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[EN] New algorithms to deal with missing values in predictive modelling are presented in this article. Specifically, 2 trimmed scores regression adaptations are proposed, one from principal component analysis model building with missing data (MD) and other from partial least squares regression model exploitation with missing values. Using these methods, practitioners can impute MD both in the explanatory/predictor and the dependent/response variables. Partial least squares is used here to build the multivariate calibration models; however, any regression method can be used after MD imputation. Four case studies, with different latent structures, are analysed here to compare the trimmed scores regression¿based methods against state-of-the-art approaches. The MATLAB code for these methods is also provided for its direct implementation at http://mseg.webs.upv.es, under a GNU license. ; Spanish Ministry of Science and Innovation; FEDER; European Union, Grant/Award Number: DPI2011-28112-C04-02 and DPI2014-55276-C5-1R; Spanish Ministry of Economy and Competitiveness, Grant/Award Number: ECO2013-43353-R ; Folch-Fortuny, A.; Arteaga, F.; Ferrer, A. (2017). PLS model building with missing data: New algorithms and a comparative study. Journal of Chemometrics. 31(7):1-12. https://doi.org/10.1002/cem.2897 ; S ; 1 ; 12 ; 31 ; 7 ; Grung, B., & Manne, R. (1998). Missing values in principal component analysis. Chemometrics and Intelligent Laboratory Systems, 42(1-2), 125-139. doi:10.1016/s0169-7439(98)00031-8 ; Arteaga, F., & Ferrer-Riquelme, A. J. (2009). Missing Data. Comprehensive Chemometrics, 285-314. doi:10.1016/b978-044452701-1.00125-3 ; Folch-Fortuny, A., Arteaga, F., & Ferrer, A. (2015). PCA model building with missing data: New proposals and a comparative study. Chemometrics and Intelligent Laboratory Systems, 146, 77-88. doi:10.1016/j.chemolab.2015.05.006 ; Arteaga, F., & Ferrer, A. (2002). Dealing with missing data in MSPC: several methods, different interpretations, some examples. Journal of ...

386 393 30 7 ; S ; Maximum likelihood principal component analysis (MLPCA) was originally proposed to incorporate measurement error variance information in principal component analysis (PCA) models. MLPCA can be used to fit PCA models in the presence of missing data, simply by assigning very large variances to the non-measured values. An assessment of maximum likelihood missing data imputation is performed in this paper, analysing the algorithm of MLPCA and adapting several methods for PCA model building with missing data to its maximum likelihood version. In this way, known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR) methods are implemented within the MLPCA method to work as different imputation steps. Six data sets are analysed using several percentages of missing data, comparing the performance of the original algorithm, and its adapted regression-based methods, with other state-of-the-art methods. Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02 and DPI2014-55276-C5-1R, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R. Folch Fortuny, A.; Arteaga Moreno, FJ.; Ferrer, A. (2016). Assessment of maximum likelihood PCA missing data imputation. Journal of Chemometrics. 30(7):386-393. https://doi.org/10.1002/cem.2804

Maximum likelihood principal component analysis (MLPCA) was originally proposed to incorporate measurement error variance information in principal component analysis (PCA) models. MLPCA can be used to fit PCA models in the presence of missing data, simply by assigning very large variances to the non-measured values. An assessment of maximum likelihood missing data imputation is performed in this paper, analysing the algorithm of MLPCA and adapting several methods for PCA model building with missing data to its maximum likelihood version. In this way, known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR) methods are implemented within the MLPCA method to work as different imputation steps. Six data sets are analysed using several percentages of missing data, comparing the performance of the original algorithm, and its adapted regression-based methods, with other state-of-the-art methods. ; Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02 and DPI2014-55276-C5-1R, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R. ; Folch Fortuny, A.; Arteaga Moreno, FJ.; Ferrer, A. (2016). Assessment of maximum likelihood PCA missing data imputation. Journal of Chemometrics. 30(7):386-393. https://doi.org/10.1002/cem.2804 ; S ; 386 ; 393 ; 30 ; 7

[EN] Here we introduce a graphical user-friendly interface to deal with missing values called Missing Data Imputation (MDI) Toolbox. This MATLAB toolbox allows imputing missing values, following missing completely at random patterns, exploiting the relationships among variables. In this way, principal component anal- ysis (PCA) models are fitted iteratively to impute the missing data until convergence. Different methods, using PCA internally, are included in the toolbox: trimmed scores regression (TSR), known data regres- sion (KDR), KDR with principal component regression (KDR-PCR), KDR with partial least squares regression (KDR-PLS), projection to the model plane (PMP), iterative algorithm (IA), modified nonlinear iterative partial least squares regression algorithm (NIPALS) and data augmentation (DA). MDI Toolbox presents a general procedure to impute missing data, thus can be used to infer PCA models with missing data, to estimate the covariance structure of incomplete data matrices, or to impute the missing values as a preprocessing step of other methodologies. ; Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02 and DPI2014-55276-C5-1 R, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R. ; Folch Fortuny, A.; Arteaga Moreno, FJ.; Ferrer, A. (2016). Missing Data Imputation Toolbox for MATLAB. Chemometrics and Intelligent Laboratory Systems. 154:93-100. https://doi.org/10.1016/j.chemolab.2016.03.019 ; S ; 93 ; 100 ; 154

Principal component analysis (PCA) has been widely applied in fluxomics to compress data into a few latent structures in order to simplify the identification of metabolic patterns. These latent structures lack a direct biological interpretation due to the intrinsic constraints associated with a PCA model. Here we introduce a new method that significantly improves the interpretability of the principal components with a direct link to metabolic pathways. This method, called principal elementary mode analysis (PEMA), establishes a bridge between a PCA-like model, aimed at explaining the maximum variance in flux data, and the set of elementary modes (EMs) of a metabolic network. It provides an easy way to identify metabolic patterns in large fluxomics datasets in terms of the simplest pathways of the organism metabolism. The results using a real metabolic model of Escherichia coli show the ability of PEMA to identify the EMs that generated the different simulated flux distributions. Actual flux data of E. coli and Pichia pastoris cultures confirm the results observed in the simulated study, providing a biologically meaningful model to explain flux data of both organisms in terms of the EM activation. The PEMA toolbox is freely available for non-commercial purposes on http://mseg.webs.upv.es. ; Research in this study was partially supported by the Spanish Ministry of Economy and Competitiveness and FEDER funds from the European Union through grants DPI2011-28112-C04-02 and DPI2014-55276-C5-1R. We would also acknowledge Fundacao para a Ciencia e Tecnologia for PhD fellowships with references SFRH/BD/67033/2009, SFRH/BD/70768/2010 and PTDC/BBB-BSS/2800/2012. ; Folch Fortuny, A.; Marques, R.; Isidro, IA.; Oliveira, R.; Ferrer, A. (2016). Principal elementary mode analysis (PEMA). Molecular BioSystems. 12(3):737-746. doi:10.1039/c5mb00828j ; S ; 737 ; 746 ; 12 ; 3

77 88 146 ; S ; [EN] This paper introduces new methods for building principal component analysis (PCA) models with missing data: projection to the model plane (PMP), known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR). These methods are adapted from their PCA model exploitation version to deal with the more general problem of PCA model building when the training set has missing values. A comparative study is carried out comparing these new methods with the standard ones, such as the modified nonlinear iterative partial least squares (NIPALS), the it- erative algorithm (IA), the data augmentation method (DA) and the nonlinear programming approach (NLP). The performance is assessed using the mean squared prediction error of the reconstructed matrix and the cosines between the actual principal components and the ones extracted by each method. Four data sets, two simulated and two real ones, with several percentages of missing data, are used to perform the comparison. Guardar / Salir Siguiente > Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R. The authors gratefully acknowledge Salvador Garcia-Munoz for providing the Phi toolbox (version 1.7) to perform the nonlinear programming approach (NLP) method. Folch-Fortuny, A.; Arteaga Moreno, FJ.; Ferrer Riquelme, AJ. (2015). PCA model building with missing data: New proposals and a comparative study. Chemometrics and Intelligent Laboratory Systems. 146:77-88. https://doi.org/10.1016/j.chemolab.2015.05.006

The inference of complex networks from data is a challenging problem in biological sciences, as well as in a wide range of disciplines such as chemistry, technology, economics, or sociology. The quantity and quality of the data greatly affect the results. While many methodologies have been developed for this task, they seldom take into account issues such as missing data or outlier detection and correction, which need to be properly addressed before network inference. Results Here we present an approach to (i) handle missing data and (ii) detect and correct outliers based on multivariate projection to latent structures. The method, called trimmed scores regression (TSR), enables network inference methods to analyse incomplete datasets by imputing the missing values coherently with the latent data structure. Furthermore, it substitutes the faulty values in a dataset by proper estimations. We provide an implementation of this approach, and show how it can be integrated with any network inference method as a preliminary data curation step. This functionality is demonstrated with a state of the art network inference method based on mutual information distance and entropy reduction, MIDER. Conclusion The methodology presented here enables network inference methods to analyse a large number of incomplete and faulty datasets that could not be reliably analysed so far. Our comparative studies show the superiority of TSR over other missing data approaches used by practitioners. Furthermore, the method allows for outlier detection and correction. ; Research in this study was partially supported by the European Union through project BioPreDyn (FP7-KBBE 289434), and the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grants MultiScales (DPI2011-28112-C04-02, DPI2011-28112-C04-03), and SynBioFactory (DPI2014-55276-C5-1-R, DPI2014-55276-C5-2-R). AF Villaverde also acknowledges funding from the Xunta de Galicia through an I2C postdoctoral fellowship (I2C ED481B 2014/133-0). We also ...

[EN] This paper introduces new methods for building principal component analysis (PCA) models with missing data: projection to the model plane (PMP), known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR). These methods are adapted from their PCA model exploitation version to deal with the more general problem of PCA model building when the training set has missing values. A comparative study is carried out comparing these new methods with the standard ones, such as the modified nonlinear iterative partial least squares (NIPALS), the it- erative algorithm (IA), the data augmentation method (DA) and the nonlinear programming approach (NLP). The performance is assessed using the mean squared prediction error of the reconstructed matrix and the cosines between the actual principal components and the ones extracted by each method. Four data sets, two simulated and two real ones, with several percentages of missing data, are used to perform the comparison. Guardar / Salir Siguiente > ; Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grant DPI2011-28112-C04-02, and the Spanish Ministry of Economy and Competitiveness through grant ECO2013-43353-R. The authors gratefully acknowledge Salvador Garcia-Munoz for providing the Phi toolbox (version 1.7) to perform the nonlinear programming approach (NLP) method. ; Folch-Fortuny, A.; Arteaga Moreno, FJ.; Ferrer Riquelme, AJ. (2015). PCA model building with missing data: New proposals and a comparative study. Chemometrics and Intelligent Laboratory Systems. 146:77-88. https://doi.org/10.1016/j.chemolab.2015.05.006 ; S ; 77 ; 88 ; 146

[EN] Within the emergent field of Systems Biology, mathematical models obtained from physical chemical laws (the so-called first principles-based models) of microbial systems are employed to discern the principles that govern cellular behaviour and achieve a predictive understanding of cellular functions. The reliance on this biochemical knowledge has the drawback that some of the assumptions (specific kinetics of the reaction system, unknown dynamics and values of the model parameters) may not be valid for all the metabolic possible states of the network. In this uncertainty context, the combined use of fundamental knowledge and data measured in the fermentation that describe the behaviour of the microorganism in the manufacturing process is paramount to overcome this problem. In this paper, a grey modelling approach is presented combining data-driven and first principles information at different scales, developed for Pichia pastoris cultures grown on different carbon sources. This approach will allow us to relate patterns of recombinant protein production to intracellular metabolic states and correlate intra and extracellular reactions in order to understand how the internal state of the cells determines the observed behaviour in P. pastoris cultivations. ; Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grants DPI2011-28112-C04-01 and DPI2011-28112-C04-02. The authors are also grateful to Biopolis SL for supporting this research. We also gratefully acknowledge Associate Professor Jose Camacho for providing the Exploratory Data Analysis Toolbox. ; González Martínez, JM.; Folch-Fortuny, A.; Llaneras Estrada, F.; Tortajada Serra, M.; Picó Marco, JA.; Ferrer, A. (2014). Metabolic flux understanding of Pichia pastoris grown on heterogenous culture media. Chemometrics and Intelligent Laboratory Systems. 134:89-99. https://doi.org/10.1016/j.chemolab.2014.02.003 ; S ; 89 ; 99 ; 134

[EN] With the aim of understanding the flux distributions across a metabolic network, i.e. within living cells, Principal Component Analysis (PCA) has been proposed to obtain a set of orthogonal components (pathways) capturing most of the variance in the flux data. The problems with this method are (i) that no additional information can be included in the model, and (ii) that orthogonality imposes a hard constraint, not always reasonably. To overcome these drawbacks, here we propose to use a more flexible approach such as Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) to obtain this set of biological pathways through the network. By using this method, different constraints can be included in the model, and the same source of variability can be present in different pathways, which is reasonable from a biological standpoint. This work follows a methodology developed for Pichia pastoris cultures grown on different carbon sources, lately presented in González-Martínez et al. (2014). In this paper a different grey modelling approach, which aims to incorporate a priori knowledge through constraints on the modelling algorithms, is applied to the same case of study. The results of both models are compared to show their strengths and weaknesses. ; Research in this study was partially supported by the Spanish Ministry of Science and Innovation and FEDER funds from the European Union through grants DPI2011-28112-C04-01 and DPI2011-28112-C04-02. The authors are also grateful to Biopolis SL for supporting this research. ; Folch-Fortuny, A.; Tortajada Serra, M.; Prats-Montalbán, JM.; Llaneras Estrada, F.; Picó Marco, JA.; Ferrer Riquelme, AJ. (2015). MCR-ALS on metabolic networks: Obtaining more meaningful pathways. Chemometrics and Intelligent Laboratory Systems. 142:293-303. https://doi.org/10.1016/j.chemolab.2014.10.004 ; S ; 293 ; 303 ; 142