Multiblock PLS Research Articles

Adaptive Sparse Multi-Block PLS Discriminant Analysis: An Integrative Method for Identifying Key Biomarkers from Multi-Omics Data.

With the growing use of high-throughput technologies, multi-omics data containing various types of high-dimensional omics data is increasingly being generated to explore the association between the molecular mechanism of the host and diseases. In this study, we present an adaptive sparse multi-block partial least square discriminant analysis (asmbPLS-DA), an extension of our previous work, asmbPLS. This integrative approach identifies the most relevant features across different types of omics data while discriminating multiple disease outcome groups. We used simulation data with various scenarios and a real dataset from the TCGA project to demonstrate that asmbPLS-DA can identify key biomarkers from each type of omics data with better biological relevance than existing competitive methods. Moreover, asmbPLS-DA showed comparable performance in the classification of subjects in terms of disease status or phenotypes using integrated multi-omics molecular profiles, especially when combined with other classification algorithms, such as linear discriminant analysis and random forest. We have made the R package called asmbPLS that implements this method publicly available on GitHub. Overall, asmbPLS-DA achieved competitive performance in terms of feature selection and classification. We believe that asmbPLS-DA can be a valuable tool for multi-omics research.

Internal reflectance cell fluorescence measurement combined with multi-way analysis to detect fluorescence signatures of undiluted honeys and a fusion of fluorescence and NIR to enhance predictability

Honey is a complex food matrix that contains diverse polyphenolic compounds. Some phenolics exhibit fluorescence signatures which can be used to evaluate honey quality, and authenticity and to determine botanical origin. Mānuka honey contains two unique fluorescence markers: Leptosperin (MM1) and LepteridineTM (MM2) that are derived from Leptospermum scoparium nectar. Fluorescence measurement of supersaturated solutions such as undiluted honeys can be challenged by complex inner filter effects. The current study shows the ability of internal reflectance cell fluorescence measurement and multi-way analysis to detect fluorophores in undiluted honeys. This study scanned honeys from different geographic districts generating excitation emission matrices (250–400/300–600 nm), and by near infrared (NIR) hyperspectral camera (547–1701 nm). PARAFAC and tri-PLS could track two fluorescence markers: MM1 (R2 = 0.82 & RMSEP = 138.65) and MM2 (R2 = 0.82 & RMSEP = 2.75) from undiluted honey fluorescence data with > 80 % accuracy. Classification of mono-floral, multi-floral and non-mānuka honeys achieved 90 % overall accuracy. Fusion of fluorescence data at ƛex 270 & 330 nm and NIR hyperspectral data combined with multi-block PLS analysis enhances predictability of fluorescence markers further. The study revealed the potential of internal reflectance cell fluorescence measurement combined with chemometrics and data fusion for rapid evaluation of honey quality and botanical origin.

A Multiblock Approach to Fuse Process and Near-Infrared Sensors for On-Line Prediction of Polymer Properties.

Petrochemical companies aim at assessing final product quality in real time, in order to rapidly deal with possible plant faults and to reduce chemical wastes and staff effort resulting from the many laboratory analyses performed every day. In order to answer these needs, the main purpose of the current work is to explore the feasibility of multiblock regression methods to build real-time monitoring models for the prediction of two quality properties of Acrylonitrile-Butadiene-Styrene (ABS) by fusing near-infrared (NIR) and process sensors data. Data come from a production plant, which operates continuously, and where four NIR probes are installed on-line, in addition to standard process sensors. Multiblock-PLS (MB-PLS) and Response-Oriented Sequential Alternation (ROSA) methods were here utilized to assess which of such sensors and plant areas were the most relevant for the quality parameters prediction. Several prediction models were constructed exploiting measurements provided by sensors active at different ABS production process stages. Both methods provided good prediction performances and permitted identification of the most relevant data blocks for the quality parameters’ prediction. Moreover, models built without considering recordings from the final stage of the process yielded prediction errors comparable to those involving all available data blocks. Thus, in principle, allowing final ABS quality to be estimated in real-time before the end of the process itself.

Cox-sMBPLS: An Algorithm for Disease Survival Prediction and Multi-Omics Module Discovery Incorporating Cis-Regulatory Quantitative Effects.

BackgroundThe development of high-throughput techniques has enabled profiling a large number of biomolecules across a number of molecular compartments. The challenge then becomes to integrate such multimodal Omics data to gain insights into biological processes and disease onset and progression mechanisms. Further, given the high dimensionality of such data, incorporating prior biological information on interactions between molecular compartments when developing statistical models for data integration is beneficial, especially in settings involving a small number of samples.ResultsWe develop a supervised model for time to event data (e.g., death, biochemical recurrence) that simultaneously accounts for redundant information within Omics profiles and leverages prior biological associations between them through a multi-block PLS framework. The interactions between data from different molecular compartments (e.g., epigenome, transcriptome, methylome, etc.) were captured by using cis-regulatory quantitative effects in the proposed model. The model, coined Cox-sMBPLS, exhibits superior prediction performance and improved feature selection based on both simulation studies and analysis of data from heart failure patients.ConclusionThe proposed supervised Cox-sMBPLS model can effectively incorporate prior biological information in the survival prediction system, leading to improved prediction performance and feature selection. It also enables the identification of multi-Omics modules of biomolecules that impact the patients’ survival probability and also provides insights into potential relevant risk factors that merit further investigation.

Multi-block PLS discriminant analysis for the joint analysis of metabolomic and epidemiological data.

Metabolomics is a powerful phenotyping tool in nutrition and health research, generating complex data that need dedicated treatments to enrich knowledge of biological systems. In particular, to investigate relations between environmental factors, phenotypes and metabolism, discriminant statistical analyses are generally performed separately on metabolomic datasets, complemented by associations with metadata. Another relevant strategy is to simultaneously analyse thematic data blocks by a multi-block partial least squares discriminant analysis (MBPLSDA) allowing determining the importance of variables and blocks in discriminating groups of subjects, taking into account data structure. The present objective was to develop a full open-source standalone tool, allowing all steps of MBPLSDA for the joint analysis of metabolomic and epidemiological data. This tool was based on the mbpls function of the ade4 R package, enriched with functionalities, including some dedicated to discriminant analysis. Provided indicators help to determine the optimal number of components, to check the MBPLSDA model validity, and to evaluate the variability of its parameters and predictions. To illustrate the potential of this tool, MBPLSDA was applied to a real case study involving metabolomics, nutritional and clinical data from a human cohort. The availability of different functionalities in a single R package allowed optimizing parameters for an efficient joint analysis of metabolomics and epidemiological data to obtain new insights into multidimensional phenotypes. In particular, we highlighted the impact of filtering the metabolomic variables beforehand, and the relevance of a MBPLSDA approach in comparison to a standard PLS discriminant analysis method.

UNCOVERING PSYCHOLOGICAL GRATIFICATIONS AFFECTING SOCIAL MEDIA UTILIZATION: A MULTIBLOCK HIERARCHICAL ANALYSIS

The purpose of this study is to examine internet users’ experience and gratifications of social media, which affect the utilization of the medium. The research model was developed in hierarchical multiblock, which consists of three key psychological components–personal, tension release, and social–that are derived from the Uses and Gratifications theoretical perspective. Data were collected through stratified probability sampling of 428 social media users using a web-based questionnaire. They were selected because they spend a significant amount of time on social media sites, at least on Facebook, Twitter, YouTube, LinkedIn, and Instagram. Based on hierarchical multiblock PLS analysis, the results confirmed that social media utilization is affected by three key component psychological factors. All of these factors play a significant part in influencing user attitude toward utilizing social media. The findings are believed to increase understanding, especially for user-experience designers (UXD) concerning venues that can be used for direct targeting in designing social media marketing. The implications and recommendations for future research are discussed.

The Sequential Multi-block PLS algorithm (SMB-PLS): Comparison of performance and interpretability

The Sequential Multi-block PLS algorithm, called SMB-PLS, was recently proposed to improve interpretability of large multi-block data structures. It combines the strengths of Multi-block PLS (MB-PLS) and those of the Sequential Orthogonal PLS (SO-PLS) methods. It uses the two-level hierarchical structure of the first (i.e., block and super levels) providing two levels of scrutiny for the analysis of large datasets, and the sequential orthogonalization scheme of SO-PLS, while keeping between block correlated information in the model. This enables the exploration and interpretation of the full data structure without loss of information. SMB-PLS also allows the selection of a different number of latent variables for each regressor block. The modelling performance and interpretation of SMB-PLS were illustrated using two datasets, covering different types of structural relationships between the regressor blocks. SMB-PLS leads to similar predictive performance of response data as MB-PLS and SO-PLS. However, it was shown that SMB-PLS clearly reveals the correlation structure between the regressor blocks, while MB-PLS leads to more ambiguous results. The correlated information between the blocks extracted with SMB-PLS also improves interpretability, for example, by identifying control actions made to attenuate disturbances, such as raw materials variations. Such information cannot be obtained with SO-PLS since it removes between block correlated variations.

Clusterwise analysis for multiblock component methods

Multiblock component methods are applied to data sets for which several blocks of variables are measured on a same set of observations with the goal to analyze the relationships between these blocks of variables. In this article, we focus on multi-block component methods that integrate the information found in several blocks of explanatory variables in order to describe and explain one set of dependent variables. In the following, multiblock PLS and multiblock redundancy analysis are chosen, as particular cases of multiblock component methods when one set of variables is explained by a set of predictor variables that is organized into blocks. Because these multiblock techniques assume that the observations come from a homogeneous population they will provide suboptimal results when the observations actually come from different populations. A strategy to palliate this problem-presented in this article-is to use a technique such as clusterwise regression in order to identify homogeneous clusters of observations. This approach creates two new methods that provide clusters that have their own sets of regression coefficients. This combination of clustering and regres-B Stephanie Bougeard 123 S. Bougeard et al. sion improves the overall quality of the prediction and facilitates the interpretation. In addition, the minimization of a well-defined criterion-by means of a sequential algorithm-ensures that the algorithm converges monotonously. Finally, the proposed method is distribution-free and can be used when the explanatory variables outnumber the observations within clusters. The proposed clusterwise multiblock methods are illustrated with of a simulation study and a (simulated) example from marketing.

Advanced predictive methods for wine age prediction: Part II – A comparison study of multiblock regression approaches

In this article, we extend the scope of the first paper of the sequel, which was dedicated to the analysis of advanced single-block regression methods (Rendall et al., 2016) [1], to the class of multiblock regression approaches. The datasets contemplated for developing the multiblock approaches are the same as in the former publication: volatile, polyphenols, organic acids composition and the UV–Vis spectra. The context is still the prediction of the ageing time of one of finest Portuguese fortified wines, the Madeira Wine, but now the data collected from the different analytical sources is explored simultaneously, in a more structured and informative way, through multiblock methodologies. The goal of this paper is to provide a critical assessment of a rich variety of multiblock regression methods, namely: Concatenated PLS, Multiblock PLS (MBPLS), Hierarchical PLS (HPLS), Network-Induced Supervised Learning (NI-SL) and Sequential Orthogonalised Partial Least Squares (SO-PLS). A comparison of block scaling methods was also undertaken for the Concatenated PLS algorithm, and new block scaling methods were proposed that led to better prediction performances. This study explores and reveals the potential advantages of applying multiblock methods for fusing datasets from different sources, from both the predictive and interpretability perspectives.

Extension of SO-PLS to multi-way arrays: SO-N-PLS

Multi-way data arrays are becoming more common in several fields of science. For instance, analytical instruments can sometimes collect signals at different modes simultaneously, as e.g. fluorescence and LC/GC-MS. Higher order data can also arise from sensory science, were product scores can be reported as function of sample, judge and attribute. Another example is process monitoring, where several process variables can be measured over time for several batches. In addition, so-called multi-block data sets where several blocks of data explain the same set of samples are becoming more common. Several methods exist for analyzing either multi-way or multi-block data, but there has been little attention on methods that combine these two data properties. A common procedure is to “unfold” multi-way arrays in order to obtain two-way data tables on which classical multi-block methods can be applied. However, it is a known fact that unfolding can lead to overfitted models due to increased flexibility in parameter estimation. In this paper we present a novel multi-block regression method that can handle multi-way data blocks. This method is a combination of a multi-block method called Sequential and Orthogonalized-PLS (SO-PLS) and the multi-way version of PLS, N-PLS. The new method is therefore called SO-N-PLS. We have compared the method to Multi-block-PLS (MB-PLS) and SO-PLS on unfolded data. We investigate the hypotheses that SO-N-PLS has better performances on small data sets and noisy data, and that SO-N-PLS models are easier to interpret. The hypotheses are investigated by a simulation study and two real data examples; one dealing with regression and one with classification. The simulation study show that SO-N-PLS predicts better than the unfolded methods when the sample size is small and the data is noisy. This is due to the fact that it filters out the noise better than MB-PLS and SO-PLS. For the real data examples, the differences in prediction are small but the multi-way method allows easier interpretation.

Effect of local hydroclimate on phytoplankton groups in the Charente estuary

This study aimed to describe seasonal variations of phytoplankton abundances in relation to the physical and chemical (nutrients and metals) environment under the influence of freshwater input in the Charente river estuary (Marennes-Oléron bay, France) over three years, from 2011 to 2014. Phytoplankton abundances were determined using microscopy and flow cytometry. Considering high frequency temperature and salinity data, breakpoints in each series led to the identification of two local hydroclimatic periods: the first (2011 and early 2012) being warmer and higher in salinity than the second (from spring 2012 to the beginning of 2014). A multiblock PLS analysis highlighted the significant contribution of the physical environment (temperature, salinity and Photosynthetically Active Radiation (PAR)) on phytoplankton abundances. Two partial triadic analyses (PTA) were run in order to visualize seasonal variations of i) phytoplankton groups and ii) nutrients and trace elements, irrespective of spatial gradient: picoeukaryote occurrence showed a difference between year 2011 and the years 2012 and 2013 (as did cadmium, nickel and silica levels). However, both PTA revealed greater differences between year 2013 and the years 2011 and 2012, as shown by occurrences of cryptophytes, dinoflagellates and nanoeukaryotes, as well as copper and phosphate levels. These results showed a shift between the hydroclimate breakpoint and some phytoplankton responses, suggesting that their development and succession might depend on conditions early in the year. Finally, a STATICO analysis was performed on the paired PTA in order to examine the relations of phytoplankton with nutrients and metals more closely. Most phytoplankton groups were represented on the first axis, together with cadmium on the one hand, and nitrates, silica and nickel on the other. This analysis revealed the separation of phytoplankton groups on the second axis that represented phosphates and copper. Hydroclimatic conditions and the nature of freshwater inputs, especially phosphates and copper content, might be key factors driving phytoplankton structure in the Charente estuary.

Semi-quantitative prediction of a multiple API solid dosage form with a combination of vibrational spectroscopy methods

Quality control (QC) in the pharmaceutical industry is a key activity in ensuring medicines have the required quality, safety and efficacy for their intended use. QC departments at pharmaceutical companies are responsible for all release testing of final products but also all incoming raw materials. Near-infrared spectroscopy (NIRS) and Raman spectroscopy are important techniques for fast and accurate identification and qualification of pharmaceutical samples.Tablets containing two different active pharmaceutical ingredients (API) [bisoprolol, hydrochlorothiazide] in different commercially available dosages were analysed using Raman- and NIR Spectroscopy. The goal was to define multivariate models based on each vibrational spectroscopy to discriminate between different dosages (identity) and predict their dosage (semi-quantitative). Furthermore the combination of spectroscopic techniques was investigated. Therefore, two different multiblock techniques based on PLS have been applied: multiblock PLS (MB-PLS) and sequential-orthogonalised PLS (SO-PLS).NIRS showed better results compared to Raman spectroscopy for both identification and quantitation. The multiblock techniques investigated showed that each spectroscopy contains information not present or captured with the other spectroscopic technique, thus demonstrating that there is a potential benefit in their combined use for both identification and quantitation purposes.

A sequential algorithm for multiblock orthogonal projections to latent structures

Methods of multiblock bilinear factorizations have increased in popularity in chemistry and biology as recent increases in the availability of information-rich spectroscopic platforms have made collecting multiple spectroscopic observations per sample a practicable possibility. Of the existing multiblock methods, consensus PCA (CPCA-W) and multiblock PLS (MB-PLS) have been shown to bear desirable qualities for multivariate modeling, most notably their computability from single-block PCA and PLS factorizations. While MB-PLS is a powerful extension to the nonlinear iterative partial least squares (NIPALS) framework, it still spreads predictive information across multiple components when response-uncorrelated variation exists in the data. The OnPLS extension to O2PLS provides a means of simultaneously extracting predictive and uncorrelated variation from a set of matrices, but is more suited to unsupervised data discovery than regression. We describe the union of NIPALS MB-PLS with an orthogonal signal correction (OSC) filter, called MB-OPLS, and illustrate its equivalence to single-block OPLS for regression and discriminant analysis.

Establishing Multivariate Specification Regions for Raw Materials using SMB-PLS

The new Sequential Multi-block PLS algorithm is applied for establishing multivariate specification regions jointly on multiple types of raw materials. SMB-PLS distinguishes between process variations associated with raw materials from other orthogonal sources of variations such as operating policies. Combinations of raw material properties not compensated by the control schemes are clearly identified. Multivariate specifications are required for these combinations to avoid negative impact on process performance and product quality. The method was applied to an industrial aluminum smelter. Bad combinations of raw material properties were identified and validated against process knowledge.

Quantitative Analysis of Lavender (<i>Lavandula angustifolia</i>) Essential Oil Using Multiblock Data from Infrared Spectroscopy

Near-infrared and mid-infrared spectroscopies were currently used to analyze natural compounds. During the last ten years various multiblocks methods were developed such as Concatenated PLS, Hierarchical-PLS (H-PLS), and MultiBlock-PLS (MB-PLS). These three algorithms were used to analyze 55 lavender (Lavandula angustifolia) essential oil samples. The results obtained were compared to the ones obtained respectively in NIR and MIR ranges. The accuracies of the models depend on the spectroscopic technique, pretreatment and the PLS methods. The results showed that the choice of the factor numbers used to build the multiblock models was the most important parameter for the H-PLS and MB-PLS methods.

A multiblock PLS model of cortico-cortical and corticomuscular interactions in Parkinson's disease

Electroencephalography (EEG) and simultaneously-recorded electromyography (EMG) data are a means to assess integrity of the functional connection between the cortex and the muscle during movement. EEG-EMG coupling is typically assessed with pair-wise squared coherence, resulting in a small, but statistically-significant coherence between a single EEG and a single EMG channel. However, a means to combine results across subjects is not straightforward with this approach because the exact frequency of maximal EEG-EMG coupling may vary between individuals, and it emphasizes the role of an individual locus in the brain in driving the muscle activity, when interactions between head regions may in fact be more influential on ongoing EMG activity. To deal with these issues, we implemented a multiblock Partial Least Squares (mbPLS) procedure, previously proposed in chemical applications, which incorporates a hierarchical structure into the ordinary two-block PLS often used in neuroimaging studies. In the current implementation, each subject's data features are collected in individual data blocks on a sub-level, while simultaneously aggregating the sub-level information to obtain a super-level group "consensus". We further extended the mbPLS model to include 3-dimensional matrices: time-frequency-EEG channel and a time-frequency-connection utilizing Partial Directed Coherence (PDC). We applied the proposed method to concurrent EEG and EMG data collected from ten normal subjects and nine patients with mild-moderate Parkinson's disease (PD) performing a dynamic motor task-that of sinusoidal squeezing. The results demonstrate that connections between EEG electrodes, rather than activity at individual electrodes, correspond more closely to ongoing EMG activity. In PD subjects, there was enhanced connectivity to and from occipital regions, likely related to the previously-described enhanced use of visual information during motor performance in this group. The proposed mbPLS framework is a promising technique for performing multi-subject, multi-modal data analysis and it allows for robust group inferences even in the face of large inter-subject variability.

Exploring a Tobacco Data Set with a Multiblock PLS Method

In chemistry, multiblock datasets are easily encountered with variables of different natures, or measured at different times for example, here, we use the sequential multiblock regression method GOMCIA-PLS1 to predict quantitative variables from several predictors gathered according to their nature and used simultaneously. In this article, it will be applied to predict a chemical variable from Near Infrared Spectrometry (NIRS) chemical and thermolyze data measured on different tobacco samples. The multiblock GOMCIA-PLS1 method is compared to other methods and its good performances are shown. Keywords: GOMCIA-PLS, Multiblock PLS, Multivariate data analysis, Regression

Sensory analysis via multi-block multivariate additive PLS splines

In the last decade, much effort has been spent on modelling dependence between sensory variables and chemical–physical ones, especially when observed at different occasions/spaces/times or if collected from several groups (blocks) of variables. In this paper, we propose a nonlinear generalization of multi-block partial least squares with the inclusion of variable interactions. We show the performance of the method on a known data set.

Preference mapping by PO-PLS: Separating common and unique information in several data blocks

In food development, preference mapping is an important tool for relating product sensory attributes to consumer preferences. The sensory attributes are often divided into several categories, such as visual appearance, smell, taste and texture. This forms a so-called multi-block data set, where each block is a collection of related attributes. The current paper presents a new method for analysing such multi-block data: Parallel Orthogonalised Partial Least Squares regression (PO-PLS). The main objective of PO-PLS is to find common and unique components among several data blocks, and thereby improve interpretation of models. In addition to that, PO-PLS overcomes some challenges from the standard multi-block PLS regression when it comes to scaling and dimensionality of blocks.The method is illustrated by two case studies. One of them is based on a collection of flavoured waters that are characterised by both odour and flavour attributes, forming two blocks of sensory descriptors. A consumer test has also been performed, and PO-PLS is used to create a preference map relating the sensory blocks to consumer liking. The new method is also compared to a preference map created by standard PLS regression. The same is done for the other data set where instrumental data are applied together with sensory data when predicting consumer liking. Here the sensory variables are divided into two blocks: one related to appearance and mouth feel attributes and the other one describing odour and taste properties. In both cases the results clearly illustrate that PO-PLS and PLS regression are equivalent in terms of model fit, but PO-PLS offer some interpretative advantages.

Coupling of Electroanalysis with Multiblock and Hierarchical PCA and PLS Models for Copper ECD Process Control

not Available.