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\title{Bioconductor mAPKL Package}
\author{Argiris Sakellariou$^{1,2}$\\[1cm]
\small{$^1$ Biomedical Informatics Unit, Biomedical Research Foundation of the 
Academy of Athens, Athens, Greece}\\[0cm]
\small{$^2$ Department of Informatics and Telecommunications, National and 
Kapodistrian Univ. of Athens, Athens, Greece}\\[0cm]
\texttt{\small{argisake@gmail.com}}
}

\maketitle
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\section{Introduction}
\noindent The mAPKL bioconductor R package implements a hybrid gene selection 
method, which is based on the hypothesis that among the statistically 
significant genes in a ranked list, there should be clusters of genes that share
similar biological functions related to the investigated disease.Thus, instead 
of keeping a number of $N$ top ranked genes, it would be more appropriate to 
define and keep a number of gene cluster exemplars. 

\noindent The proposed methodology combines filtering and cluster analysis to 
select a small  yet highly discriminatory set of non-redundant genes. Regarding 
the filtering step, a multiple hypothesis testing approach from \emph{multtest} 
r-package (maxT) is employed to rank the genes of the training set according to 
their differential expression.Then the top N genes (e.g. N = 200) are reserved 
for cluster analysis. First the index of Krzanowski and Lai as included in the 
\emph{ClusterSim} r-package is applied on the disease samples of the training 
set to determine the number of clusters. The Krzanowski and Lai index is defined 
by $DIFF(k)=(k-1)^\frac{2}{p}W_{k-1}-k^\frac{2}{p}W_{k}$ when choosing the 
number of clusters $(k)$ to maximize the 
quantity $KL(k)=\Big|\frac{DIFF(k)}{DIFF_(k+1)}\Big|$.
The $W_k$ denotes the within-cluster sum of squared errors. 

\noindent Finally, cluster analysis is performed with the aid of Affinity 
Propagation (AP) clustering algorithm, which detects $n (n=k$ the Krzanowski 
and Lai index) clusters among the top $N$ genes, the so called exemplars.Those 
$n$ exemplars are expected to form a classifier that shall discriminate between 
normal and disease samples (Sakellariou et al. 2012, \emph{BMC Bioinformatics} 
\textbf{13}:270).
\noindent This package implements the pre-mentioned methodology through a core 
function, the \emph{mAPKL}. In the upcoming sections follows a guidance of the 
included functions and its functionality through differential expression 
analysis scenarios on a breast cancer dataset (GSE5764) which is part of the 
\emph{mAPKLData} package.

\section{Identification of deferentially expressed genes}
\subsection{Breast cancer data}
\noindent Throught this tutorial we utilized a publicly available breast cancer 
dataset comprised of 30 samples, where 20 of them represent normal cases and the 
remaining 10 samples  stand for tumor cases. We first load the package and then 
the breast cancer data. Then with the aid of the \emph{sampling} function we  
create a separate training and validation sets where 60\% of the samples will 
be used for training and the rest 40\% of the samples will 
be used for evaluation purposes.

<<results='hide',message=FALSE>>=
library(mAPKL)
library(mAPKLData)
data(mAPKLData)
varLabels(mAPKLData)
breast <- sampling(Data=mAPKLData, valPercent=40, classLabels="type", seed=135)
@

\noindent The \emph{sampling} function returns an S3 class (breast) with two 
eSet class objects that nest the relevant training and validation sampes. Those 
two objects are used throughout the rest of the analysis.

<<tidy=TRUE>>=
breast
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\subsection{Data normalization and transformation}
\noindent We perform normalization to the expression values through the 
\emph{preprocess} function.

<<tidy=TRUE,results='hide',message=FALSE>>=
normTrainData <- preprocess(breast$trainData)
normTestData <- preprocess(breast$testData)
@

\noindent The \emph{preprocess} function produces a list of several available 
normalization and transformation options. Besides density plots per method are 
produced and saved to current working directory to assist the user to decide 
upon which method to select before proceeding to mAPKL analysis.

<<tidy=TRUE>>=
attributes(normTrainData)
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\noindent The following graph presents the density plots of 8 possible 
normalization process with or without log2 transformation. The \emph{preprocess} 
function applies all of them and it is up to the user, which one will engage for 
the rest of the analysis. In brief, the available approaches are mean-centering, 
z-score, quantile, and cyclic loess. 
During this case study we will proceed with the expression values folowing log2 
transformation and cyclic loess normalization.

\begin{figure}[]
\centering
\includegraphics[width=15cm,height=15cm,keepaspectratio]{../man/figures/density_train}
\caption{Density plots of normalized intensity values}
\end{figure}

\subsection{mAPKL gene selection}
\noindent In this example we employ the expresion values of log2 transformation 
and cyclic loess normalization to proceed with the \emph{mAPKL} analysis.

<<tidy=TRUE,tidy.opts=list(width.cutoff=60)>>=
exprs(breast$trainData)<-normTrainData$clL2.normdata
exprs(breast$testData)<-normTestData$clL2.normdata
out.clL2 <- mAPKL(trObj=breast$trainData, classLabels="type", 
valObj=breast$testData,dataType=7)
@

\subsection{Building and evaluating classification models}
\noindent  After having get the exemplars from \emph{mAPKL} analysis we build an 
SVM classifier to test their discriminatory performance. Regarding the SVM 
setup, we utilize a linear kernel for which the cost attribute is infered by the 
tune.svm function. however, the user may freely use another kernel and a 
different Cross Validation approach than 5-folds.

<<tidy=TRUE,tidy.opts=list(width.cutoff=60)>>=
clasPred <- classification(out.clL2@exemplTrain,"type",out.clL2@exemplTest)
@

\noindent  The output of the \emph{classification} inform us about the SVM set 
up, the number of Support Vectors and finally show the the predicted labels 
along with the initial. In this example there is a validation set different from 
the training set and therefore we may use the respective labels to obtain the 
performance characteristcs. The relevant function \emph{metrics} called inside 
the \emph{classification} function, calculates five key meassures: the Area 
Under the ROC curve AUC, the classification accuracy, the Matthews correlation 
coefficient MCC classification meassure, the degree of true negative's 
identification Specificity, and finally the degree of true positive's 
identification Sensitivity.

\section{Advanced usage of the package}
\subsection{Annotation analysis}
\noindent  For each contemporary chip technology, there is a relevant annotation 
file, in which the the user may drag several \emph{genome oriented} information. 
Regarding the breast cancer microarray data, the gene expression values were 
stored on Affumetrix gene chips. Using the \emph{annotate} function, the user 
may obtain several info related to probe id, gene symbol, Entrez id, ensembl id, 
and chromosomal location.

<<tidy=TRUE,tidy.opts=list(width.cutoff=60),message=FALSE>>=
gene.info <- annotate(out.clL2@exemplars,"hgu133plus2.db")
gene.info@results
@

\noindent  We may exploit the output of the \emph{annotate} function to extent 
our analysis. For instance, we may perform \emph{pathway analysis} on the 
exemplars. For this purpose we will utilize the \emph{probes2pathways} function that utilizes the \emph{reactome.db} package.This function employs the probe ids to identify the relevant pathways.

<<tidy=TRUE,tidy.opts=list(width.cutoff=60),message=FALSE>>=
probes2pathways(gene.info)
@

\subsection{Network characteristics}
\noindent  Regarding the network charcteristics, we compute through the 
\emph{netwAttr} function three different types of centralities 
(degree, closeness, betweenness) and a meassure for clustering coefficient 
called transitivity. The degree centrality of a node refer to the number of 
connections or edges of that node to other nodes.The closeness centrality 
describes the reciprocal accumulated shortest length distance from a node to all 
other connected nodes.The betweeness centrality depicts the number of times a 
node intervenes along the shortest path of two other nodes. Transitivity 
meassures the degree of nodes to create clusters within a network.For all four 
network meassures we provide both global and local values. Furthermore, we 
compose an edge list (Node1-Node2-weight) based on the \emph{N} top ranked genes.
\noindent  We may exploit that meassures to depict the exemplars' network 
characteristics
<<tidy=TRUE,tidy.opts=list(width.cutoff=60),message=FALSE>>=
net.attr <- netwAttr(out.clL2)
wDegreeL <- net.attr@degree$WdegreeL[out.clL2@exemplars]
wClosenessL <- net.attr@closeness$WclosenessL[out.clL2@exemplars]
wBetweenessL <- net.attr@betweenness$WbetweennessL[out.clL2@exemplars]
wTransitivityL <- net.attr@transitivity$WtransitivityL[out.clL2@exemplars]
@
<<tidy=TRUE,tidy.opts=list(width.cutoff=60)>>=
Global.val <- c(net.attr@degree$WdegreeG, net.attr@closeness$WclosenessG, 
net.attr@betweenness$WbetweennessG, net.attr@transitivity$WtransitivityG)
@
<<tidy=TRUE>>=
Global.val <- round(Global.val,2)
exempl.netattr <- rbind(wDegreeL,wClosenessL,wBetweenessL,wTransitivityL)
@
<<tidy=TRUE>>=
netAttr <- cbind(Global.val,exempl.netattr)
netAttr <- t(netAttr)
netAttr
@

\noindent and identify potential hubs.The calculations of this example are based on the "clr" network reconstruction method. However, there are for the time being two more options, including the "aracne.a" and "aracne.m".
<<tidy=TRUE,tidy.opts=list(width.cutoff=60),message=FALSE>>=
# For local degree > global + standard deviation
sdev<-sd(net.attr@degree$WdegreeL)
msd <- net.attr@degree$WdegreeG + sdev
hubs <- wDegreeL[which(wDegreeL > msd)]
hubs
@

\noindent Finally, we may plot the network for those nodes that their local 
weighted degree is greater than Global weithed degree plus 2 times the standard 
deviation. We set  this rule for both significance and illustartion purposes 
(that edge list has dimension 604 x 3).
\vfill
\begin{figure}[]
\centering
\includegraphics[width=15cm,height=15cm,keepaspectratio]{../man/figures/network}
\caption{Degree centrality network}
\end{figure}

<<tidy=TRUE,tidy.opts=list(width.cutoff=60),message=FALSE>>=
sdev<-sd(net.attr@degree$WdegreeL)
ms2d <- net.attr@degree$WdegreeG + 2*sdev
net <- net.attr@degree$WdegreeL[which(net.attr@degree$WdegreeL > ms2d)]
idx <- which(net.attr@edgelist[,1] %in% names(net))
new.edgeList <- net.attr@edgelist[idx,]
dim(new.edgeList)
require(igraph)
g=graph.data.frame(new.edgeList,directed=FALSE)
#tkplot(g,layout=layout.fruchterman.reingold)
@
\vfill
\section{Reporting}
\noindent The overall analysis is summarized in an \textbf{html} report produced 
by the \emph{report} function. It covers the dataset repsresentation depicting 
the samples' names and their respective class labels, the exemplars section 
where statistical results and network characteristcs are included. The 
classification performance section illustrates the performance metrics achieved 
in either cross-validation or hold-out validation.Finally, several annotation 
info are presented if an annotation analysis has occured.

\section{Session info}
<<tidy=TRUE,tidy.opts=list(width.cutoff=60)>>=
sessionInfo()
@

\section{Reference}
\begin{list}{}{\itemindent=-1.0cm}

\item Sakellariou, A., D. Sanoudou, and G. Spyrou. "Combining Multiple 
Hypothesis Testing and Affinity Propagation Clustering Leads to Accurate, 
Robust and Sample Size Independent Classification on Gene Expression Data.
" BMC Bioinformatics 13 (2012): 270.
\item http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE5764

\end{list}

\begin{figure}
\centering
\includegraphics[width=16cm,height=25cm,keepaspectratio]{../man/figures/report}
\caption{mAPKL analysis report}
\end{figure}

\end{document}
