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Analysis of -omics data: Graphical interpretation- and validation tools in multi-block methods

CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2010年第1期104卷 140-153页

作者： Hassani, Sahar Martens, Harald Qannari, El Mostafa Hanafi, Mohamed Borge, Grethe Iren Kohler, Achim Nofima Mat AS Ctr Biospect & Data Modelling N-1430 As Norway Univ Life Sci CIGENE Ctr Integrat Genet N-1432 As Norway Norwegian Univ Life Sci Dept Math Sci & Technol IMT N-1432 As Norway ONIRIS Unite Sensometrie & Chimiometrie F-44322 Nantes 3 France

As systems biology develops, various types of high-throughput -omics data become rapidly available. An increasing challenge is to analyze such massive data, interpret the results and validate the findings. Data analysis for most of the omics-techniques is in a fledgling immature stage. Alone the dimensionality of the data tables calls for new ways to reveal structure in the data, without cognitive overflow and excessive false discovery rate. multi-block methods have been developed and adapted in order to find common variation patterns in data and depict these findings on graphical displays while providing tools to enhance the interpretation of the outcomes. In particular, multi-block methods based on latent variables are powerful tools to study block and global variation patterns, e.g. by inspecting block and global score plots. These methods can be used to achieve a graphical overview over sample and variable variation patterns in an efficient way. However, a visual detection of patterns may be subjective and, therefore, there is a need for validation tools. In this paper tools for validation of visually identified patterns in multi-block results are presented. Cross-validated estimates of Root Mean Square Error (RMSE) for block results are introduced for estimating the number of relevant PCs of the Consensus Principal Component Analysis (CPCA) models. Furthermore, important variables are identified by approximate t-tests based on Procrustes-corrected jackknifing. For the assessment of the stability of score patterns, block stability plots are introduced. Outliers can be revealed graphically on block and global level by stability plots. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Omics data multi-block methods Validation tools

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A sensory approach for the monitoring of accelerated red wine aging processes using multi-block methods

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FOOD QUALITY AND PREFERENCE 2013年第2期28卷 519-530页

作者： Pizarro, Consuelo Esteban-Diez, Isabel Rodriguez-Tecedor, Sofia Maria Gonzalez-Saiz, Jose Univ La Rioja Dept Chem Logrono 26006 La Rioja Spain

Two young red wines from D.O. Navarra (Spain) were separately subjected to accelerated aging in tanks with oak chips added and micro-oxygenation. Wine samples were collected during each process and were analyzed by a sensory panel according to 17 descriptors. A two-fold monitoring approach, aimed at both checking panel performance and tracking the impact of chips/micro-oxygenation treatments on sensory properties, was proposed for process control and optimisation. In a first stage this approach focused on investigating panel performance by suitably combining uni- and multivariate methods. Significant product effects were found for 7 and 6 attributes in the first and second aging series, respectively. Although panel performance was acceptable in both cases, moderate differences between assessors were detected, stressing the need for adopting a consensus approach to properly handle them. Thus, the STATIS method was subsequently applied to find an optimal compromise solution for the significant attributes describing each process. The resulting compromise matrix provided the consensus sensory profiles of samples at different aging stages. The assignment of individual weights was consistent with previous findings on assessors' agreement. The first principal component of the compromise matrix, which accounted for 86.5% and 90.9% of the variance in each trial data, revealed a sample trend directly related to the time-course evolution of each process, and contrasted the attributes fruit and herbaceous with the other significant descriptors (related to the wood-wine interaction). This is the first time that a multi-block methodology has been used for monitoring sensory changes during accelerated aging processes. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Red wine aging Oak chips Micro-oxygenation Sensory panel performance multi-block methods Process monitoring

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Application of multi-block methods in cement production

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JOURNAL OF CHEMOMETRICS 2008年第11-12期22卷 587-593页

作者： Svinning, Ketil Hoskuldsson, Agnar Norcem AS Heidelberg Cement Norway AS Proc & Environm Dept Brevik Norway Ctr Adv Data Anal DK-2800 Lyngby Denmark

Compressive strength at 1 day of Portland cement as a function of the microstructure of cement was statistically modelled by application of multi-block regression method. The observation X-matrix was partitioned into four blocks, the first block representing the mineralogy, the second particle size distribution and the two last blocks the superficial microstructure analysed by differential thermo gravimetric analysis. The multi-block method is used to identify the role of each part. The score vectors of each block can be analysed separately or together with score vectors of other blocks. Stepwise regression is used to find minimum number of variables of each block. The multi-block method proved useful in determining the modelling strength of each data block and finding minimum number of variables within each data block. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： multi-block methods cement properties microstructure of cement

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Application of multi-block methods in cement production

Application of multi-block methods in cement production

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10th Scandinavian Symposium on Chemometrics

作者： Svinning, Ketil Hoskuldsson, Agnar Norcem AS Heidelberg Cement Norway AS Proc & Environm Dept Brevik Norway Ctr Adv Data Anal DK-2800 Lyngby Denmark

关键词： multi-block methods cement properties microstructure of cement

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Estimation of missing data using latent variable methods with auxiliary information

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2005年第1-2期78卷 41-50页

作者： Muteki, K MacGregor, JF Ueda, T McMaster Univ Dept Chem Engn Hamilton ON L8S 4L7 Canada Mitsubishi Chem Corp Yokaichi Mie Japan

Estimating missing data in a matrix is often done with methods, such as the EM algorithm, using the existing data in that matrix. However, if auxiliary data that is related to the missing measurements is available, it can help to estimate the missing values. This paper presents latent variable approaches that exploit an auxiliary data information matrix, as well as the data matrix itself, for estimating missing data on raw material properties of rubbers used in formulating industrial polymer blends. The use of auxiliary information is most useful when the percentage of missing data is high, and when there exist certain combinations of missing data that show little correlation with the data that are present. Two approaches to incorporating the auxiliary information are presented: a multi-block approach and a novel two-stage projection approach. The latter approach is shown to be more flexible and to provide slightly better estimates in two industrial polymer blending problems. However, in both cases, the addition of the auxiliary information is shown to significantly improve the estimates. (c) 2004 Published by Elsevier B.V.

关键词： missing data principal component analysis (PCA) EM algorithm partial least square (PLS) mixture designs polymer blends multi-block methods

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PARALLEL SOLUTION OF ODES BY multiblock methods

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SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING 1987年第3期8卷 342-353页

作者： CHU, MT HAMILTON, H

The notion of linear multi-step methods for solving ordinary differential equations is generalized to a class of multi-block methods. In a multi-block method step values are all obtained together in a single block advance which is accomplished by allocating the parallel tasks on separate processors. The expected benefit of multi-block methods is the speedup in the computation of solutions. The basic formulation is described. Examples are given to demonstrate the existence of such schemes. The predictor-corrector type combination is formed and the resulting stability problem is considered. Test results of one of these multi-block methods on the Denelcor HEP machine are reported.

关键词： 65L05 multi-block methods parallel processing absolute stability Denelcor HEP

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H-methods in applied sciences

H-methods in applied sciences

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International Chemometric Conference (Conferentia Chemometrica 2007)

作者： Hoskuldsson, Agnar Ctr Adv Data Anal DK-2800 Lyngby Denmark

The author has developed a framework for mathematical modelling within applied sciences. It is characteristic for data from 'nature and industry' that they have reduced rank for inference. It means that full rank solutions normally do not give satisfactory solutions. The basic idea of H-methods is to build up the mathematical model in steps by using weighing schemes. Each weighing scheme produces a score and/or a loading vector that are expected to perform a certain task. Optimisation procedures are used to obtain 'the best' solution at each step. At each step, the optimisation is concerned with finding a balance between the estimation task and the prediction task. The name H-methods has been chosen because of close analogy with the Heisenberg uncertainty inequality. A similar situation is present in modelling data. The mathematical modelling stops, when the prediction aspect of the model cannot be improved. H-methods have been applied to wide range of fields within applied sciences. In each case, the H-methods provide with superior solutions compared to the traditional ones. A background for the H-methods is presented. The H-principle of mathematical modelling is explained. It is shown how the principle leads to well-defined optimisation procedures. This is illustrated in the case of linear regression. The H-methods have been applied in different areas: general linear models, nonlinear models, multi-block methods, path modelling, multi-way data analysis, growth models, dynamic models and pattern recognition. Copyright (c) 2008 John Wiley & Sons, Ltd.

关键词： PLS regression H-methods weighing schemes multi-block methods nonlinear methods path models

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Correlation-aware probabilistic data summarization for large-scale multi-block scientific data visualization

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Computational Visual Media 2023年第3期9卷 513-529页

作者： Yang Yang Kecheng Lu Yu Wu Yunhai Wang Yi Cao Institute of Applied Physics and Computational Mathematics Beijing 100094China School of Computer Science and Technology Shandong UniversityQingdao 266237China

In this paper,we propose a correlationaware probabilistic data summarization technique to efficiently analyze and visualize large-scale multi-block volume data generated by massively parallel scientific *** core of our technique is correlation modeling of distribution representations of adjacent data blocks using copula functions and accurate data value estimation by combining numerical information,spatial location,and correlation distribution using Bayes’*** effectively preserves statistical properties without merging data blocks in different parallel computing nodes and repartitioning them,thus significantly reducing the computational ***,this enables reconstruction of the original data more accurately than existing *** demonstrate the effectiveness of our technique using six datasets,with the largest having one billion grid *** experimental results show that our approach reduces the data storage cost by approximately one order of magnitude compared to state-of-the-art methods while providing a higher reconstruction accuracy at a lower computational cost.

关键词： correlation-awareness large-scale data multi-block methods probabilistic data summarization

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Model validation and error estimation in multi-block partial least squares regression

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2012年 117卷 42-53页

作者： Hassani, Sahar Martens, Harald Qannari, El Mostafa Hanafi, Mohamed Kohler, Achim Nofima Mat AS Norwegian Food Res Inst N-1430 As Norway Norwegian Univ Life Sci Dept Math Sci & Technol IMT Ctr Integrat Genet CIGENE N-1432 As Norway ONIRIS INRA Unite Sensometrie & Chimiometrie F-44322 Nantes 3 France

While validation of Partial Least Squares Regression (PLSR) models has been discussed extensively, validation tools that are tailored to multi-block Partial Least Squares Regression (MBPLSR) have not been discussed in literature yet. This paper introduces validation tools for estimating predictive ability and model stability in MBPLSR models on block level and on global level. Predictive ability on the block level and global level are estimated by calculating the predictive power of block and global parameters. Model stability is estimated by checking the stability of block model parameters and global parameters. By comparing error plots for model stability and predictive ability the user can decide on the number of component to be used. The number of components to be chosen depends on the data set and the purpose of the investigation. (C) 2011 Elsevier B.V. All rights reserved.

关键词： multi-block methods multi-block Partial Least Squares Regression (MBPLSR) Validation tools Cross validation Number of components

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Identifying outlying assessors in sensory profiling using fuzzy clustering and multi-block methodology

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FOOD QUALITY AND PREFERENCE 2009年第4期20卷 287-294页

作者： Dahl, Tobias Naes, Tormod Nofima Food N-1430 As Norway Univ Oslo Dept Informat N-0316 Oslo Norway

In this paper we discuss methods for detecting outlying assessors in descriptive sensory analysis. A new method is proposed which is based on fuzzy clustering with the use of the noise cluster method. The technique ends up with a plot which can be used to provide information about which assessors that are different from the rest and also to suggest reasons why the assessors are different. The method is based on data compression by the use of either Tucker-1 or Tucker-2 for multi-block data. The technique is used on a dataset based on an oxidation experiment of cheese. There are 9 trained and 3 untrained assessors in the panel. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Fuzzy clustering Noise cluster multi-block methods Outliers Principal components

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