of legitimate changes in the scale factors that occur on weekly-to-seasonal timescales.
In this example, the relative uncertainty attributed to χ cirrus is reduced from a single sample value of ∼ 25 % to mean values of 0. 93 % ± 0. 20 % during the day and 0. 97 % ± 0. 24 % at night. Both in this ex-ample and throughout the entire V4 data set, χ cirrus remains the dominant random uncertainty in estimating F V4. The CALIOP V4 data products report estimates of random uncertainties in the 532 and 1064 nm calibration coefficients on a profile-by-profile basis. Figure  17a  plots the mean values of the relative calibration coefficient uncertainties at both wavelengths as functions of latitude for all of November 2015. The dip in sample counts shown at ∼ 20 • N in the right-hand panel of Fig. 16  is echoed by the increase in 1064 nm calibration uncertainty seen at the same latitude in Fig.
Comparisons to other techniques and measurements While CALIOP uses cirrus clouds to calibrate its 1064 nm measurements, other calibration targets are also available. SNR limitations rule out molecular normalization as an option. However, water clouds and ocean surfaces offer potentially attractive alternatives; both are typically measured with very high SNR, and their spectral differences in backscatter are well-characterized by theory. In this section we explore the relative merits of using water clouds and/or ocean surfaces as 1064 nm calibration targets. Calibration algorithms for both targets are briefly described, and the calibration coefficients derived using these algorithms are compared to the standard values reported in the CALIOP level 1 data products. In addition, we compare CALIOP's 1064 nm attenuated backscatter profiles to coincident attenuated backscatter profiles acquired independently by the airborne high spectral resolution lidar (HSRL) developed at NASA's Langley Research Center (LaRC).
Acknowledgements. This paper is dedicated to the  memory of William H. (Bill)  Hunt: lidar pioneer, instrument designer extraordinaire, gentleman, mentor, and friend. No man or woman on the planet contributed more to the success of the CALIPSO lidar than Bill Hunt. The authors also acknowledge a huge debt of gratitude owed to the CALIOP engineers and technicians at  NASA Langley Research Center and Ball Aerospace Technology Corporation. These men and women built a magnificent instrument that continues to perform superbly far, far beyond its original design lifetime. Edited by: James Campbell Reviewed by: two anonymous referees.