Forster, Thorsten

Ghazal, Peter

McGeever, Sean

Robertson, Kevin

Roy, Douglas

English

PubMed

Crossref

Douglas Roy

Thorsten Forster

Sean McGeever

Kevin Robertson

Peter Ghazal

Meeting Review: Bioinformatics of Biochips: Accelerating Discovery in Functional Genomics

Roy, D

Forster, T

McGeever, S

Robertson, K N

Ghazal, P

Edinburgh Research Explorer

     Edinburgh Research Explorer                                      Meeting review: Bioinformatics of biochips: Acceleratingdiscovery in functional genomicsCitation for published version:Roy, D, Forster, T, McGeever, S, Robertson, KN & Ghazal, P 2002, 'Meeting review: Bioinformatics ofbiochips: Accelerating discovery in functional genomics', Comparative and functional genomics, vol. 3, no.4, pp. 380-386. https://doi.org/10.1002/cfg.179Digital Object Identifier (DOI):10.1002/cfg.179Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Publisher's PDF, also known as Version of recordPublished In:Comparative and functional genomicsGeneral rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately andinvestigate your claim.Download date: 29. Nov. 2025Comparative and Functional GenomicsComp Funct Genom 2002; 3: 375–379.Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cfg.192Conference ReviewThe curse of normalizationOlaf Wolkenhauer,1,2* Carla Möller-Levet2 and Fatima Sanchez-Cabo11 Department of Biomolecular Sciences, Control Systems Centre, UMIST, Manchester M60 1QD, UK2 Department of Electrical Engineering, Control Systems Centre, UMIST, Manchester M60 1QD, UK*Correspondence to:Olaf Wolkenhauer, Departmentof Biomolecular Sciences,Department of ElectricalEngineering, ControlSystems Centre, UMIST,Manchester M60 1QD, UK.E-mail:o.wolkenhauer@umist.ac.ukReceived: 31 May 2002Accepted: 12 June 2002AbstractDespite its enormous promise to further our understanding of cellular processesinvolved in the regulation of gene expression, microarray technology generates datafor which statistical pre-processing has become a necessity before any interpretationof data can begin. The process by which we distinguish (and remove) non-biologicalvariation from biological variation is called normalization. With a multitude ofexperimental designs, techniques and technologies influencing the acquisition of data,numerous approaches to normalization have been proposed in the literature. Thepurpose of this short review is not to add to the many suggestions that have beenmade, but to discuss some of the difficulties we encounter when analysing microarraydata. Copyright  2002 John Wiley & Sons, Ltd.Keywords: microarrays; bioinformatics; normalization; singular value decom-positionIntroductionFigure 1 outlines some of issues dealt with inmicroarray bioinformatics. An important point isthat ‘data analysis’ is distinct from ‘data manage-ment’ and that the analysis of data begins alreadywith the acquisition of images. At this early stagedecisions have to be made about how poor or emptyspots are dealt with. Statistics extracted from theimages form the basis for these decisions, whichnaturally will influence the ‘downstream’ analy-sis (e.g. clustering and classification). While ‘poorspots’ should naturally be excluded from the anal-ysis, in the absence of replicates, a missing valuein a time series may force the analyst to ignore thegene associated with a missing data point.Removing noise, detecting outliers and filling inmissing values are problems for which solutionsare developed in statistics. The basis for any suchapproach is to use information in the data setto fill in gaps or remove undesirable effects. Inthe absence of sufficiently reliable information(e.g. through replicates or large time series), dataanalysis becomes an art, enjoyed by statisticians,dreaded by the rest.What is normal in normalization?Table 1 summarizes one approach to the norma-lization of array data, divided into four (five) se-quential steps. There are many different approachesto normalization, all of which depend on the tech-nology employed and the experiments considered.Serving as an example, the table does not claimcompleteness (e.g. housekeeping genes and spikedcontrols are not considered) and we refer to the listof selected references for further reading [1–7].The problem we wish to illustrate here is thatthrough normalization we correct for possible non-biological variation but thereby can also reducethe informative content of the data. This doesnot mean one should not normalize; however, onepays a price for correcting something that is notcompletely known. Let us consider the followingsequential steps in the normalization process, sum-marized in Table 1.Copyright  2002 John Wiley & Sons, Ltd.376 O. Wolkenhauer et al.Array ProductionExperimental DesignData CaptureDATA  ANALYSISDATA  MANAGEMENTData InterpretationMicroarray Bioinformatics:1. Background & Gain Correction2. Flag Handling3. Outliers & Missing Values4. Normalization5. Replicate Handling6. Multivariate Data Analysis7. Visualization8. Mathematical Modelling9. SimulationFigure 1. Microarray bioinformatics begins with the acquisition of data and their management (storage of experimentaldata and information associated with the experiment). Data analysis, visualization and interpretation are the aim of thewhole process, one that can be daunting at timesTable 1. An example for the normalization of DNA microarray dataNormalization Variation Options ImplementationBackgroundsubtractionBackground subtractionfor all genes i = 1, . . .si = si − bsiri = ri − briNo subtraction si = siri = riDye correction Dye effects Lowess function Ai = 1/2·(log2 si + log2 ri)Mi = log2(si/ri)si = siri = rik(Ai)Linear regression(RNA vs. RNA)From scatter plot:s = m·r + asi = (si − a)/mri = riGain correction(DNA vs. RNA)mi = bri/bsi si = si·miri = riPer-spotnormalizationArray and geneeffectspi = si/riWithin-arraynormalizationGene effects Median (50% percentile) qi = pi/medi(pi)Percentiles (e.g. 25%,75%)qi = pi/perci(pi)DNA vs. RNA time course experiments: (after averaging replicates for every time point.)Across-arraysnormalizationArray effects Against all arrays ei = qi/medj(qj) for all genesi, for all arrays j = 1, . . .Against arrays in J ei = qi/medj(qj) for all genesi, and for arrays j e JThe values s, r refer to intensities in the signal and reference channel, respectively; bs, br denote the intensity of the background measuredfor both channels. Note that gain correction may not be appropriate for experiments with swapped dyes and if the relationship existingbetween background intensities of both channels is different to the one of signal intensities.Background subtraction and gaincorrectionInformation about background intensities can beused in different ways to normalize the dataset. Some authors [1] suggest subtracting thebackground intensity from the signal intensity inboth channels (we hereafter refer to one channelas the reference and the other as the signal). Thisprocess makes the assumption that background andCopyright  2002 John Wiley & Sons, Ltd. Comp Funct Genom 2002; 3: 375–379.Microarray data normalization 377signal intensities are additive. The background canalso be useful to correct for different gain settingsduring scanning of the array to accommodate forthe different labelling efficiencies of the dyes. Ifbackground intensities in both channels differ, weassume the existence of external factors that mod-ify the measurements of intensities and potentiallymask biological variation. We calculate (for eachspot) a constant, mi, to equal the background inten-sities for both channels and, in consequence, toremove non-biological variation due to the inter-action between dye and sample (see Table 1).In an RNA vs. RNA microarray experiment weexpect the quantity of initial mRNA to be the samefor both labelled samples. In terms of intensities,this means that the total intensity measured forboth channels should be very similar. In a scatterplot (reference against signal intensities) we wouldtherefore expect the data points to be distributedalong a 45◦ line (i.e. a line with a slope equal to1). We can fit a regression line through the pointsin the scatter plot and subsequently transform thedata to align them along the ideal line, with aslope equal to 1. The calculations are shown inTable 1 for a useful illustration of this process,see [5]. We note in passing that for non-linearrelationships between both channels, the use of theLowess function approach is more appropriate thanlinear regression [7].Per spot normalizationWith the handling of liquids in minute quantitiesand measurements at relatively small scales, manyexperimental variations can occur. The most obvi-ous experimental errors (e.g. liquid remains on thearray surface) are visible in the scanned image.These spatial effects usually affect both channels.We account for this artificial variation by dividingthe signal intensity of one channel by the other.With this simple operation we are at the same timecomparing the relative intensity of both channels,something that is the principal aim of RNA vs.RNA experiments.Within-array normalizationThe hybridization efficiency may vary from geneto gene spotted in the microarray. With thenormalization within an array we balance this vari-ation. Relating each intensity ratio to one and thesame number, we ensure that these are compara-ble. This number should be representative of theoverall intensity in the array. In practice, this num-ber is chosen to be a percentile of intensities inthe array (or subregions of the array). Which per-centile is chosen depends on the number of genesthat are expected to be differentially expressed, e.g.in RNA vs. RNA experiments we use the median(50% percentile) of the intensity ratios because weassume the same proportion of genes being up- anddownregulated.Replicate handlingIf we are dealing with replicated experiments, werequire a value that summarizes the biologicalinformation collected by the different experimen-tal replicates. One value that fulfils this criterion isthe average. In the particular case of a time seriesexperiment, every new value obtained throughaveraging is going to represent a time point. Asfor genes within an array, in time course experi-ments we require the same gene to be comparableacross arrays. This is what in Table 1 is referred toas normalization across arrays. Following normal-ization, we consider the obtained expression levelsin log-space.Other ways to normalize: SVD andANOVAThe biggest challenge the biologist faces in theanalysis of array data is to identify a suitablenormalization method for his/her experiment. Wecan illustrate the effect of non-biological varia-tion using singular value decomposition (SVD)of the gene expression matrix (GEM). The SVDof the GEM allows us to describe every geneexpression profile as the linear combination ofsome ‘fundamental’ or ‘principal’ patterns of vari-ation. Figure 2 illustrates principal patterns, whichare also referred to as ‘eigengenes’, for a dataset that is not normalized. Figure 3 shows theSVD on the same data set but after normaliza-tion. We notice that the second eigengene for thenon-normalized data disappears in the SVD of thenormalized data, while the other principal patternsCopyright  2002 John Wiley & Sons, Ltd. Comp Funct Genom 2002; 3: 375–379.378 O. Wolkenhauer et al.remain. This suggests that the second eigen-gene does represent the non-biological variationremoved by the normalization process describedin previous sections. An alternative approach tonormalization would therefore be the ‘filtering’of the gene expression profiles by subtracting theeigengene corresponding to the ‘noise’ (unwantedvariation).6 14 20 30-1-0.500.51 Eigengene 1-1-0.500.516 14 20 30-1-0.500.51 Eigengene 2-1-0.500.516 14 20 30-1-0.500.51 Eigengene 3-1-0.500.516 14 20 30-1-0.500.51 Eigengene 4-1-0.500.51Figure 2. The decomposition of the gene expression matrixshows four ‘principal patterns’ (bold lines) that occur in thedata. Each graph shows four original expression profiles thatcorrelate well with the principal or eigengene6 14 20 30 6 14 20 306 14 20 30-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.516 14 20 30Normalisedeigengene 3Normalisedeigengene 4Normalisedeigengene 2Normalisedeigengene 1Figure 3. The SVD of the normalized data set shows thatthe second eigengene in Figure 2 has vanished. This suggeststhat eigengene 2 captures the non-biological variation weremoved through the normalization process described inTable 1ANOVA (analysis of variance) is a popular sta-tistical approach to consider sources variation inarray data. ANOVA tries to achieve a valid esti-mator to understand the variability of a data set,detecting all the possible sources of variation.We can define the main sources of variationin a microarray experiment and summarize themin one equation. As described in [3,4], we couldexpress every realization of the experiment as acombination of all these factors:log(yijkg) = µ + Ai + Dj + Vk + Gg + (AG)ig+ (DV )jk + εijkgwhere yijkg = measurement of the gene g in thearray i for the dye j and the variety k ; µ = overallaverage signal; Ai = effect of the i th array; Dj =effect of the j th dye; Vk = effect of the k th variety;Gg = effect of the g th gene; (AG)ig = a particu-lar gene in a particular array; (DV )jk = interactionbetween the k th variety and the j th dye; and εijkg =error term. Using ANOVA we can obtain an esti-mator for every one of these variables and use theexpression above to correct the signal intensities.ConclusionThe diversity of methods on offer and the manyconsiderations necessary in the process of normal-ization can be daunting for anyone for whom theprimary focus of array data analysis is their inter-pretation. Microarray data analysis therefore servesas a good example of the need for close inter-disciplinary collaborations between biologists anddata analysts.AcknowledgementsWe would like to acknowledge the support of the BacterialMicroarray Group at St George’s Hospital, London. Theynot only provided the authors with good quality data setsbut also proved to be outstanding collaborators. Their guid-ance and support helped the authors to better understand theproduction of microarrays. One conclusion from this workon data analysis is that such close interdisciplinary links arevital for the analysis and interpretation of array data. Weare also grateful to The Wellcome Trust for their supportin bringing the UMIST and St. George’s groups together.Copyright  2002 John Wiley & Sons, Ltd. Comp Funct Genom 2002; 3: 375–379.Microarray data normalization 379References1. Herzel H, Beule D, Kielbasa S, et al. 2001. Extractinginformation from cDNA arrays. CHAOS 11: 98–107.2. Huber W, von Heydebreck A, Sültmann H, Poustka A,Vingron M. 2002. Variance stabilization applied to microarraydata calibration and to the quantification of differentialexpression. Bioinformatics (in press).3. Kerr K, Churchill GA. 2001. Experimental design for geneexpression analysis. Biostatistics 2: 183–201.4. Kerr K, Martin M, Churchill GA. 2000. Analysis of variancefor gene expression microarray data. J Comput Bio 7: 819–837.5. Quackenbush J. 2001. Computational Analysis of MicroarrayData. Nature Rev Genet 2: 418–425.6. Tsodikov A, Szabo A, Jones D. 2002. Adjustments andmeasures of differential expression for microarray data.Bioinformatics 18(2): 251–260.7. Yang YH, Dudoit S, Luu P, et al. 2001. Normalization forMicroarray Data: http://stat-www.berkeley.edu/users/terry/zarray/Html/normspie.html.Copyright  2002 John Wiley & Sons, Ltd. Comp Funct Genom 2002; 3: 375–379.Submit your manuscripts athttp://www.hindawi.comEnzyme ResearchHindawi Publishing Corporation http://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.comNucleic AcidsJournal ofVolume 2013Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Advances inVirolog yISRN BiotechnologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013ArchaeaHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2013BioinformaticsAdvances inHindawi Publishing Corporationhttp://www.hindawi.comGenomicsInternational Journal ofVolume 2013ISRN MicrobiologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Signal TransductionJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013PeptidesInternational Journal ofISRN ZoologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Stem CellsInternationalHindawi Publishing Corporation http://www.hindawi.com Volume 2013ISRN Cell BiologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013BioMed Research InternationalHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Biochemistry Research InternationalHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Journal ofMarine BiologyHindawi Publishing Corporation http://www.hindawi.com Volume 2013The Scientific World JournalISRN Molecular BiologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013International Journal ofEvolutionary BiologyHindawi Publishing Corporation http://www.hindawi.com Volume 2013

Meeting review: Bioinformatics of biochips: Accelerating discovery in functional genomics

     Edinburgh Research Explorer                                      Meeting review: Bioinformatics of biochips: Acceleratingdiscovery in functional genomicsCitation for published version:Roy, D, Forster, T, McGeever, S, Robertson, KN & Ghazal, P 2002, 'Meeting review: Bioinformatics ofbiochips: Accelerating discovery in functional genomics' Comparative and functional genomics, vol. 3, no. 4,pp. 380-386. DOI: 10.1002/cfg.179Digital Object Identifier (DOI):10.1002/cfg.179Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Publisher's PDF, also known as Version of recordPublished In:Comparative and functional genomicsGeneral rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately andinvestigate your claim.Download date: 05. Apr. 2019Comparative and Functional GenomicsComp Funct Genom 2002; 3: 375–379.Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cfg.192Conference ReviewThe curse of normalizationOlaf Wolkenhauer,1,2* Carla Mo¨ller-Levet2 and Fatima Sanchez-Cabo11 Department of Biomolecular Sciences, Control Systems Centre, UMIST, Manchester M60 1QD, UK2 Department of Electrical Engineering, Control Systems Centre, UMIST, Manchester M60 1QD, UK*Correspondence to:Olaf Wolkenhauer, Departmentof Biomolecular Sciences,Department of ElectricalEngineering, ControlSystems Centre, UMIST,Manchester M60 1QD, UK.E-mail:o.wolkenhauer@umist.ac.ukReceived: 31 May 2002Accepted: 12 June 2002AbstractDespite its enormous promise to further our understanding of cellular processesinvolved in the regulation of gene expression, microarray technology generates datafor which statistical pre-processing has become a necessity before any interpretationof data can begin. The process by which we distinguish (and remove) non-biologicalvariation from biological variation is called normalization. With a multitude ofexperimental designs, techniques and technologies influencing the acquisition of data,numerous approaches to normalization have been proposed in the literature. Thepurpose of this short review is not to add to the many suggestions that have beenmade, but to discuss some of the difficulties we encounter when analysing microarraydata. Copyright  2002 John Wiley & Sons, Ltd.Keywords: microarrays; bioinformatics; normalization; singular value decom-positionIntroductionFigure 1 outlines some of issues dealt with inmicroarray bioinformatics. An important point isthat ‘data analysis’ is distinct from ‘data manage-ment’ and that the analysis of data begins alreadywith the acquisition of images. At this early stagedecisions have to be made about how poor or emptyspots are dealt with. Statistics extracted from theimages form the basis for these decisions, whichnaturally will influence the ‘downstream’ analy-sis (e.g. clustering and classification). While ‘poorspots’ should naturally be excluded from the anal-ysis, in the absence of replicates, a missing valuein a time series may force the analyst to ignore thegene associated with a missing data point.Removing noise, detecting outliers and filling inmissing values are problems for which solutionsare developed in statistics. The basis for any suchapproach is to use information in the data setto fill in gaps or remove undesirable effects. Inthe absence of sufficiently reliable information(e.g. through replicates or large time series), dataanalysis becomes an art, enjoyed by statisticians,dreaded by the rest.What is normal in normalization?Table 1 summarizes one approach to the norma-lization of array data, divided into four (five) se-quential steps. There are many different approachesto normalization, all of which depend on the tech-nology employed and the experiments considered.Serving as an example, the table does not claimcompleteness (e.g. housekeeping genes and spikedcontrols are not considered) and we refer to the listof selected references for further reading [1–7].The problem we wish to illustrate here is thatthrough normalization we correct for possible non-biological variation but thereby can also reducethe informative content of the data. This doesnot mean one should not normalize; however, onepays a price for correcting something that is notcompletely known. Let us consider the followingsequential steps in the normalization process, sum-marized in Table 1.Copyright  2002 John Wiley & Sons, Ltd.376 O. Wolkenhauer et al.Array ProductionExperimental DesignData CaptureDATA  ANALYSISDATA  MANAGEMENTData InterpretationMicroarray Bioinformatics:1. Background & Gain Correction2. Flag Handling3. Outliers & Missing Values4. Normalization5. Replicate Handling6. Multivariate Data Analysis7. Visualization8. Mathematical Modelling9. SimulationFigure 1. Microarray bioinformatics begins with the acquisition of data and their management (storage of experimentaldata and information associated with the experiment). Data analysis, visualization and interpretation are the aim of thewhole process, one that can be daunting at timesTable 1. An example for the normalization of DNA microarray dataNormalization Variation Options ImplementationBackgroundsubtractionBackground subtractionfor all genes i = 1, . . .si = si − bsiri = ri − briNo subtraction si = siri = riDye correction Dye effects Lowess function Ai = 1/2·(log2 si + log2 ri)Mi = log2(si/ri)si = siri = rik(Ai)Linear regression(RNA vs. RNA)From scatter plot:s = m·r + asi = (si − a)/mri = riGain correction(DNA vs. RNA)mi = bri/bsi si = si·miri = riPer-spotnormalizationArray and geneeffectspi = si/riWithin-arraynormalizationGene effects Median (50% percentile) qi = pi/medi(pi)Percentiles (e.g. 25%,75%)qi = pi/perci(pi)DNA vs. RNA time course experiments: (after averaging replicates for every time point.)Across-arraysnormalizationArray effects Against all arrays ei = qi/medj(qj) for all genesi, for all arrays j = 1, . . .Against arrays in J ei = qi/medj(qj) for all genesi, and for arrays j e JThe values s, r refer to intensities in the signal and reference channel, respectively; bs, br denote the intensity of the background measuredfor both channels. Note that gain correction may not be appropriate for experiments with swapped dyes and if the relationship existingbetween background intensities of both channels is different to the one of signal intensities.Background subtraction and gaincorrectionInformation about background intensities can beused in different ways to normalize the dataset. Some authors [1] suggest subtracting thebackground intensity from the signal intensity inboth channels (we hereafter refer to one channelas the reference and the other as the signal). Thisprocess makes the assumption that background andCopyright  2002 John Wiley & Sons, Ltd. Comp Funct Genom 2002; 3: 375–379.Microarray data normalization 377signal intensities are additive. The background canalso be useful to correct for different gain settingsduring scanning of the array to accommodate forthe different labelling efficiencies of the dyes. Ifbackground intensities in both channels differ, weassume the existence of external factors that mod-ify the measurements of intensities and potentiallymask biological variation. We calculate (for eachspot) a constant, mi, to equal the background inten-sities for both channels and, in consequence, toremove non-biological variation due to the inter-action between dye and sample (see Table 1).In an RNA vs. RNA microarray experiment weexpect the quantity of initial mRNA to be the samefor both labelled samples. In terms of intensities,this means that the total intensity measured forboth channels should be very similar. In a scatterplot (reference against signal intensities) we wouldtherefore expect the data points to be distributedalong a 45◦ line (i.e. a line with a slope equal to1). We can fit a regression line through the pointsin the scatter plot and subsequently transform thedata to align them along the ideal line, with aslope equal to 1. The calculations are shown inTable 1 for a useful illustration of this process,see [5]. We note in passing that for non-linearrelationships between both channels, the use of theLowess function approach is more appropriate thanlinear regression [7].Per spot normalizationWith the handling of liquids in minute quantitiesand measurements at relatively small scales, manyexperimental variations can occur. The most obvi-ous experimental errors (e.g. liquid remains on thearray surface) are visible in the scanned image.These spatial effects usually affect both channels.We account for this artificial variation by dividingthe signal intensity of one channel by the other.With this simple operation we are at the same timecomparing the relative intensity of both channels,something that is the principal aim of RNA vs.RNA experiments.Within-array normalizationThe hybridization efficiency may vary from geneto gene spotted in the microarray. With thenormalization within an array we balance this vari-ation. Relating each intensity ratio to one and thesame number, we ensure that these are compara-ble. This number should be representative of theoverall intensity in the array. In practice, this num-ber is chosen to be a percentile of intensities inthe array (or subregions of the array). Which per-centile is chosen depends on the number of genesthat are expected to be differentially expressed, e.g.in RNA vs. RNA experiments we use the median(50% percentile) of the intensity ratios because weassume the same proportion of genes being up- anddownregulated.Replicate handlingIf we are dealing with replicated experiments, werequire a value that summarizes the biologicalinformation collected by the different experimen-tal replicates. One value that fulfils this criterion isthe average. In the particular case of a time seriesexperiment, every new value obtained throughaveraging is going to represent a time point. Asfor genes within an array, in time course experi-ments we require the same gene to be comparableacross arrays. This is what in Table 1 is referred toas normalization across arrays. Following normal-ization, we consider the obtained expression levelsin log-space.Other ways to normalize: SVD andANOVAThe biggest challenge the biologist faces in theanalysis of array data is to identify a suitablenormalization method for his/her experiment. Wecan illustrate the effect of non-biological varia-tion using singular value decomposition (SVD)of the gene expression matrix (GEM). The SVDof the GEM allows us to describe every geneexpression profile as the linear combination ofsome ‘fundamental’ or ‘principal’ patterns of vari-ation. Figure 2 illustrates principal patterns, whichare also referred to as ‘eigengenes’, for a dataset that is not normalized. Figure 3 shows theSVD on the same data set but after normaliza-tion. We notice that the second eigengene for thenon-normalized data disappears in the SVD of thenormalized data, while the other principal patternsCopyright  2002 John Wiley & Sons, Ltd. Comp Funct Genom 2002; 3: 375–379.378 O. Wolkenhauer et al.remain. This suggests that the second eigen-gene does represent the non-biological variationremoved by the normalization process describedin previous sections. An alternative approach tonormalization would therefore be the ‘filtering’of the gene expression profiles by subtracting theeigengene corresponding to the ‘noise’ (unwantedvariation).6 14 20 30-1-0.500.51 Eigengene 1-1-0.500.516 14 20 30-1-0.500.51 Eigengene 2-1-0.500.516 14 20 30-1-0.500.51 Eigengene 3-1-0.500.516 14 20 30-1-0.500.51 Eigengene 4-1-0.500.51Figure 2. The decomposition of the gene expression matrixshows four ‘principal patterns’ (bold lines) that occur in thedata. Each graph shows four original expression profiles thatcorrelate well with the principal or eigengene6 14 20 30 6 14 20 306 14 20 30-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.516 14 20 30Normalisedeigengene 3Normalisedeigengene 4Normalisedeigengene 2Normalisedeigengene 1Figure 3. The SVD of the normalized data set shows thatthe second eigengene in Figure 2 has vanished. This suggeststhat eigengene 2 captures the non-biological variation weremoved through the normalization process described inTable 1ANOVA (analysis of variance) is a popular sta-tistical approach to consider sources variation inarray data. ANOVA tries to achieve a valid esti-mator to understand the variability of a data set,detecting all the possible sources of variation.We can define the main sources of variationin a microarray experiment and summarize themin one equation. As described in [3,4], we couldexpress every realization of the experiment as acombination of all these factors:log(yijkg) = µ + Ai + Dj + Vk + Gg + (AG)ig+ (DV )jk + εijkgwhere yijkg = measurement of the gene g in thearray i for the dye j and the variety k ; µ = overallaverage signal; Ai = effect of the i th array; Dj =effect of the j th dye; Vk = effect of the k th variety;Gg = effect of the g th gene; (AG)ig = a particu-lar gene in a particular array; (DV )jk = interactionbetween the k th variety and the j th dye; and εijkg =error term. Using ANOVA we can obtain an esti-mator for every one of these variables and use theexpression above to correct the signal intensities.ConclusionThe diversity of methods on offer and the manyconsiderations necessary in the process of normal-ization can be daunting for anyone for whom theprimary focus of array data analysis is their inter-pretation. Microarray data analysis therefore servesas a good example of the need for close inter-disciplinary collaborations between biologists anddata analysts.AcknowledgementsWe would like to acknowledge the support of the BacterialMicroarray Group at St George’s Hospital, London. Theynot only provided the authors with good quality data setsbut also proved to be outstanding collaborators. Their guid-ance and support helped the authors to better understand theproduction of microarrays. One conclusion from this workon data analysis is that such close interdisciplinary links arevital for the analysis and interpretation of array data. Weare also grateful to The Wellcome Trust for their supportin bringing the UMIST and St. George’s groups together.Copyright  2002 John Wiley & Sons, Ltd. Comp Funct Genom 2002; 3: 375–379.Microarray data normalization 379References1. Herzel H, Beule D, Kielbasa S, et al. 2001. Extractinginformation from cDNA arrays. CHAOS 11: 98–107.2. Huber W, von Heydebreck A, Su¨ltmann H, Poustka A,Vingron M. 2002. Variance stabilization applied to microarraydata calibration and to the quantification of differentialexpression. Bioinformatics (in press).3. Kerr K, Churchill GA. 2001. Experimental design for geneexpression analysis. Biostatistics 2: 183–201.4. Kerr K, Martin M, Churchill GA. 2000. Analysis of variancefor gene expression microarray data. J Comput Bio 7: 819–837.5. Quackenbush J. 2001. Computational Analysis of MicroarrayData. Nature Rev Genet 2: 418–425.6. Tsodikov A, Szabo A, Jones D. 2002. Adjustments andmeasures of differential expression for microarray data.Bioinformatics 18(2): 251–260.7. Yang YH, Dudoit S, Luu P, et al. 2001. Normalization forMicroarray Data: http://stat-www.berkeley.edu/users/terry/zarray/Html/normspie.html.Copyright  2002 John Wiley & Sons, Ltd. 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Meeting Review: Bioinformatics of Biochips: Accelerating Discovery in Functional Genomics

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