Probabilistic PARAFAC2.

The Parallel Factor Analysis 2 (PARAFAC2) is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example, because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable to improve robustness to noise and provide a principled approach for determining the number of factors, but challenging because direct model fitting requires that factor loadings be decomposed into a shared matrix specifying how the components are consistently co-expressed across samples and sample-specific orthogonality-constrained component profiles. We develop two probabilistic formulations of the PARAFAC2 model along with variational Bayesian procedures for inference: In the first approach, the mean values of the factor loadings are orthogonal leading to closed form variational updates, and in the second, the factor loadings themselves are orthogonal using a matrix Von Mises-Fisher distribution. We contrast our probabilistic formulations to the conventional direct fitting algorithm based on maximum likelihood on synthetic data and real fluorescence spectroscopy and gas chromatography-mass spectrometry data showing that the probabilistic formulations are more robust to noise and model order misspecification. The probabilistic PARAFAC2, thus, forms a promising framework for modeling multi-way data accounting for uncertainty.

Exploring individual and group differences in latent brain networks using cross-validated simultaneous component analysis.

Component models such as PCA and ICA are often used to reduce neuroimaging data into a smaller number of components, which are thought to reflect latent brain networks. When data from multiple subjects are available, the components are typically estimated simultaneously (i.e., for all subjects combined) using either tensor ICA or group ICA. As we demonstrate in this paper, neither of these approaches is ideal if one hopes to find latent brain networks that cross-validate to new samples of data. Specifically, we note that the tensor ICA model is too rigid to capture real-world heterogeneity in the component time courses, whereas the group ICA approach is too flexible to uniquely identify latent brain networks. For multi-subject component analysis, we recommend comparing a hierarchy of simultaneous component analysis (SCA) models. Our proposed model hierarchy includes a flexible variant of the SCA framework (the Parafac2 model), which is able to both (i) model heterogeneity in the component time courses, and (ii) uniquely identify latent brain networks. Furthermore, we propose cross-validation methods to tune the relevant model parameters, which reduces the potential of over-fitting the observed data. Using simulated and real data examples, we demonstrate the benefits of the proposed approach for finding credible components that reveal interpretable individual and group differences in latent brain networks.

Untargeted Metabolomic Profile for the Detection of Prostate Carcinoma-Preliminary Results from PARAFAC2 and PLS-DA Models.

Prostate-specific antigen (PSA) is the main biomarker for the screening of prostate cancer (PCa), which has a high sensibility (higher than 80%) that is negatively offset by its poor specificity (only 30%, with the European cut-off of 4 ng/mL). This generates a large number of useless biopsies, involving both risks for the patients and costs for the national healthcare systems. Consequently, efforts were recently made to discover new biomarkers useful for PCa screening, including our proposal of interpreting a multi-parametric urinary steroidal profile with multivariate statistics. This approach has been expanded to investigate new alleged biomarkers by the application of untargeted urinary metabolomics. Urine samples from 91 patients (43 affected by PCa; 48 by benign hyperplasia) were deconjugated, extracted in both basic and acidic conditions, derivatized with different reagents, and analyzed with different gas chromatographic columns. Three-dimensional data were obtained from full-scan electron impact mass spectra. The PARADISe software, coupled with NIST libraries, was employed for the computation of PARAFAC2 models, the extraction of the significative components (alleged biomarkers), and the generation of a semiquantitative dataset. After variables selection, a partial least squares-discriminant analysis classification model was built, yielding promising performances. The selected biomarkers need further validation, possibly involving, yet again, a targeted approach.

Estimating latent trends in multivariate longitudinal data via Parafac2 with functional and structural constraints.

Longitudinal data are inherently multimode in the sense that such data are often collected across multiple modes of variation, for example, time × variables × subjects. In many longitudinal studies, multiple variables are collected to measure some latent construct(s) of interest. In such cases, the goal is to understand temporal trends in the latent variables, as well as individual differences in the trends. Multimode component analysis models provide a powerful framework for discovering latent trends in longitudinal data. However, classic implementations of multimode models do not take into consideration functional information (i.e., the temporal sequence of the collected data) or structural information (i.e., which variables load onto which latent factors) about the study design. In this paper, we reveal how functional and structural constraints can be imposed in multimode models (Parafac and Parafac2) in order to elucidate trends in longitudinal data. As a motivating example, we consider a longitudinal study on per capita alcohol consumption trends conducted from 1970 to 2013 by the U.S. National Institute on Alcohol Abuse and Alcoholism. We demonstrate how functional and structural information about the study design can be incorporated into the Parafac and Parafac2 alternating least squares algorithms to understand temporal and regional trends in three latent constructs: beer consumption, spirits consumption, and wine consumption. Our results reveal that Americans consume more than the recommended amount of alcohol, and total alcohol consumption trends show no signs of decreasing in the last decade.

New Nordic Diet versus Average Danish Diet: A Randomized Controlled Trial Revealed Healthy Long-Term Effects of the New Nordic Diet by GC-MS Blood Plasma Metabolomics.

A previous study has shown effects of the New Nordic Diet (NND) to stimulate weight loss and lower systolic and diastolic blood pressure in obese Danish women and men in a randomized, controlled dietary intervention study. This work demonstrates long-term metabolic effects of the NND as compared with an Average Danish Diet (ADD) in blood plasma and reveals associations between metabolic changes and health beneficial effects of the NND including weight loss. A total of 145 individuals completed the intervention and blood samples were taken along with clinical examinations before the intervention started (week 0) and after 12 and 26 weeks. The plasma metabolome was measured using GC-MS, and the final metabolite table contained 144 variables. Significant and novel metabolic effects of the diet, resulting weight loss, gender, and intervention study season were revealed using PLS-DA and ASCA. Several metabolites reflecting specific differences in the diets, especially intake of plant foods and seafood, and in energy metabolism related to ketone bodies and gluconeogenesis formed the predominant metabolite pattern discriminating the intervention groups. Among NND subjects, higher levels of vaccenic acid and 3-hydroxybutanoic acid were related to a higher weight loss, while higher concentrations of salicylic, lactic, and N-aspartic acids and 1,5-anhydro-d-sorbitol were related to a lower weight loss. Specific gender and seasonal differences were also observed. The study strongly indicates that healthy diets high in fish, vegetables, fruit, and whole grain facilitated weight loss and improved insulin sensitivity by increasing ketosis and gluconeogenesis in the fasting state.

Integrative, high-resolution analysis of single cells across experimental conditions with PARAFAC2.

Effective tools for exploration and analysis are needed to extract insights from large-scale single-cell measurement data. However, current techniques for handling single-cell studies performed across experimental conditions (e.g., samples, perturbations, or patients) require restrictive assumptions, lack flexibility, or do not adequately deconvolute condition-to-condition variation from cell-to-cell variation. Here, we report that the tensor decomposition method PARAFAC2 (Pf2) enables the dimensionality reduction of single-cell data across conditions. We demonstrate these benefits across two distinct contexts of single-cell RNA-sequencing (scRNA-seq) experiments of peripheral immune cells: pharmacologic drug perturbations and systemic lupus erythematosus (SLE) patient samples. By isolating relevant gene modules across cells and conditions, Pf2 enables straightforward associations of gene variation patterns across specific patients or perturbations while connecting each coordinated change to certain cells without pre-defining cell types. The theoretical grounding of Pf2 suggests a unified framework for many modeling tasks associated with single-cell data. Thus, Pf2 provides an intuitive universal dimensionality reduction approach for multi-sample single-cell studies across diverse biological contexts.

PARASIAS: A new method for analyzing higher-order tensors with shifting profiles.

Higher-order tensor data analysis has been extensively employed to understand complicated data, such as multi-way GC-MS data in untargeted/targeted analysis. However, the analysis can be complicated when one of the modes shifts e.g., the elution profiles of specific compounds often with respect to retention time; something which violates the assumptions of more traditional models. In this paper, we introduce a new analysis method named PARASIAS for analyzing shifted higher-order tensor data by combining spectral transformation and the simple PARAFAC modeling. The proposed method is validated by applications on both simulated and real multi-way datasets. Compared to the state-of-art PARAFAC2 model, the results indicate that fitting of PARASIAS is 13 times faster on simulated datasets and more than eight times faster on average on the real datasets studied. PARASIAS has significant advantages in terms of model simplicity, convergence speed, the robustness to shift changes in the data, the ability to impose non-negativity constraint on the shift mode and the possibility of easily extending to data with multiple shift modes. However, the resolved profiles of PARASIAS model are always a little worse when the number of components in the data are larger than three and without using additional factors in PARASIAS model. In such cases, more components are necessary for PARASIAS to model the data than that would be needed e.g., by PARAFAC2. The reason for this is also discussed in this work.

PARAFAC2×N: Coupled decomposition of multi-modal data with drift in N modes.

Analysis of GC×GC-TOFMS data for large numbers of poorly-resolved peaks, and for large numbers of samples remains an enduring problem that hinders the widespread application of the technique. For multiple samples, GC×GC-TOFMS data for specific chromatographic regions manifests as a 4th order tensor of I mass spectral acquisitions, J mass channels, K modulations, and L samples. Chromatographic drift is common along both the first-dimension (modulations), and along the second-dimension (mass spectral acquisitions), while drift along the mass channel is for all practical purposes nonexistent. A number of solutions to handling GC×GC-TOFMS data have been proposed: these involve reshaping the data to make it amenable to either 2nd order decomposition techniques based on Multivariate Curve Resolution (MCR), or 3rd order decomposition techniques such as Parallel Factor Analysis 2 (PARAFAC2). PARAFAC2 has been utilised to model chromatographic drift along one mode, which has enabled its use for robust decomposition of multiple GC-MS experiments. Although extensible, it is not straightforward to implement a PARAFAC2 model that accounts for drift along multiple modes. In this submission, we demonstrate a new approach and a general theory for modelling data with drift along multiple modes, for applications in multidimensional chromatography with multivariate detection. The proposed model captures over 99.9% of variance for a synthetic data set, presenting an extreme example of peak drift and co-elution across two modes of separation.

Temperature effects on microbial dissolved organic matter metabolisms: Linking size fractions, fluorescent compositions, and functional groups.

This study elucidated the compositional and structural variations of size fractions of microbially-induced dissolved organic matter (DOM) caused by short-term temperature changes (5 to 35 °C), taking riverine DOM as an example. A simple and efficient method combining fractionation-[parallel factor analysis and two-dimensional Fourier-transform infrared correlation spectroscopy (PARAFAC-2D FTIR COS)]-correlation was introduced to link fluorescent DOM components and their structures in terms of surface functional groups. Results indicated that the higher temperature stimulated the decomposition of aromatics (sizes decreased from 10 kDa-0.22 µm to <10 kDa) and the transformation of proteins to humics (with sizes <0.22 µm); while both the higher and lower temperatures inhibited the utilization of larger-sized DOM (>0.22 µm, especially the non-fluorescence part) and synthesis of larger-sized microbial-derived proteins and humics (>0.22 µm), which may result in more smaller-sized (<10 kDa) and refractory aromatics transported from rivers to oceans in the warming future. However, the structure-determined DOM behaviors could be less affected by temperature since the fluorescent proteins and humics revealed similar functional group compositions, such as carboxyl, hydroxyl, carbonyl/aldehyde, carboxylic anhydride, and carboxamide groups. These findings have strong implications for DOM biogeochemistry in future temperature-shock scenarios. The proposed method will support in-depth analyses of structure-regulated processes from a mechanistic perspective.

Automatic and non-targeted analysis of the volatile profile of natural and alkalized cocoa powders using SBSE-GC-MS and chemometrics.

A total of 56 key volatile compounds present in natural and alkalized cocoa powders have been rapidly evaluated using a non-target approach using stir bar sorptive extraction gas chromatography mass spectrometry (SBSE-GC-MS) coupled to Parallel Factor Analysis 2 (PARAFAC2) automated in PARADISe. Principal component analysis (PCA) explained 80% of the variability of the concentration, in four PCs, which revealed specific groups of volatile characteristics. Partial least squares discriminant analysis (PLS-DA) helped to identify volatile compounds that were correlated to the different degrees of alkalization. Dynamics between compounds such as the acetophenone increasing and toluene and furfural decreasing in medium and strongly alkalized cocoas allowed its differentiation from natural cocoa samples. Thus, the proposed comprehensive analysis is a useful tool for understanding volatiles, e.g., for the quality control of cocoa powders with significant time and costs savings.

Tracing Evolving Networks Using Tensor Factorizations vs. ICA-Based Approaches.

Analysis of time-evolving data is crucial to understand the functioning of dynamic systems such as the brain. For instance, analysis of functional magnetic resonance imaging (fMRI) data collected during a task may reveal spatial regions of interest, and how they evolve during the task. However, capturing underlying spatial patterns as well as their change in time is challenging. The traditional approach in fMRI data analysis is to assume that underlying spatial regions of interest are static. In this article, using fractional amplitude of low-frequency fluctuations (fALFF) as an effective way to summarize the variability in fMRI data collected during a task, we arrange time-evolving fMRI data as a subjects by voxels by time windows tensor, and analyze the tensor using a tensor factorization-based approach called a PARAFAC2 model to reveal spatial dynamics. The PARAFAC2 model jointly analyzes data from multiple time windows revealing subject-mode patterns, evolving spatial regions (also referred to as networks) and temporal patterns. We compare the PARAFAC2 model with matrix factorization-based approaches relying on independent components, namely, joint independent component analysis (ICA) and independent vector analysis (IVA), commonly used in neuroimaging data analysis. We assess the performance of the methods in terms of capturing evolving networks through extensive numerical experiments demonstrating their modeling assumptions. In particular, we show that (i) PARAFAC2 provides a compact representation in all modes, i.e., subjects, time, and voxels, revealing temporal patterns as well as evolving spatial networks, (ii) joint ICA is as effective as PARAFAC2 in terms of revealing evolving networks but does not reveal temporal patterns, (iii) IVA's performance depends on sample size, data distribution and covariance structure of underlying networks. When these assumptions are satisfied, IVA is as accurate as the other methods, (iv) when subject-mode patterns differ from one time window to another, IVA is the most accurate. Furthermore, we analyze real fMRI data collected during a sensory motor task, and demonstrate that a component indicating statistically significant group difference between patients with schizophrenia and healthy controls is captured, which includes primary and secondary motor regions, cerebellum, and temporal lobe, revealing a meaningful spatial map and its temporal change.

LogPar: Logistic PARAFAC2 Factorization for Temporal Binary Data with Missing Values.

Binary data with one-class missing values are ubiquitous in real-world applications. They can be represented by irregular tensors with varying sizes in one dimension, where value one means presence of a feature while zero means unknown (i.e., either presence or absence of a feature). Learning accurate low-rank approximations from such binary irregular tensors is a challenging task. However, none of the existing models developed for factorizing irregular tensors take the missing values into account, and they assume Gaussian distributions, resulting in a distribution mismatch when applied to binary data. In this paper, we propose Logistic PARAFAC2 (LogPar) by modeling the binary irregular tensor with Bernoulli distribution parameterized by an underlying real-valued tensor. Then we approximate the underlying tensor with a positive-unlabeled learning loss function to account for the missing values. We also incorporate uniqueness and temporal smoothness regularization to enhance the interpretability. Extensive experiments using large-scale real-world datasets show that LogPar outperforms all baselines in both irregular tensor completion and downstream predictive tasks. For the irregular tensor completion, LogPar achieves up to 26% relative improvement compared to the best baseline. Besides, LogPar obtains relative improvement of 13.2% for heart failure prediction and 14% for mortality prediction on average compared to the state-of-the-art PARAFAC2 models.

Deep metabolome: Applications of deep learning in metabolomics.

In the past few years, deep learning has been successfully applied to various omics data. However, the applications of deep learning in metabolomics are still relatively low compared to others omics. Currently, data pre-processing using convolutional neural network architecture appears to benefit the most from deep learning. Compound/structure identification and quantification using artificial neural network/deep learning performed relatively better than traditional machine learning techniques, whereas only marginally better results are observed in biological interpretations. Before deep learning can be effectively applied to metabolomics, several challenges should be addressed, including metabolome-specific deep learning architectures, dimensionality problems, and model evaluation regimes.

Using deep learning to evaluate peaks in chromatographic data.

Analysis of untargeted gas-chromatographic data is time consuming. With the earlier introduction of the PARAFAC2 (PARAllel FACtor analysis 2) based PARADISe (PARAFAC2 based Deconvolution and Identification System) approach in 2017, this task was made considerably more time-efficient. However, there are still a number of manual steps in the analysis which require data analytical expertise. One of these is the need to define whether or not each PARAFAC2 resolved component represents a peak suitable for integration. As the peaks may change in both shape and location on the elution time-axis, this presents a problem which cannot be readily solved by applying a linear classifier, such as PLS-DA (Partial Least Squares regression for Discriminant Analysis). As part of our ongoing efforts to further automate analysis of Gas Chromatography with Mass Spectrometry (GC-MS), we therefore explore a convolutional neural network classifier, capable of handling these shifts and variations in shape. The theory of convolutional neural networks and application on vector samples is briefly explained, and the performance is tested against a PLS-DA classifier, a shallow artificial neural network and a locally weighted regression model. The models are built on a training set with PARAFAC2 resolved components from eight different aroma related GC-MS runs with a total of over 70,000 elution profile samples, and validated using another, independent, GC-MS dataset. Based on Receiver Operating Characteristic curves (ROC) and manual analysis of the misclassified cases, it is shown that the convolutional network consistently outperforms the competing models, yielding an Area Under the Curve (AUC) value of 0.95 for peak classification. Examples are given illustrating that this new approach provides convincing means to automatically assess and evaluate modelled elution profiles of chromatographic data and thereby remove this laborious manual step.

Blind fMRI source unmixing via higher-order tensor decompositions.

BACKGROUND: The growing interest in neuroimaging technologies generates a massive amount of biomedical data of high dimensionality. Tensor-based analysis of brain imaging data has been recognized as an effective analysis that exploits its inherent multi-way nature. In particular, the advantages of tensorial over matrix-based methods have previously been demonstrated in the context of functional magnetic resonance imaging (fMRI) source localization. However, such methods can also become ineffective in realistic challenging scenarios, involving, e.g., strong noise and/or significant overlap among the activated regions. Moreover, they commonly rely on the assumption of an underlying multilinear model generating the data. NEW METHOD: This paper aims at investigating the possible gains from exploiting the 4-dimensional nature of the brain images, through a higher-order tensorization of the fMRI signal, and the use of less restrictive generative models. In this context, the higher-order block term decomposition (BTD) and the PARAFAC2 tensor models are considered for the first time in fMRI blind source separation. A novel PARAFAC2-like extension of BTD (BTD2) is also proposed, aiming at combining the effectiveness of BTD in handling strong instances of noise and the potential of PARAFAC2 to cope with datasets that do not follow the strict multilinear assumption. COMPARISON WITH EXISTING METHODS: The methods were tested using both synthetic and real data and compared with state of the art methods. CONCLUSIONS: The simulation results demonstrate the effectiveness of BTD and BTD2 for challenging scenarios (presence of noise, spatial overlap among activation regions and inter-subject variability in the haemodynamic response function (HRF)).

Olive oil quality classification and measurement of its organoleptic attributes by untargeted GC-MS and multivariate statistical-based approach.

The capabilities of dynamic headspace entrainment followed by thermal desorption in combination with gas chromatography (GC) coupled to single quadrupole mass spectrometry (MS) have been tested for the determination of volatile components of olive oil. This technique has shown a great potential for olive oil quality classification by using an untargeted approach. The data processing strategy consisted of three different steps: component detection from GC-MS data using novel data treatment software PARADISe, a multivariate analysis using EZ-Info, and the creation of the statistical models. The great number of compounds determined enabled not only the development of a quality classification method as a complementary tool to the official established method "PANEL TEST" but also a correlation between these compounds and different types of defect. Classification method was finally validated using blind samples. An accuracy of 85% in oil classification was obtained, with 100% of extra virgin samples correctly classified.

Improvement in the identification and quantification of UV filters and additives in sunscreen cosmetic creams by gas chromatography/mass spectrometry through three-way calibration techniques.

The simultaneous determination of 2,6-di-tert-butyl-4-methyl-phenol (BHT), benzophenone (BP), benzophenone-3 (BP3) and diisobutyl phthalate (DiBP) in seven sunscreen creams was carried out by gas chromatography/mass spectrometry (GC/MS) using DiBP-d4 as internal standard. The content of BP3, which is a UV filter, must not exceed 6% (w/w) in cosmetic products according to Regulation (EU) 2017/238 and the use of DiBP in cosmetic products shall be prohibited according to Regulation (EC) No 1223/2009. The conclusions obtained with the univariate standard methodology in the identification of the analytes contained in the creams were wrong. However, a calibration based on PARAFAC or PARAFAC2 decompositions, where the samples of the prediction set were projected on the model obtained previously with the calibration set, enabled the unequivocal identification and quantification of the analytes even in the presence of interferents not considered in the calibration model. The PARAFAC2 decomposition was used to overcome the shifts in the retention time of BP and BP3. These three-way calibration techniques are needed to avoid false negative results. The method had not proportional or constant bias. The presence of BHT was detected in the seven sunscreen creams analysed at an amount of 6.48 10-2%, 8.53 10-2%, 1.70 10-4%, 1.11 10-4%, 2.51 10-3%, 3.20 10-5% and 6.35 10-3%. The concentrations of DiBP found in four creams were 3.49 10-2%, 3.19 10-2%, 3.26 10-2% and 2.51 10-2%. On the other hand, BP was only detected in two of the cosmetic creams analysed at an amount of 7.84 10-3% and 1.04 10-2%. In addition, BP3 was detected in six of the creams at an amount of 4.73%, 3.49%, 4.94 10-3%, 1.98 10-3%, 6.62 10-1% and 1.73%. Therefore, none of the cosmetic creams contained BP3 in an amount higher than 6%.

Geometric search: A new approach for fitting PARAFAC2 models on GC-MS data.

PARAFAC2 is a powerful decomposition method which is ideally suited for modeling gas chromatography-mass spectrometry (GC-MS) data. However, the most widely used fitting algorithms (alternating least squares, ALS) are very slow which hinders use of the model. In this paper, an iterative method called geometric search is proposed to fit the PARAFAC2 model. This method models the PARAFAC2 loading parameters as geometric sequences with offsets during the ALS iterations. It extrapolates the optimal parameters from prior iterations to accelerate ALS convergence process. The performance of this method was evaluated by simulated datasets and two GC-MS datasets of wine and tobacco samples. This geometric search method proved an efficient way to fit PARAFAC2 models, compared with a standard ALS algorithm and two widely used line search algorithms in terms of convergence speed and fitting quality.

Gas chromatography - mass spectrometry data processing made easy.

Evaluation of GC-MS data may be challenging due to the high complexity of data including overlapped, embedded, retention time shifted and low S/N ratio peaks. In this work, we demonstrate a new approach, PARAFAC2 based Deconvolution and Identification System (PARADISe), for processing raw GC-MS data. PARADISe is a computer platform independent freely available software incorporating a number of newly developed algorithms in a coherent framework. It offers a solution for analysts dealing with complex chromatographic data. It allows extraction of chemical/metabolite information directly from the raw data. Using PARADISe requires only few inputs from the analyst to process GC-MS data and subsequently converts raw netCDF data files into a compiled peak table. Furthermore, the method is generally robust towards minor variations in the input parameters. The method automatically performs peak identification based on deconvoluted mass spectra using integrated NIST search engine and generates an identification report. In this paper, we compare PARADISe with AMDIS and ChromaTOF in terms of peak quantification and show that PARADISe is more robust to user-defined settings and that these are easier (and much fewer) to set. PARADISe is based on non-proprietary scientifically evaluated approaches and we here show that PARADISe can handle more overlapping signals, lower signal-to-noise peaks and do so in a manner that requires only about an hours worth of work regardless of the number of samples. We also show that there are no non-detects in PARADISe, meaning that all compounds are detected in all samples.

Untargeted GC-MS Metabolomics Reveals Changes in the Metabolite Dynamics of Industrial Scale Batch Fermentations of Streptoccoccus thermophilus Broth.

An industrial scale biomass production using batch or fed-batch fermentations usually optimized by selection of bacterial strains, tuning fermentation media, feeding strategy, and temperature. However, in-depth investigation of the biomass metabolome during the production may reveal new knowledge for better optimization. In this study, for the first time, the authors investigated seven fermentation batches performed on five Streptoccoccus thermophilus strains during the biomass production at Chr. Hansen (Denmark) in a real life large scale fermentation process. The study is designed to investigate effects of batch fermentation, fermentation time, production line, and yeast extract brands on the biomass metabolome using untargeted GC-MS metabolomics. Processing of the raw GC-MS data using PARAFAC2 revealed a total of 90 metabolites out of which 64 are identified. Partitioning of the data variance according to the experimental design was performed using ASCA and revealed that batch and fermentation time effects and their interaction term were the most significant effects. The yeast extract brand had a smaller impact on the biomass metabolome, while the production line showed no effect. This study shows that in-depth metabolic analysis of fermentation broth provides a new tool for advanced optimization of high-volume-low-cost biomass production by lowering the cost, increase the yield, and augment the product quality.