BACKGROUND
genome-wide analyses provide an unprecedented amount of data leading to new interpretation challenges.
classical microarrays can monitor the expression of potentially all genes within a cell or a tissue sample.
more recently, new applications have been developed.
they include chromatin-immunoprecipitation-chip , analysis of alternative splicing , characterization of the methylome, polymorphism genotyping , copy-number measurements  and genome resequencing .
a great interest in the statistical analysis of these 'omics' data has emerged and many methodologies have been developed.
however, if the inferential statistics analyses are now guided by consensual methods  <cit> , the descriptive analysis is often succinct if not neglected.
two reasons can be advanced:  the great volume of information makes difficult the interpretation of the results, and  heterogeneous data and multiple sources of information are difficult to integrate in a global analysis.
methods that overcome these difficulties are necessary as the understanding of a biological phenomenon would greatly benefit from considering simultaneously several types of 'omics' data and particularly with biological knowledge.
this could be done in a multidimensional exploratory approach.
in a multidimensional exploratory approach, a microarray data set is usually analyzed by multivariate analysis  among which principal components analysis  is the most used.
pca is well adapted to the framework of 'omics' data as it can handle data sets with much more variables  than samples .
to analyze simultaneously several data sets, the proper way is to use mva's dedicated to the analysis of multi-way data tables; the method of reference being the generalized canonical analysis   <cit> .
in the field of microarray, gca is however limited by the problem of multi-colinearity.
to bypass this limitation, only two alternatives have still been proposed: the generalized co-inertia analysis   <cit>  and the recently applied regularized canonical correlation analysis   <cit> .
the need for integrating external information in mva to ease the interpretation of microarray data have also been pointed out.
as proposed by busold et al.
<cit> , fagan et al.
<cit>  superimposed gene ontology  terms as supplementary elements onto cia projections.
in this study, go terms are formalized as boolean vectors that are projected onto cia plots after matrix transformations.
although cia approach provide good results in combining molecular data sets, the way go terms are added is not straightforward and appears incomplete.
indeed, this method codes the links between genes and go terms and do not take into account the microarray values or molecular data of the genes related to each go term.
other computational methods, such as gene set enrichment analysis   <cit> , have shown the importance of focusing on groups of genes as opposed to individual genes for incorporating biological information and gene sets into microarray data analysis.
following this philosophy, a proper integration of biological information in mva will gain in accuracy by grouping genes into knowledge-related modules, and thus by considering a 'modular approach'  <cit> .
such an approach studies as a whole the behavior and structure of a biological process in addition to analyzing its components  individually.
in this article, we suggest to use multiple factor analysis  in the sense of escofier-pagès  <cit>  to integrate bio-molecular data sets as well as informations on the genes structured in modules.
mfa is dedicated to the simultaneous exploration of multi-way data sets where the same individuals are described by several groups of variables.
mfa is commonly applied to sensory and ecology data and it has already been applied to the analysis of metabonomic data  <cit> .
mfa can be related to gca and cia since it could be considered as a particular generalized canonical analysis were the inertia criteria replaces the correlation criteria.
these methods display a low-dimensional projection of the data highlighting the main sources of variability.
results should therefore be interpreted with caution as sources of variability are not always due to specific biological factors of interest.
it is also important to note that at the sample level, the structures provided either by mfa or cia are highly similar  <cit> .
the assets of mfa appear when integrating both numerical and categorical groups of variables, and when supplementary groups of data need to be added in the analysis.
here, we present our approach by introducing the basis of mfa and we state how mfa is particularly well adapted to integrate formalized biological knowledge.
we illustrate our method with a glioma study  <cit>  performed with both cgh array and expression microarray on the same tumor samples.
results shows that both dna copy number alteration and transcriptome data sets induce a good separation of the gliomas according to the who classification.
the superimposition of the gene modules built since go annotation identify regulatory mechanisms implicated in gliomagenesis.
we also show that our approach can handle a single data set with associated go annotations and therefore be used as an exploratory tool in the case of classical single 'omics' study.
finally we present another illustration focused on a nutrition study in mice and integrating microarray and lipidomic data.
RESULTS
mfa is used to analyze several groups of 'omics' variables  defined on the same samples.
the core of mfa is a pca applied to the whole set of variables in which each group of variables is weighted, rendering possible the analysis of different points of view by taking them equally into account.
to illustrate the main features of our approach a schematic is provided in figure  <dig>  each time, mfa is applied to published-data selections .
resulting graphical outputs for the first two principal components  are used.
we describe the results and discuss the following points:
the combination of paired cgh array and microarray data of glial tumors;
the assemblage of genes into modules based on gene ontology terms and their superimposition on the principal components issued of point , supporting interpretation of the study;
the application of our approach in the case of a single 'omics' study ;
an other illustration of our method with a different experimental setting using a nutrition study including microarrays and fatty acids gas chromatography data.
the analyses have been performed with r and the package factominer  <cit> .
multi-way glioma data set
joining 'omics' distinct points of view
mfa is applied to the paired cgh array and microarray glioma data of bredel et al.
<cit> .
the resulting sample plots  are presented figure  <dig> and figure  <dig>  the mean representation of the samples according to both cgh and gene expression data sets is presented figure  <dig>  mean samples are represented by points colored following who classification of the tumors.
figure 3a shows the partial representation associated to each type of tumors .
this representation is obtained from the consensus between the cgh and expression  points of view .
each type of tumors is represented by three points: the consensus between the two points of view and a point for each point of view.
both scatter plots show a well-defined partition of the samples into who classification.
this is particularly true along pc <dig> that underlines a partition of the samples into glioblastomas  and lower grade gliomas .
partial representation  and groups representation  show that this partition exists  on pc <dig> at the genome and at the transcriptome levels and  only at the genome level on pc <dig>  indeed, the projections on pc <dig> of the partial points for each category of tumors  are each time very close, meaning that cgh and ex define similar structures upon tumors on pc <dig>  in a same manner, the projections of groups cgh and ex on pc <dig> have coordinates close to  <dig>  on pc <dig>  all the mean individuals from the partial expression representation  are located around the origin, which is not the case for the genomic one ; meaning that pc <dig> is specific to the genomic point of view.
in the same manner, only projection of group cgh on pc <dig> has coordinates close to  <dig> .
regarding cgh data, pc <dig> provides a partition of the histological subtypes and particularly stresses differences between oligodendrogliomas  and astrocytomas .
the one-variable group who summarizing the tumor classification is projected as an illustrative group .
since its coordinate on pc <dig> is rather high, the structure induced by this group is linked to pc1: the types of tumors are well separated along this dimension.
its coordinate on pc <dig> is also relatively important, showing that the types of tumors are also separated on pc <dig>  following the examination of these graphical outputs, pc <dig> is linked to glioblastoma characteristics and pc <dig> corresponds to oligodendroglioma characteristics as it stresses the differences between these tumors and the other gliomas.
beyond the partition of the tumors, the challenge lies in interpreting the results to gain insights into biological mechanisms.
the classical way is to identify the genes most correlated with each principal component, see variables representation .
this scatter plot representing the genes is read as in pca.
briefly, the genes are projected on the factor map and represented as vectors.
the more a vector has a magnitude close to  <dig>  the best the projection is.
the vector points in the direction of the high values, e.g.
in our case, a gene with a corresponding vector pointing in the right side takes higest values in oligodendrogliomas compared to glioblastomas.
we thus retrieved the genes most correlated with pc <dig> and pc <dig>  once the identifiers recovered, they can be annotated manually by gathering functional information from a large panel of databases and annotation tools.
for example, the manual examination of the genes linked to pc <dig> underlines genomic status modifications of genes located on 1p and 19q positions .
allelic alterations of chromosomes  <dig>  and  <dig>  are frequently reported as important events in gliomas  <cit>  and especially in oligodendrogliomas  <cit> .
indeed, it is reported that these chromosomal aberrations patterns vary according to the categories of glial neoplasms and could be marks of malignant progression  <cit> .
this process is however laborious and highly time consuming.
moreover, the interpretation of such emphasized structures remains difficult when only associated gene ids are accessible or when lots of genes have to be taken into account.
for that reason, providing gene annotations in a corresponding plot is necessary to obtain a concise way of understanding these results.
the first  <dig> genes most strongly correlating with pc <dig> are shown with identifiers and corresponding chromosome locations.
pc <dig> stresses differences between oligodendrogliomas  and other gliomas and is linked to the modifications of the genomic status of genes located on 1p and 19q.
this highlights that oligodendrogliomas could be associated with a specific allelic alterations of chromosomes  <dig>  and  <dig> .
integrating biological knowledge: superimposition of go gene modules
as we pointed out, the interpretation of the structures emerging from mfa constitute a difficult and time-consuming step.
our approach aims at easing this task.
firstly, the biological knowledge is formalized.
here, gene ontology  biological process  terms are used to assemble gene modules.
secondly, the gene modules are superimposed on the same principal components and aid interpretation of the study.
this is allowed by the capacity of mfa to integrate supplementary groups of data.
the results has to be read as follow: the coordinate of a given group is all the more close to  <dig> than the variables of this group are highly correlated with the dimension issued from the mfa.
hence, two groups are all the more close than the structures they induce on the observations are close.
thus, the coordinate of one gene module provides a direct measure of the link between its constituting genes and the corresponding principal component .
single glioma data set
we used the same approach to analyze the transcriptome data from freije et al.. to achieve this, we applied mfa to the duplicated data set.
performing such task is strictly equivalent to applying a pca on the initial data set.
the results provided correspond to those obtained with a pca and it becomes possible to manage additional informative groups of variables.
to analyze the results, we follow a step-by-step interpretation of the principal components: based firstly on the typology of the tumors, secondly on the gene expression signatures and then, on the associated biological knowledge.
we focus on the first two principal components that explain  <dig> % of the total variability carried by the  <dig> genes.
the corresponding individuals factor map is provided in figure  <dig>  mean observations are added for each glioma subtype to help with the interpretation of the plot.
this map shows a relatively well-defined partition of tumors into who classification.
it also shows that the position of the samples belonging to a glioma subtype varies from one to another.
this variability could be assigned to the well known cellular heterogeneity of gliomas and particularly of glioblastomas.
it could also be the result of the who classification that is somehow controversial: this standard classification is said to suffer from a lack of reproducibility among pathologists  <cit> .
the projections on pc <dig> of the mean observations underline that the maximum of variability captured in the analysis separates glioblastomas  from lower grade gliomas .
pc <dig> differentiates oligo-astrocytomas  from the other subtypes .
as a result, pc <dig> is linked to glioblastoma characteristics stating transcriptional differences between grade iv and lower grade gliomas and pc <dig> is related to oligoastrocytoma characteristics, highlighting oa particular signature.
to assign a meaning, based on gene expression, to the glioblastoma characteristics, we retrieved the ten genes most strongly correlated with the first axis .
these genes were manually annotated by gathering some information from pubmed and were analyzed using the ingenuity pathway analysis .
among these ten genes, four are co-cited with 'glioma' on pubmed and five with 'cancer'.
and the ipa analyses gives links between anxa <dig>  clic <dig>  hexb, mapt and s100a <dig> in a network related to 'cellular movement, cell-to-cell signaling and interaction, nervous system development and function'.
these findings are in adequacy with the invasive nature of glioblastoma compare to lower grade glioma i.e.
with glioblastoma characteristics.
however, this interpretation step is partial as it was limited to only few genes; it thus will gain by integrating a global view of the associated knowledge.
the first  <dig> genes most strongly correlating with pc <dig> are shown with identifiers and corresponding coordinate.
among these ten genes, four are co-cited with 'glioma' on pubmed and five with 'cancer'.
and the ingenuity pathway analysis gives links between anxa <dig>  clic <dig>  hexb, mapt and s100a <dig> in a network related to 'cellular movement, cell-to-cell signaling and interaction, nervous system development and function'.
we superimpose the associated biological knowledge as go modules on the previously analyzed plots.
the corresponding map  provides a typology of the functional modules and highlights shared dimensions between go bp terms and tumor groups.
as seen before, the coordinates of the annotation groups onto each principal component provide a direct measure of the links between modules and the corresponding factors .
we focus on the gene modules linked to the glioblastomas and retrieved  <dig> direct go terms strongly associated with grading .
among them,  <dig> go terms were picked as they can be grouped into three main biological process categories .
the first main category is related to cell death and cell cycle regulation and the second one stresses that glioblastoma have a particular proliferative behavior.
the third one indicates a link with developmental functions, more precisely in brain.
these groups of annotations underline the well known characteristics of glioblastomas among other gliomas: a rapid cellular proliferation sustained by cell cycle dysfunctions and invasion of the parenchyma by isolated tumor cells.
moreover, our approach emphasizes the existence of a relation from neurogenesis-related genes to glioma grades of malignity.
this supports the evidence that glioblastomas contain and may arise from neural stem cells or from differentiated cell types that display multipotential stem cell-like properties.
the annotation are grouped by meaningful categories  and are ordered by go depth.
pc <dig> coordinates for each go annotation is provided in the third column.
these groups of annotations underline the well known characteristics of glioblastomas among other gliomas: a rapid progression with parenchyma invasion by isolated tumor cells sustained by cell cycle dysfunctions.
it also emphasizes the existence of a relation from neurogenesis-related genes to gliobastoma.
enriched terms  are marked with a star.
the factor delineating the oligo-astrocytic tumors from the other ones  is particularly associated with modules related to the cytoskeleton.
it is thus possible to highlight 'cytoskeleton-dependent intracellular transport' , 'cortical actin cytoskeleton organization and biogenesis'  and 'positive regulation of nucleocytoplasmic transport' .
these biological processes stress that the main dissimilarity existing between oa and other gliomas may emerge from a transcriptional modification of genes linked to actin cytoskeleton which is one of the possible determinants of human astrocytoma migration  <cit> .
seven genes are annotated with these go bp terms: dync1h <dig>  epb41l <dig>  kif3a, kif5b, myl <dig>  myo9b, trip <dig>  among them, some are reported to be involved in cancer cell migration.
specifically, cytoskeleton rearrangements have been shown to be induced by a down-regulation of trip <dig> in carcinoma cell lines  <cit> .
it was also suggested that myl <dig> could have an effect on the migration of breast cancer cells  <cit> .
thus, the gene epb41l <dig> codes a protein belonging to the protein  <dig>  family which is proposed to have roles in human cancer  <cit> .
and an increased expression of kif3a may also be associated with autocrine motility factor-induced signaling for cell motility and metastasis  <cit> .
to our knowledge, none of these genes have been so far shown to be involved in glioma invasiveness.
multi-way nutrimouse data set
in this section we describe another scenario with controlled experimental design where biological units  are cross-classified according to two factors: genotype  versus pparα deficient mice ) and diet  compositions).
the measurements come from two different sources of information: transcriptome variables and hepatic fa measurements.
with this example, we wish to illustrate the relevance of mfa-based interpretations in accordance with the conclusions drawn by specialists in  <cit> .
the superimposition of prior biological knowledge is presented in figure 8d.
annotations correlated to pc <dig> and pc <dig> are generally linked to energetic metabolism.
most of the go terms strongly associated with pc <dig>  are related to lipid metabolism and particularly 'fatty acid oxidation' .
it is known that hepatic fa catabolism is down-regulated with a saturated diet leading to an accumulation of fa in the liver.
this is in accordance with the results discussed by martin et al.
<cit> .
the go terms associated with pc <dig> are related to -ose metabolism.
they reveal an effect of the diet fa content on glucose metabolism.
the associated genes  also suggest a possible role of pparα in these mechanisms.
these gene expression changes were highlighted in the table  <dig> in  <cit>  but not further discussed.
it would however be of great interest to precise this putative role of fa diet composition in relation to metabolic syndromes and diabetes.
CONCLUSIONS
our approach based on mfa in the sense of escofier-pagès aims at providing a multivariate data analytic technique for applications in biological systems.
it is dedicated to combined 'omics' data structured into groups and its purpose is also particularly to help on their functional interpretations.
mfa is firstly used to simultaneously analyze the structure emerging from the separate analysis of each molecular levels and to supply principal components which summarize parts of the data variability.
the common structures are underlined and graphical outputs are provided such that biological meaning becomes retrievable.
partial representations allow the visualization of each 'omics' point of view.
the addition of sample annotations as categorical supplementary variables is used to attach a biological meaning to each component.
functional interpretation is obtained by superimposing biological knowledge on the experimentally interpreted plots.
such work is done by building gene modules from formalized annotations.
modules assembled as sets of genes are projected as supplementary information onto the plane spanned by the two principal components issued from mfa.
in this way, we provide a measurement of the correlation between each module and each component.
it thus becomes possible to attach functionally meaningful characteristics to each experimentally interpreted component.
with our method, investigation of microarray data is supported by a step-by-step sequence of graphical representations.
mfa plots provide a clear visualization of the data.
each plot corresponds to one interpretable entity: individual factor map, variables correlation circle and groups representation; all of them sharing closely related dimensions.
exploration and functional interpretation are thus based on the understanding of these dimensions.
moreover, in our approach, annotations are not transformed but are used to create go modules.
go modules are assembled with the expression values of all its constituting genes.
when projecting the corresponding annotation, this allows the consideration of the transcriptome structure of a go module instead of only appreciate go annotations via boolean vectors.
we have illustrated our approach on a complex setting which is the study of human brain cancers.
firstly, we focused on a study combining the genome and the transcriptome of gliomas and secondly, an other study related only to the transcriptome of these tumors.
the latter one allows us to show that our approach could be applied to a single group of data , which is the most frequently methodology used in the high-througthput area of biology.
the addition of annotations as supplementary gene modules give very good insights into the molecular bases of malignant primary brain tumors.
relevant mechanisms involved in cancer were identified, and more precisely some well defined in glioblastoma .
using the nutrimouse study, we have tried to show the general applicability of mfa to any investigations needing a comprehensive view of the data.
futhermore, one major advantage of this method is not to be bound to any specific experimental design nor to any type of annotation.
gene modules can therefore be created with any gene related knowledge: processes , pathways , structural or promoter informations .

 genome-wide analyses provide an unprecedented amount of data leading to new interpretation challenges. classical microarrays can monitor the expression of potentially all genes within a cell or a tissue sample. more recently, new applications have been developed. they include chromatin-immunoprecipitation-chip, analysis of alternative splicing, characterization of the methylome, polymorphism genotyping, copy-number measurements and genome resequencing. a great interest in the statistical analysis of these'omics' data has emerged and many methodologies have been developed. however, if the inferential statistics analyses are now guided by consensual methods, the descriptive analysis is often succinct if not neglected. two reasons can be advanced: the great volume of information makes difficult the interpretation of the results, and heterogeneous data and multiple sources of information are difficult to integrate in a global analysis. methods that overcome these difficulties are necessary as the understanding of a biological phenomenon would greatly benefit from considering simultaneously several types of'omics' data and particularly with biological knowledge. this could be done in a multidimensional exploratory approach. in a multidimensional exploratory approach, a microarray data set is usually analyzed by multivariate analysis among which principal components analysis is the most used. pca is well adapted to the framework of'omics' data as it can handle data sets with much more variables than samples. to analyze simultaneously several data sets, the proper way is to use mva's dedicated to the analysis of multi-way data tables; the method of reference being the generalized canonical analysis. in the field of microarray, gca is however limited by the problem of multi-colinearity. to bypass this limitation, only two alternatives have still been proposed: the generalized co-inertia analysis and the recently applied regularized canonical correlation analysis. the need for integrating external information in mva to ease the interpretation of microarray data have also been pointed out. as proposed by busold et al., fagan et al. superimposed gene ontology terms as supplementary elements onto cia projections. in this study, go terms are formalized as boolean vectors that are projected onto cia plots after matrix transformations. although cia approach provide good results in combining molecular data sets, the way go terms are added is not straightforward and appears incomplete. indeed, this method codes the links between genes and go terms and do not take into account the microarray values or molecular data of the genes related to each go term. other computational methods, such as gene set enrichment analysis, have shown the importance of focusing on groups of genes as opposed to individual genes for incorporating biological information and gene sets into microarray data analysis. following this philosophy, a proper integration of biological information in mva will gain in accuracy by grouping genes into knowledge-related modules, and thus by considering a'modular approach'. such an approach studies as a whole the behavior and structure of a biological process in addition to analyzing its components individually. in this article, we suggest to use multiple factor analysis in the sense of escofier-pagès to integrate bio-molecular data sets as well as informations on the genes structured in modules. mfa is dedicated to the simultaneous exploration of multi-way data sets where the same individuals are described by several groups of variables. mfa is commonly applied to sensory and ecology data and it has already been applied to the analysis of metabonomic data. mfa can be related to gca and cia since it could be considered as a particular generalized canonical analysis were the inertia criteria replaces the correlation criteria. these methods display a low-dimensional projection of the data highlighting the main sources of variability. results should therefore be interpreted with caution as sources of variability are not always due to specific biological factors of interest. it is also important to note that at the sample level, the structures provided either by mfa or cia are highly similar. the assets of mfa appear when integrating both numerical and categorical groups of variables, and when supplementary groups of data need to be added in the analysis. here, we present our approach by introducing the basis of mfa and we state how mfa is particularly well adapted to integrate formalized biological knowledge. we illustrate our method with a glioma study performed with both cgh array and expression microarray on the same tumor samples. results shows that both dna copy number alteration and transcriptome data sets induce a good separation of the gliomas according to the who classification. the superimposition of the gene modules built since go annotation identify regulatory mechanisms implicated in gliomagenesis. we also show that our approach can handle a single data set with associated go annotations and therefore be used as an exploratory tool in the case of classical single'omics' study. finally we present another illustration focused on a nutrition study in mice and integrating microarray and lipidomic data.  mfa is used to analyze several groups of'omics' variables defined on the same samples. the core of mfa is a pca applied to the whole set of variables in which each group of variables is weighted, rendering possible the analysis of different points of view by taking them equally into account. to illustrate the main features of our approach a schematic is provided in figure each time, mfa is applied to published-data selections. resulting graphical outputs for the first two principal components are used. we describe the results and discuss the following points: the combination of paired cgh array and microarray data of glial tumors; the assemblage of genes into modules based on gene ontology terms and their superimposition on the principal components issued of point, supporting interpretation of the study; the application of our approach in the case of a single'omics' study; an other illustration of our method with a different experimental setting using a nutrition study including microarrays and fatty acids gas chromatography data. the analyses have been performed with r and the package factominer. multi-way glioma data set joining'omics' distinct points of view mfa is applied to the paired cgh array and microarray glioma data of bredel et al.. the resulting sample plots are presented figure and figure the mean representation of the samples according to both cgh and gene expression data sets is presented figure mean samples are represented by points colored following who classification of the tumors. figure 3a shows the partial representation associated to each type of tumors. this representation is obtained from the consensus between the cgh and expression points of view. each type of tumors is represented by three points: the consensus between the two points of view and a point for each point of view. both scatter plots show a well-defined partition of the samples into who classification. this is particularly true along pc that underlines a partition of the samples into glioblastomas and lower grade gliomas. partial representation and groups representation show that this partition exists on pc at the genome and at the transcriptome levels and only at the genome level on pc indeed, the projections on pc of the partial points for each category of tumors are each time very close, meaning that cgh and ex define similar structures upon tumors on pc in a same manner, the projections of groups cgh and ex on pc have coordinates close to on pc all the mean individuals from the partial expression representation are located around the origin, which is not the case for the genomic one; meaning that pc is specific to the genomic point of view. in the same manner, only projection of group cgh on pc has coordinates close to. regarding cgh data, pc provides a partition of the histological subtypes and particularly stresses differences between oligodendrogliomas and astrocytomas. the one-variable group who summarizing the tumor classification is projected as an illustrative group. since its coordinate on pc is rather high, the structure induced by this group is linked to pc1: the types of tumors are well separated along this dimension. its coordinate on pc is also relatively important, showing that the types of tumors are also separated on pc following the examination of these graphical outputs, pc is linked to glioblastoma characteristics and pc corresponds to oligodendroglioma characteristics as it stresses the differences between these tumors and the other gliomas. beyond the partition of the tumors, the challenge lies in interpreting the results to gain insights into biological mechanisms. the classical way is to identify the genes most correlated with each principal component, see variables representation. this scatter plot representing the genes is read as in pca. briefly, the genes are projected on the factor map and represented as vectors. the more a vector has a magnitude close to the best the projection is. the vector points in the direction of the high values, e.g. in our case, a gene with a corresponding vector pointing in the right side takes higest values in oligodendrogliomas compared to glioblastomas. we thus retrieved the genes most correlated with pc and pc once the identifiers recovered, they can be annotated manually by gathering functional information from a large panel of databases and annotation tools. for example, the manual examination of the genes linked to pc underlines genomic status modifications of genes located on 1p and 19q positions. allelic alterations of chromosomes and are frequently reported as important events in gliomas and especially in oligodendrogliomas. indeed, it is reported that these chromosomal aberrations patterns vary according to the categories of glial neoplasms and could be marks of malignant progression. this process is however laborious and highly time consuming. moreover, the interpretation of such emphasized structures remains difficult when only associated gene ids are accessible or when lots of genes have to be taken into account. for that reason, providing gene annotations in a corresponding plot is necessary to obtain a concise way of understanding these results. the first genes most strongly correlating with pc are shown with identifiers and corresponding chromosome locations. pc stresses differences between oligodendrogliomas and other gliomas and is linked to the modifications of the genomic status of genes located on 1p and 19q. this highlights that oligodendrogliomas could be associated with a specific allelic alterations of chromosomes and. integrating biological knowledge: superimposition of go gene modules as we pointed out, the interpretation of the structures emerging from mfa constitute a difficult and time-consuming step. our approach aims at easing this task. firstly, the biological knowledge is formalized. here, gene ontology biological process terms are used to assemble gene modules. secondly, the gene modules are superimposed on the same principal components and aid interpretation of the study. this is allowed by the capacity of mfa to integrate supplementary groups of data. the results has to be read as follow: the coordinate of a given group is all the more close to than the variables of this group are highly correlated with the dimension issued from the mfa. hence, two groups are all the more close than the structures they induce on the observations are close. thus, the coordinate of one gene module provides a direct measure of the link between its constituting genes and the corresponding principal component. single glioma data set we used the same approach to analyze the transcriptome data from freije et al.. to achieve this, we applied mfa to the duplicated data set. performing such task is strictly equivalent to applying a pca on the initial data set. the results provided correspond to those obtained with a pca and it becomes possible to manage additional informative groups of variables. to analyze the results, we follow a step-by-step interpretation of the principal components: based firstly on the typology of the tumors, secondly on the gene expression signatures and then, on the associated biological knowledge. we focus on the first two principal components that explain % of the total variability carried by the genes. the corresponding individuals factor map is provided in figure mean observations are added for each glioma subtype to help with the interpretation of the plot. this map shows a relatively well-defined partition of tumors into who classification. it also shows that the position of the samples belonging to a glioma subtype varies from one to another. this variability could be assigned to the well known cellular heterogeneity of gliomas and particularly of glioblastomas. it could also be the result of the who classification that is somehow controversial: this standard classification is said to suffer from a lack of reproducibility among pathologists. the projections on pc of the mean observations underline that the maximum of variability captured in the analysis separates glioblastomas from lower grade gliomas. pc differentiates oligo-astrocytomas from the other subtypes. as a result, pc is linked to glioblastoma characteristics stating transcriptional differences between grade iv and lower grade gliomas and pc is related to oligoastrocytoma characteristics, highlighting oa particular signature. to assign a meaning, based on gene expression, to the glioblastoma characteristics, we retrieved the ten genes most strongly correlated with the first axis. these genes were manually annotated by gathering some information from pubmed and were analyzed using the ingenuity pathway analysis. among these ten genes, four are co-cited with'glioma' on pubmed and five with'cancer'. and the ipa analyses gives links between anxa clic hexb, mapt and s100a in a network related to'cellular movement, cell-to-cell signaling and interaction, nervous system development and function'. these findings are in adequacy with the invasive nature of glioblastoma compare to lower grade glioma i.e. with glioblastoma characteristics. however, this interpretation step is partial as it was limited to only few genes; it thus will gain by integrating a global view of the associated knowledge. the first genes most strongly correlating with pc are shown with identifiers and corresponding coordinate. among these ten genes, four are co-cited with'glioma' on pubmed and five with'cancer'. and the ingenuity pathway analysis gives links between anxa clic hexb, mapt and s100a in a network related to'cellular movement, cell-to-cell signaling and interaction, nervous system development and function'. we superimpose the associated biological knowledge as go modules on the previously analyzed plots. the corresponding map provides a typology of the functional modules and highlights shared dimensions between go bp terms and tumor groups. as seen before, the coordinates of the annotation groups onto each principal component provide a direct measure of the links between modules and the corresponding factors. we focus on the gene modules linked to the glioblastomas and retrieved direct go terms strongly associated with grading. among them, go terms were picked as they can be grouped into three main biological process categories. the first main category is related to cell death and cell cycle regulation and the second one stresses that glioblastoma have a particular proliferative behavior. the third one indicates a link with developmental functions, more precisely in brain. these groups of annotations underline the well known characteristics of glioblastomas among other gliomas: a rapid cellular proliferation sustained by cell cycle dysfunctions and invasion of the parenchyma by isolated tumor cells. moreover, our approach emphasizes the existence of a relation from neurogenesis-related genes to glioma grades of malignity. this supports the evidence that glioblastomas contain and may arise from neural stem cells or from differentiated cell types that display multipotential stem cell-like properties. the annotation are grouped by meaningful categories and are ordered by go depth. pc coordinates for each go annotation is provided in the third column. these groups of annotations underline the well known characteristics of glioblastomas among other gliomas: a rapid progression with parenchyma invasion by isolated tumor cells sustained by cell cycle dysfunctions. it also emphasizes the existence of a relation from neurogenesis-related genes to gliobastoma. enriched terms are marked with a star. the factor delineating the oligo-astrocytic tumors from the other ones is particularly associated with modules related to the cytoskeleton. it is thus possible to highlight'cytoskeleton-dependent intracellular transport','cortical actin cytoskeleton organization and biogenesis' and'positive regulation of nucleocytoplasmic transport'. these biological processes stress that the main dissimilarity existing between oa and other gliomas may emerge from a transcriptional modification of genes linked to actin cytoskeleton which is one of the possible determinants of human astrocytoma migration. seven genes are annotated with these go bp terms: dync1h epb41l kif3a, kif5b, myl myo9b, trip among them, some are reported to be involved in cancer cell migration. specifically, cytoskeleton rearrangements have been shown to be induced by a down-regulation of trip in carcinoma cell lines. it was also suggested that myl could have an effect on the migration of breast cancer cells. thus, the gene epb41l codes a protein belonging to the protein family which is proposed to have roles in human cancer. and an increased expression of kif3a may also be associated with autocrine motility factor-induced signaling for cell motility and metastasis. to our knowledge, none of these genes have been so far shown to be involved in glioma invasiveness. multi-way nutrimouse data set in this section we describe another scenario with controlled experimental design where biological units are cross-classified according to two factors: genotype versus pparα deficient mice ) and diet compositions). the measurements come from two different sources of information: transcriptome variables and hepatic fa measurements. with this example, we wish to illustrate the relevance of mfa-based interpretations in accordance with the conclusions drawn by specialists in. the superimposition of prior biological knowledge is presented in figure 8d. annotations correlated to pc and pc are generally linked to energetic metabolism. most of the go terms strongly associated with pc are related to lipid metabolism and particularly'fatty acid oxidation'. it is known that hepatic fa catabolism is down-regulated with a saturated diet leading to an accumulation of fa in the liver. this is in accordance with the results discussed by martin et al.. the go terms associated with pc are related to -ose metabolism. they reveal an effect of the diet fa content on glucose metabolism. the associated genes also suggest a possible role of pparα in these mechanisms. these gene expression changes were highlighted in the table in but not further discussed. it would however be of great interest to precise this putative role of fa diet composition in relation to metabolic syndromes and diabetes.  our approach based on mfa in the sense of escofier-pagès aims at providing a multivariate data analytic technique for applications in biological systems. it is dedicated to combined'omics' data structured into groups and its purpose is also particularly to help on their functional interpretations. mfa is firstly used to simultaneously analyze the structure emerging from the separate analysis of each molecular levels and to supply principal components which summarize parts of the data variability. the common structures are underlined and graphical outputs are provided such that biological meaning becomes retrievable. partial representations allow the visualization of each'omics' point of view. the addition of sample annotations as categorical supplementary variables is used to attach a biological meaning to each component. functional interpretation is obtained by superimposing biological knowledge on the experimentally interpreted plots. such work is done by building gene modules from formalized annotations. modules assembled as sets of genes are projected as supplementary information onto the plane spanned by the two principal components issued from mfa. in this way, we provide a measurement of the correlation between each module and each component. it thus becomes possible to attach functionally meaningful characteristics to each experimentally interpreted component. with our method, investigation of microarray data is supported by a step-by-step sequence of graphical representations. mfa plots provide a clear visualization of the data. each plot corresponds to one interpretable entity: individual factor map, variables correlation circle and groups representation; all of them sharing closely related dimensions. exploration and functional interpretation are thus based on the understanding of these dimensions. moreover, in our approach, annotations are not transformed but are used to create go modules. go modules are assembled with the expression values of all its constituting genes. when projecting the corresponding annotation, this allows the consideration of the transcriptome structure of a go module instead of only appreciate go annotations via boolean vectors. we have illustrated our approach on a complex setting which is the study of human brain cancers. firstly, we focused on a study combining the genome and the transcriptome of gliomas and secondly, an other study related only to the transcriptome of these tumors. the latter one allows us to show that our approach could be applied to a single group of data, which is the most frequently methodology used in the high-througthput area of biology. the addition of annotations as supplementary gene modules give very good insights into the molecular bases of malignant primary brain tumors. relevant mechanisms involved in cancer were identified, and more precisely some well defined in glioblastoma. using the nutrimouse study, we have tried to show the general applicability of mfa to any investigations needing a comprehensive view of the data. futhermore, one major advantage of this method is not to be bound to any specific experimental design nor to any type of annotation. gene modules can therefore be created with any gene related knowledge: processes, pathways, structural or promoter informations. 
functional interpretations are then supported by a step-by-step sequence of graphical representations. the common structures are underlined and graphical outputs are provided such that biological meaning becomes easily retrievable. it is thus of great importance to provide useful integrative approaches dedicated to ease the interpretation of microarray data. genomic analysis will greatly benefit from considering in a global way various sources of molecular data with the related biological knowledge. gene ontology terms are used to build gene modules that are superimposed on the experimentally interpreted plots. here, we introduce a data-mining approach, multiple factor analysis, to combine multiple data sets and to add formalized knowledge.
 genomic analysis will greatly benefit from considering in a global way various sources of molecular data with the related biological knowledge. it is thus of great importance to provide useful integrative approaches dedicated to ease the interpretation of microarray data.  here, we introduce a data-mining approach, multiple factor analysis, to combine multiple data sets and to add formalized knowledge. mfa is used to jointly analyse the structure emerging from genomic and transcriptomic data sets. the common structures are underlined and graphical outputs are provided such that biological meaning becomes easily retrievable. gene ontology terms are used to build gene modules that are superimposed on the experimentally interpreted plots. functional interpretations are then supported by a step-by-step sequence of graphical representations.  when applied to genomic and transcriptomic data and associated gene ontology annotations, our method prioritize the biological processes linked to the experimental settings. furthermore, it reduces the time and effort to analyze large amounts of'omics' data. 