dataesr/scientific-paragraphs-categorization huggingface dataset:
Indeed, as we will explain in Section 3, we implemented in package missMDA a method to perform standardized PCA with missing values in which scaling is considered as part of the analysis and not as a pre-processing step. Another point of difference is that the pcaMethods package and MATLAB toolboxes only provide point estimates of parameters from incomplete data, whereas an idea of variability is given in missMDA. In particular, a multiple imputation method is included with the possibility to draw confidence areas on graphical outputs in order to know how much credibility can be given to outputs obtained from incomplete data. Next, let us consider MCA for categorical variables. From a technical point of view, MCA consists of coding categorical variables with an indicator matrix of dummy variables and then performing a SVD on this matrix, weighted with weights that depend on the margins.
MCA is also known as homogeneity analysis  (Gifi 1990). In this framework, a popular approach to deal with missing value is the "missing passive" approach  (Meulman 1982) , based on the following assumption: An individual who has a missing entry for a variable is considered to have not chosen any category for that variable. Consequently, in the indicator matrix, the entries in the row and columns corresponding to this individual and variable are marked 0. This method is implemented in the function homals in the R package homals (De Leeuw and Mair 2009a) as well as in the function CATPCA in the software package SPSS  (Meulman, Heiser, and SPSS 2003). Greenacre and Pardo (2006)  showed that it is also closely related to their "subset MCA" approach, in which one adds a new category for the missing values and then treats it as an additional element.
Their strategy is implemented in the R package ca  (Nenadic and Greenacre 2007)  using the function mjca with argument subsetcol. Josse, Chavent, Liquet, and Husson (2012)  provided a review of existing methods for handling missing values in MCA and suggested a new approach named regularized iterative MCA. They distinguish between different kinds of missing values and show which method is bestsuited to each kind. In questionnaires for instance, it often happens that a missing value for a categorical variable corresponds to "a new category in itself", e. g. , when the respondent cannot find an appropriate category to select among the available categories and consequently does not answer the question. The missing value is not really a "true" missing value (which could be imputed using the available categories for instance) but corresponds to a new category like "no opinion" or "do not know".
In this case, the "missing passive" approach for estimating MCA parameters from incomplete data is appropriate. In other cases,  Josse et al. (2012)  suggest using their approach for estimating MCA parameters from incomplete data. This method is implemented in package missMDA. Note that unlike other approaches, this method allows to impute an incomplete data set when variables are categorical; see Section 7 for further details. Regarding the FAMD and MFA methods, no solution was previously available to perform them with missing values. Package missMDA therefore provides the first implementation of the regularized iterative FAMD algorithm  (Audigier, Husson, and Josse 2016a ) and the regularized iterative MFA algorithm  (Husson and Josse 2013). However, we note that related algorithms have been suggested for other multi-table and multi-way methods, including PARAFAC  (Tomasi and Bron 2005; Kroonenberg 2008; Acar, Dunlavy, Kolda, and Mrup 2011; Smilde, Bro, and Geladi 2004).
Some are available as MATLAB toolboxes  (Andersson and Bro 2000)  or as standalone software products  (Kroonenberg 2011). More information can be found at http://www. leidenuniv. nl/fsw/three-mode. Note that in these implementations, however, no attempt is made to use regularized versions of the algorithms. Note that in the current version of package missMDA, we do not address the issue of performing correspondence analysis (CA) with missing values. CA  (Greenacre 1984 (Greenacre , 2007) )  is dedicated to analyze multivariate count data. Nora-Chouteau (1974)  suggested an algorithm to estimate CA parameters with missing values which is implemented in the package anacor (De  Leeuw and Mair 2009b)  and which can be seen as underlying the algorithms dedicated to perform principal component methods with missing values.
In summary, the missMDA package provides a complete framework for performing principal component methods for different data types in the presence of missing values. In addition, it provides solutions for selecting the number of underlying dimensions from incomplete data sets. In this section, we did not detail software packages that are available for exploring and visualizing data with missing values outside the principal component framework such as the VIM package  (Templ, Alfons, Kowarik, and Prantner 2015)  as well as software packages that are available for imputing data; these implementations will be discussed in Section 7. Such packages aim at completing a data set and do not to perform principal component methods with missing values. It is still possible to perform a principal component method on a data set that has been completed by such imputation methods, e.
PCA on a genotype-environment data set We illustrate the method on a genotype-environment data set coming from the field of crop science. After installing the missMDA package, the package as well as the incomplete data set geno are loaded. R> set. seed(1234) R> library("missMDA") R> data("geno", package = "missMDA") R> summary(geno) R> head(round(geno, 2)) ACOR AORE ASAL CALB CBAD CCOR CLER CSE1 CSE2 CTO1 C_1 0. 64 0. 43 0. 37 NA -0. 64 -0. 14 NA NA 0. 16 -0. 47 C_2 2. 17 0. 86 NA 0. 01 NA 0. 04 -1. 32 -0. 56 -0. 77 -0. 53 C_3 0. 85 0. 96 -0. 26 -0. 13 -0. 39 0. 27 -0. 20 -0. 49 -0. 33 -0. 27 C_4 1. 41 1. 50 -0. 03 -0. 10 -0. 32 -0. 16 -0. 73 -0. 54 -1. 09 0. 07 C_5 0. 87 0. 86 0. 54 -0. 10 -0. 03 0. 05 -0. 88 -0. 34 -0. 66 -0. 32 C_6 1. 71 0. 34 0. 53 0. 17 NA -0. 34 -0. 83 -0. 51 -1. 03 0.
Indeed, as will be discussed in Section 7, this allows the possibility of using the missMDA package to complete data before performing any statistical analyses (on the imputed data set). The completed data set is in the object completeObs: R> head(round(res. imp$completeObs, 2)) ACOR AORE ASAL CALB CBAD CCOR CLER CSE1 CSE2 CTO1 C_1 0. 64 0. 43 0. 37 -0. 07 -0. 64 -0. 14 -0. 51 -0. 29 0. 16 -0. 47 C_2 2. 17 0. 86 0. 50 0. 01 -0. 56 0. 04 -1. 32 -0. 56 -0. 77 -0. 53 C_3 0. 85 0. 96 -0. 26 -0. 13 -0. 39 0. 27 -0. 20 -0. 49 -0. 33 -0. 27 C_4 1. 41 1. 50 -0. 03 -0. 10 -0. 32 -0. 16 -0. 73 -0. 54 -1. 09 0. 07 C_5 0. 87 0. 86 0. 54 -0. 10 -0. 03 0. 05 -0. 88 -0. 34 -0. 66 -0. 32 C_6 1. 71 0. 34 0. 53 0. 17 -0. 36 -0. 34 -0. 83 -0. 51 -1. 03 0. 06 The imputePCA function also outputs the fitted matrix X in the object recon.
The last step of the analysis is to perform PCA on the imputed data set. To this end, we propose to use the PCA function of the FactoMineR package  (Husson, Josse, Lê, and Mazet 2016; Lê, Josse, and Husson 2008) , but any other function performing PCA can be used such as prcomp or dudi. pca from the ade4 package  (Dray 2007 ): R> res. pca <-PCA(res. imp$completeObs) This provides the classical graphical outputs represented in Figure  4  for individuals and variables. Even if these outputs are obtained first by imputing the incomplete data set and then performing PCA on the completed data set, they correspond to the solution minimizing the criterion (2) which skips missing values. Therefore, they correspond to the estimates of the axes and components of a PCA performed on the incomplete data table.
Then, MCA is performed on the imputed indicator matrix to obtain an estimation of parameters, and missing values are imputed using the fitted values. After the imputation step, the margins D Σ change and thus it is necessary to incorporate a step for updating the margins like for means and standard deviations in PCA (Section 3). A regularized version of the algorithm has also been suggested, since overfitting problems are exacerbated in MCA due to high-dimensionality of the space induced by the categorical variables. I 1 I k I K J J J IJ X = D Σ = I 1 I k I K. We illustrate the method on the vnf data set which concerns a user satisfaction survey of pleasure craft operators. These were asked numerous questions with categorical answers, each with two or three categories. 1232 individuals answered 14 questions involving a total of 35 categories.
The data set has 9% of values missing, involving 42% of respondents. As in PCA (Section 3. 3), we proceed in three steps to perform MCA with missing values: R> data("vnf", package = "missMDA") R> ncomp <-estim_ncpMCA(vnf, method. cv = "Kfold") R> tab. disj. impute <-imputeMCA(vnf, ncp = 4)$tab. disj R> res. mca <-MCA(vnf, tab. disj = tab. disj. impute) The first step consists of estimating the number of dimensions, using the estim_ncpMCA function. Then, the regularized iterative MCA algorithm is performed using the imputeMCA function. The arguments of these functions are the same as those used in the analogous functions in estim_ncpPCA and imputePCA. If the seed argument of the imputeMCA function is not NULL, a random initialization is performed. More precisely, random numbers are entered in the indicator matrix that meet the constraint that the sum of the entries corresponding to each individual and each variable is 1.
The first output of the imputeMCA function is tab. disj and corresponds to the completed indicator matrix resulting from the last step of the (regularized) iterative MCA algorithm. Using this completed indicator matrix as input to the MCA function of the FactoMineR package leads to an estimation of the MCA parameters obtained from the incomplete data by skipping the missing values. Indeed, a criterion of the same form as in Equation 2 is minimized with zero weights for missing entries. More details about the analysis can be found in  Josse et al. (2012). Thus, to perform MCA using an incomplete data set, it uses the FactoMineR package (i. e. , package missMDA imports FactoMineR functions) and the MCA function needs to use the argument tab. disj. This then leads to the classical MCA outputs such as a representation of the categories (Figure  7 ).
This shows that respondents who answered response 2 for question 8. 2 often answered response 2 for question 8. 1. We can also say that category 2 of question 8. 3 is a rare choice since it lies far from the other categories. The rules of interpretation are the same as usual and can be found in books on MCA such as  Greenacre and Blasius (2006). Note that an imputed value in the indicator matrix can be seen as a degree of membership to the associated category. Consequently, each missing entry of the original data set can be imputed with the most plausible category (as we will see in Section 5). This completed data table is available in the output completeObs and thus, as we will discuss in Section 7, the missMDA package can be used to impute categorical data sets.
Iterate until convergence: (a) Perform PCA on the completed weighted data matrix to estimate the parameters U, Λ and V. (b) Impute the missing values with the fitted values using S dimensions. (c) Update the mean, standard deviations (for the continuous variables) and column margins (for the categories). We illustrate this method using the imputeFAMD function of the missMDA package and the FAMD function of the FactoMineR package on the incomplete mixed data set snorena represented in Figure  9  (left-hand side). The following lines of code perform FAMD on the incomplete data set: R> data("snorena", package = "missMDA") R> res. impute <-imputeFAMD(snorena, ncp = 3) R> res. famd <-FAMD(snorena, tab. comp = res. impute) The function imputeFAMD gives as output the object tab. disj which is the imputed matrix, i.
They applied the method to examples coming from the field of sensory analysis and also focused on missing values defined in an experimental design set-up. To apply the method to the tumor example, we run the following lines of code: R> data("gene", package = "missMDA") R> res. impute <-imputeMFA(gene[, -1], group = c(76, 356), + type = rep("s", 2), ncp = 2) R> res. mfa <-MFA(cbind. data. frame(gene[, 1], res. impute$completeObs), + group = c(1, 76, 356), type = c("n", rep("s", 2)), + name. group = c("WHO", "CGH", "expr"), num. group. sup = 1) The function imputeMFA takes as input the multi-table data gene (without its first column, corresponding to the categorical variable giving the tumor type), the argument group which specifies the number of variables per group, and the argument type which specifies the nature of the variables and the pre-processing step to apply to each group of variables.
This property can also be used for other methods and consequently, the methodology implemented in the missMDA package can be seen as an alternative to all other methods dedicated to imputing various data types (continuous, categorical and mixed) that are available in other software packages. Many methods are available to perform single imputation of continuous variables using explicit or implicit models, including imputation based on k-nearest neighbors  (Troyanskaya, Cantor, Sherlock, Brown, Hastie, Tibshirani, Botstein, and Altman 2001) , imputation based on the assumption of a joint Gaussian distribution for the variables  (Schafer 1997) , and imputation obtained by successively drawing from conditional distributions  (Van Buuren, Boshuizen, and Knook 1999; Van Buuren 2007). This latter approach consists roughly in specifying for each variable a model to predict the missing values, then cycling through the variables.
The results become more accurate whenever there are strong linear relationships between variables, as well as when there are categorical variables with small frequency categories. Thus, package missMDA provides imputed data sets with good predictions for missing values. However, as mentioned in the introduction, if a statistical method is applied to the completed data set, the variance of the estimators is underestimated because uncertainty in the missing data is not taken into account. Multiple imputation can be a solution. The PCA multiple imputation method (MIPCA) is also an alternative to the other multiple imputation methods suggested in the literature, including multiple imputation based on joint modeling  (Schafer 1997)  or conditional modeling  (Van Buuren et al. 1999; Van Buuren 2007).
The comparisons made in  Audigier et al. (2016b)  showed that MIPCA is competitive in terms of coverage for different estimators, with the advantage that it can be applied directly when the number of individuals is smaller than the number of variables. As mentioned earlier, many software products and R packages are available to perform single and multiple imputation. This includes for single imputation the R package SoftImpute  (Hastie and Mazumder 2015) , where  Mazumder et al. (2009) 's method is implemented, as well as the missForest package  (Stekhoven 2013)  for  Stekhoven and Bühlmann (2012) 's method. The main packages that implement multiple imputation methods are Amelia  (Honaker, King, and Blackwell 2011) , mice (Van Buuren and Groothuis-Oudshoorn 2011) and mi  (Su, Gelman, Hill, and Yajima 2011).
Yucel (2011)  gives a good overview of multiple imputation software products and packages. Van Buuren's web page (http://www. stefvanbuuren. nl/ mi/Software. html) is a source of information for R packages and software products performing multiple imputation, as well as the CRAN Task View on Official Statistics and Survey Methodology  (Templ 2015). The web page http://missingdata. lshtm. ac. uk/ of the maintainers of the software REALCOMP-IMPUTE  (Carpenter, Goldstein, and Kenward 2011) , which provides imputation for multi-level data, also mentions a number of resources on the topic of missing values.
Conclusion The missMDA package presented in this paper performs principal component methods with missing values (PCA, MCA, FAMD, MFA) and can be used to impute continuous, categorical and mixed data. In addition, a multiple imputation strategy is implemented to study the variability of results in PCA and can be used as an alternative to other multiple imputation methods. As a complement to the paper, several videos are available on the YouTube play list "Exploratory multivariate data analysis with R and FactoMineR" (https://www. youtube. com/ watch?v=YDbx2pk9xNY&list=PLnZgp6epRBbTsZEFXi_p6W48HhNyqwxIu&index=9) that show how to use the missMDA package. In this paper, we do not dwell on the specific kind of missing values (such as missing at random, missing non at random) exhibited. Of course, a first step in a typical analysis is to look for patterns in the missing values and the reasons for their occurrence; indeed, methods as well as the properties of the methods to deal with missing values depend on this evaluation.
To study the patterns of missing values, packages such as VIM  (Templ et al. 2015 ) may be used. We also suggest the approach consisting of coding with "o" the observed values and "m" the missing ones and performing a multiple correspondence analysis on this data set to study associations between missing entries. The following lines of code can be used to visualize the pattern of missing values in a data set called MyData: R> mis. ind <-matrix("o", nrow = nrow(MyData), ncol = ncol(MyData)) R> mis. ind[is. na(MyData)] <-"m" R> dimnames(mis. ind) <-dimnames(MyData) R> library("FactoMineR") R> resMCA <-MCA(mis. ind, graph=FALSE) R> plot(resMCA, invis = "ind", title = "MCA graph of the categories") Methods implemented in this package could be used on very large data sets. However, the implementation in package missMDA is not optimized for such purposes since it is based on the MCA and PCA functions which are as well not optimized for this.
Evolutionary change on the latent scale and associated change on the expected and observed scales In an analysis of real data, latent (breeding) values are, of course, not measured. However, given an estimate of the effect of traits on fitness, say via regression analysis, we can derive the parameters necessary to predict evolution on the latent scale. The idea is thus to relate measured fitness on the observed data scale to the latent scale, compute the evolutionary response on the latent scale, and finally compute the evolutionary response on the observed data scale. To relate the measured fitness on the observed scale to the latent scale, we need to compute the expected fitness W exp given latent trait value ℓ; which is W exp ðℓÞ ¼ X k W P ðkÞPðZ ¼ kjℓÞ; (29) where W P ðkÞ is the measure of fitness for the kth data scale category (assuming the observed data scale is discrete as in most GLMMs).
Implementation The framework developed here (including univariate and multivariate parameters computation and evolutionary predictions on the observed data scale) is implemented in the R package QGglmm available via the R comprehensive archive network, https://cran. r-project. org/. The package does not perform any GLMM inference but rather implements the hereby introduced framework for analysis posterior to a GLMM inference. While the calculations we provide will often (i. e. , when no analytical formula exists) be more computationally demanding than calculations on the latent scale, they will be direct ascertainments of specific parameters of interest, since the scale of evolutionary interest is likely to be the observed data scale, rather than the latent scale (unless some artificial selection is applied to predicted latent breeding values as in modern animal breeding).
Most applications should not be onerous. Computations of means and (additive genetic) variances took ,1 sec on a 1. 7-GHz processor when using our R functions on the Soay sheep data set. Summation over fixed effects and integration over 1000 posterior samples of the fitted model took several minutes. When analytical expressions are available (e. g. , for Poisson/log, binomial/ probit, and negative-binomial/log, see File S1 and R package documentation), these computations are considerably accelerated.
Acknowledgments We thank  Kerry Johnson ,  Paul Johnson ,  Alastair Wilson ,  Loeske Kruuk , and  Josephine Pemberton  for valuable discussions and comments on this manuscript. The Soay sheep data were provided by  Josephine Pemberton  and  Loeske Kruuk  and were collected primarily by  Jill Pilkington  and  Andrew MacColl  with the help of many volunteers. P. d. V. was supported by a doctoral studentship from the  French Ministère de la Recherche et de l'Enseignement Supérieur. H. S. was supported by an  Emmy Noether  fellowship from the.
The proposed study is divided in third steps. First, before testing the method on natural particles, we have to address an issue pointed by Duforêt-Gaurier et al. , 2015 in their discussions. Indeed, for particles of all shapes and all sizes, the polarization of the incident laser beam may impact the signal scattered by the particle and recorded by the detectors. It results that the Cytosense could still be used to measure the sideward and forward cross sections but not anymore to derive the backscattering coefficient. For that purpose, numerical computations have been realized for non-spherical particles (spheroids and aggregates) with the oriented T-matrix code (  [32] ) and the Generalized Multiparticle Mie-solution (GMM) code (  [33] ) to examine theoretically the impact of the polarization on the Cytosense signal.
Second, the comparison exercise was realized to quantify the accuracy of the Cytosense estimates over phytoplankton cells cultures. As no database of the sideward and the forward cross sections is available in the literature, the Cytosense estimates were compared with radiative transfer computations. 590,000 simulations were carried out to include homogeneous and layered sphere models representing the optical properties of a large diversity of phytoplankton cells. The backward cross section and backward efficiency factor estimates were compared with available in situ data found in the literature. Third, after the analysis of the sources of errors, few possible improvements were proposed in the conclusions. Considering the objectives cited above, the present study can be considered as technical.
2°, going up to ca. 15°. The sideward scattered light (SSC), together with the fluorescence emission, is collected at 90°(with a solid angle between ca. 45°and ca. 135°) by series of photomultiplier tubes, using a set of dichroic mirrors and band pass filters. The fluorescence emitted by photosynthetic pigments in algal cells is detected at three different spectral bands. The resulting signatures, which are displayed as red and orange fluorescence respectively, assist in determining the pigment type of each particle. The yellow fluorescence detector is specific to stains of certain calibration beads. Digital data acquisition is initiated as the particle enters into the laser beam and is terminated when the particle is no longer detected. The data recording is done at a frequency of 4 MHz. Data recording was triggered by the SSC signal (15 mV).
This trigger permitted to remove a part of the instrumental electronical noise as the smallest particles. The proprietary Cytoclus software (CytoBuoy b. v. , NL) was used to manually analyze the data (  [34] ). It enables the clustering of data points representing cells having similar optical properties, constituted by their forward and sideward scattering, and their various fluorescence signals. The clustering uses up to 10 simple mathematical signal descriptors of each available detector signal (for example, length, height, center of gravity, asymmetry, number of humps. ). The various clusters are selected manually by drawing gates in correlated bivariate scatter plots. This combines objective factors from the cytograms and subjective considerations linked to the operator expertise. Moreover, an "image-in-flow" device, mounted in the Cytosense, takes pictures of cells within a predefined zone of interest.