microarrays have become the standard way of producing genome - scale measurements of gene expression levels ( 1 ) . since the first experimental studies ( 2 ) , microarrays have been used for answering a large variety of questions , such as characterizing gene expression patterns in tumour cell lines and healthy tissues ( 3,4 ) , identifying key mechanisms of stem cell differentiation ( 5 ) , and reconstructing global transcriptional networks in model organisms ( 6 ) .
databases like arrayexpress and geo ( 7,8 ) have become goldmines of transcriptomic information with thousands of publicly available microarray datasets .
interpretation and visualization is a crucial step of microarray analysis , as measurements are abundant and the level of experimental noise is high ( 9 ) .
guilt by association , as genes with similar expression profiles may have common regulatory circuits and functions ( 10 ) .
unsupervised clustering presented as a heatmap and dendrogram is a common approach for detecting coexpressed groups of genes ( 11,12 ) .
gene ontology ( go ) annotations are often used for the biological interpretation of detected clusters ( 13 ) .
clustering has several well - identified drawbacks that affect interpretation and reproducibility ( 14 ) .
popular clustering methods rely on input parameters , for example , hierarchical clustering ( 11 ) applies a fixed dendrogram cut - off value , and k - means ( 12 ) require predefining the number ( and hence , the structure ) of expected groups .
enrichment tools that relate gene groups to go categories need to be accessed separately , which complicates the analysis of hundreds of clusters .
analysing results of hierarchical clustering is complicated , since each node of the dendrogram represents a potential cluster .
moreover , given the hundreds of potentially relevant datasets in public databases , the manual work would be unreasonable .
data visualization is also technically challenging , since heatmaps with thousands of transcripts hardly fit on computer screens .
these problems are still commonly tackled with ad hoc means , e.g. removing genes that are  not interesting due to constant expression levels .
vishic ( visualization of hierarchical clustering ) is a web server for analysis of gene expression data , that provides agile all - in - one service for hierarchical clustering , functional enrichment analysis and visualization .
the tool provides a global overview of a given expression matrix and highlights its most significant functional aspects using go analysis .
vishic builds a compact clustering using functional enrichments rather than fixed user - defined thresholds , by pruning clusters where no enrichments are found .
go enrichment analysis is a common measure of gene cluster interpretation and a wide range of related tools has been created in recent years ( 1517 ) .
several microarray analysis pipelines are available , notably expression profiler ( 18 ) , genexpress ( 19 ) and amen ( 20 ) incorporate clustering methods with downstream analysis of annotations , sequence information and protein  protein interactions .
the ambiguity of clustering methods has created a need for algorithms that assess multiple clusters ( 21 ) .
more recently , ovaska et al . ( 26 ) combine clustering of genes based on semantic similarity of go with heatmap visualization .
however , the above comprise downloadable software that require additional data and expensive local computations .
our web server , on the other hand , provides the latest information from public databases and uses speed - optimized algorithms of happieclust ( 27 ) and g : profiler ( 16 ) to provide fast clustering and functional profiling even for larger datasets . in conclusion ,
vishic ( http://biit.cs.ut.ee/vishic , figure 1 ) is a web server for integrated cluster analysis , interpretation and visualization of microarray data that : performs a fast approximate hierarchical clustering of a user - provided gene expression dataset;computes functional enrichments of all discovered clusters using go , pathways and regulatory motifs;creates a compact heatmap dendrogram of the expression dataset , revealing most important functional enrichments and hiding poorly annotated expression profiles . 

( a ) gene expression matrix and annotated dendrogram with significant clusters ; ( b ) mitochondrion cluster ( id:31732 ) , ( c ) muscle cluster ( id:36899 ) , ( d ) annotation box of the mitochondrion cluster , appears when moving the mouse over the dendrogram , ( e ) detailed view of the mitochondrion cluster with heatmap , dendrogram and lineplot ( f ) table with functional enrichments , including clusters 31 732 and 36 899 .
the data presented in the figure comprises microarray measurements of the heart tissue of cardiovascular patients with left ventricular assist device .
vishic reveals clusters with expected relevant annotations , e.g. mitochondrion , muscle tissue and ribosome ( see results section ) .
performs a fast approximate hierarchical clustering of a user - provided gene expression dataset ; computes functional enrichments of all discovered clusters using go , pathways and regulatory motifs ; creates a compact heatmap dendrogram of the expression dataset , revealing most important functional enrichments and hiding poorly annotated expression profiles . a biological case study with vishic .
( a ) gene expression matrix and annotated dendrogram with significant clusters ; ( b ) mitochondrion cluster ( id:31732 ) , ( c ) muscle cluster ( id:36899 ) , ( d ) annotation box of the mitochondrion cluster , appears when moving the mouse over the dendrogram , ( e ) detailed view of the mitochondrion cluster with heatmap , dendrogram and lineplot ( f ) table with functional enrichments , including clusters 31 732 and 36 899 . the data presented in the figure comprises microarray measurements of the heart tissue of cardiovascular patients with left ventricular assist device .
vishic reveals clusters with expected relevant annotations , e.g. mitochondrion , muscle tissue and ribosome ( see results section ) .
the input of vishic is a gene expression matrix in plain tab - delimited or gene expression omnibus soft format .
vishic supports a wide variety of gene , protein and probeset identifiers for human as well as most eukaryotic model organisms .
the output of vishic is a compact gene expression matrix represented as a heatmap dendrogram , similar to the format used in many gene expression analysis applications .
agglomerative hierarchical clustering ( ahc ) organizes the data into a dendrogram , i.e. a tree where every node represents a gene cluster ( 28 ) .
nodes in the bottom of the hierarchy ( i.e. leaf nodes ) represent single - gene clusters , all nodes except leaves are made up of two smaller clusters , and the root node contains all genes in the dataset .
the ahc algorithm starts from single - gene clusters , iteratively merges most similar neighbours and results in a hierarchical structure of n  1 non - trivial clusters given a dataset of n genes .
computational speed is an important consideration of ahc , as the standard algorithm requires all pairwise distances between expression profiles .
the vishic server incorporates happieclust , our novel approximate version of the ahc algorithm ( 27 ) . instead of computing all pairwise distances ,
happieclust takes advantage of pivot - based similarity heuristics to calculate all distances between similarly expressed genes as well as a random subset of more distant pairs .
since only a subset of all pairwise distances is calculated , happieclust approximates the full ahc based on the pairwise distances that have been calculated during the process .
computational experiments with public microarray data show that happieclust produces a biologically comparable analysis an order of magnitude faster than standard ahc .
pearson correlation is the default measure in vishic for determining similarity between expression profiles . alternatively
, one may apply the negative correlation measure that detects inverse correlation patterns such as those shared by a repressor and its targets .
absolute correlation is a combination of the two , as it detects both direct and inverse similarity .
the second stage of vishic analysis involves functional enrichment analysis of all detected clusters to infer the optimal clustering .
however , it is difficult to provide a biologically plausible cut - off value , as gene expression profiles are not uniformly distributed and a fixed cut - off for different datasets does not guarantee stability . in this work , we take a different approach and infer clusters using statistical analysis of functional annotations [ refer to ( 29 ) for a relevant review ] .
we use our g : profiler software ( 16 ) to profile all discovered clusters for go terms ( 13 ) , pathways of reactome and kegg ( 30,31 ) , regulatory motifs of transfac ( 32 ) and microrna target sites of mirbase ( 33 ) .
vishic applies the cumulative hypergeometric test to detect the significance of a functional annotation  , given that there are k genes in a cluster of n genes with an annotation  , and there are k annotated genes among the total of n genes in the genome : 

 to evaluate the total enrichment in a given cluster , vishic computes a size - weighted annotation score q that summarizes enrichments of go as well as pathways and regulatory motifs : 

 alternatively , one may opt for a strategy that assigns the best log p - value to each cluster , giving more preference to clusters with specific annotations : 
  in order to reduce the amount of false positives resulting from numerous enrichment tests , vishic computes a special multiple testing correction that accounts for the hierarchical structure of go ( 34 ) .
standard corrections such as bonferroni and benjamini  hochberg false discovery rate are also applicable .
the final stage of vishic analysis creates a compact and biologically motivated clustering of the expression dataset to reveal its functional essence .
hierarchical clustering places gene groups in a parent  child structure , where clusters up in the hierarchy naturally contain smaller clusters as subsets .
similarly , the go comprises a structured vocabulary where smaller groups of specific annotations are contained in large general groups .
hence , one expects to see specific enrichments in child clusters and corresponding general annotations in parent clusters .
as the clustering dendrogram contains a spectrum of hierarchically contained clusters from single genes to the whole genome , choosing an optimal cluster involves maximizing certain criteria within a branch .
we have devised the following two - stage greedy algorithm that determines the cluster structure based on functional annotations . 

first , we look for dense clusters , i.e. clusters with a high annotation score q , or alternatively , the term with the strongest p - value m. we scan all groups of genes that have functional enrichments , greedily starting from the one that provides the strongest annotation score . a cluster is not considered if any of its child or parent clusters is already a dense cluster .
dense clusters are shown in the final output.second , we detect sparse clusters , i.e. groups of genes that have poor or no functional enrichments .
we start the analysis from the root of the dendrogram and pass it recursively , compressing all clusters except the ones that contain dense clusters as child nodes .
sparse clusters are cut - off from the dendrogram and corresponding expression profiles are hidden in the heatmap .
first , we look for dense clusters , i.e. clusters with a high annotation score q , or alternatively , the term with the strongest p - value m. we scan all groups of genes that have functional enrichments , greedily starting from the one that provides the strongest annotation score . a cluster is not considered if any of its child or parent clusters is already a dense cluster .
second , we detect sparse clusters , i.e. groups of genes that have poor or no functional enrichments .
we start the analysis from the root of the dendrogram and pass it recursively , compressing all clusters except the ones that contain dense clusters as child nodes .
sparse clusters are cut - off from the dendrogram and corresponding expression profiles are hidden in the heatmap .
our annotation - driven clustering algorithm is fully automated and does not depend on user - defined cut - offs .
vishic excludes small ( < 5 genes ) and large ( > 1000 genes ) clusters from enrichment analysis for optimal running time .
the user may choose a different range of cluster sizes , or disable all compression to view the full expression matrix with all related enrichments .
all functional terms that remain significant after multiple testing correction are used for computing the optimal clustering .
however , one may apply a more stringent p - value threshold to reduce the number of contributing enrichments and compress the matrix to a greater extent .
the resulting expression matrix is presented as a heatmap of gene activation and repression patterns , complete with a dendrogram that highlights functional groups of coexpressed genes .
colour - coded rectangles in the dendrogram denote dense clusters and related functional categories ( go , kegg , reactome , regulatory motifs , microrna target sites ) .
cluster - specific functional annotations are additionally presented in a table and also appear when hovering over the dendrogram .
the main window displays the compact heatmap with all highlighted clusters , while one may also  zoom in to view any cluster separately .
in compact view , vertical branch stumps of the dendrogram mark places where sparse clusters are compressed .
the user may search for genes of interest , or conduct further analysis via hyperlinks to external resources , e.g. browse - related functional categories via the go web site or g : profiler .
we present a case study to demonstrate the use of vishic in biological analyses ( figure 1 ) .
the example comprises a microarray dataset of myocardial remodelling , including 38 samples from 3 clinical groups of patients with ischemic , non - ischemic and myocardial infarction , taken before and after left ventricular assist device implantation [ available in geo as part of the series gse974 ( 35 ) ] .
we clustered the dataset , detected optimal clusters with best enrichments and visualized the resulting expression matrix ( figure 1a ) .
we used a custom stringent p - value threshold ( p < 10 ) and  best annotation cluster selection strategy with pearson correlation measure to compress the matrix into a reasonable publication - sized format .
the best scoring clusters are related to mitochondrion ( figure 1b ) , muscle tissue ( figure 1c ) and extracellular matrix , all of which are expected to be present in heart tissue expression profiles .
a recent publication underlines the importance of mitochondria in the heart and relates its mutations to heart disorders ( 36 ) .
the cluster with muscle tissue enrichments ( id:36899 , see figure 1e for expression profiles and figure 1f for functional annotations ) contains 420 probesets for 251 genes and has several strong enrichments ( contractile fibre : p < 10 , muscle system process : p < 10 , cytoskeletal protein binding : p < 10 ) . in addition , our analysis reveals an enrichment for the binding site of serum response factor ( srf ) ( transfac m01007 , p < 10 ) .
srf is a known heart transcription factor which increased expression in congestive heart failure ( 37 ) .
the case study shows that vishic successfully extracts relevant functional aspects of a dataset , and compresses it into an easily perceivable compact format that fits well on screen and paper .
agglomerative hierarchical clustering ( ahc ) organizes the data into a dendrogram , i.e. a tree where every node represents a gene cluster ( 28 ) .
nodes in the bottom of the hierarchy ( i.e. leaf nodes ) represent single - gene clusters , all nodes except leaves are made up of two smaller clusters , and the root node contains all genes in the dataset .
the ahc algorithm starts from single - gene clusters , iteratively merges most similar neighbours and results in a hierarchical structure of n  1 non - trivial clusters given a dataset of n genes .
computational speed is an important consideration of ahc , as the standard algorithm requires all pairwise distances between expression profiles .
the vishic server incorporates happieclust , our novel approximate version of the ahc algorithm ( 27 ) . instead of computing all pairwise distances , happieclust takes advantage of pivot - based similarity heuristics to calculate all distances between similarly expressed genes as well as a random subset of more distant pairs . since only a subset of all pairwise distances
is calculated , happieclust approximates the full ahc based on the pairwise distances that have been calculated during the process .
computational experiments with public microarray data show that happieclust produces a biologically comparable analysis an order of magnitude faster than standard ahc .
alternatively , one may apply the negative correlation measure that detects inverse correlation patterns such as those shared by a repressor and its targets .
absolute correlation is a combination of the two , as it detects both direct and inverse similarity .
the second stage of vishic analysis involves functional enrichment analysis of all detected clusters to infer the optimal clustering .
however , it is difficult to provide a biologically plausible cut - off value , as gene expression profiles are not uniformly distributed and a fixed cut - off for different datasets does not guarantee stability . in this work ,
we take a different approach and infer clusters using statistical analysis of functional annotations [ refer to ( 29 ) for a relevant review ] .
we use our g : profiler software ( 16 ) to profile all discovered clusters for go terms ( 13 ) , pathways of reactome and kegg ( 30,31 ) , regulatory motifs of transfac ( 32 ) and microrna target sites of mirbase ( 33 ) .
vishic applies the cumulative hypergeometric test to detect the significance of a functional annotation  , given that there are k genes in a cluster of n genes with an annotation  , and there are k annotated genes among the total of n genes in the genome : 

 to evaluate the total enrichment in a given cluster , vishic computes a size - weighted annotation score q that summarizes enrichments of go as well as pathways and regulatory motifs : 

 alternatively , one may opt for a strategy that assigns the best log p - value to each cluster , giving more preference to clusters with specific annotations : 
  in order to reduce the amount of false positives resulting from numerous enrichment tests , vishic computes a special multiple testing correction that accounts for the hierarchical structure of go ( 34 ) .
standard corrections such as bonferroni and benjamini  hochberg false discovery rate are also applicable .
the final stage of vishic analysis creates a compact and biologically motivated clustering of the expression dataset to reveal its functional essence .
hierarchical clustering places gene groups in a parent  child structure , where clusters up in the hierarchy naturally contain smaller clusters as subsets .
similarly , the go comprises a structured vocabulary where smaller groups of specific annotations are contained in large general groups .
hence , one expects to see specific enrichments in child clusters and corresponding general annotations in parent clusters .
as the clustering dendrogram contains a spectrum of hierarchically contained clusters from single genes to the whole genome , choosing an optimal cluster involves maximizing certain criteria within a branch .
we have devised the following two - stage greedy algorithm that determines the cluster structure based on functional annotations . 

first , we look for dense clusters , i.e. clusters with a high annotation score q , or alternatively , the term with the strongest p - value m. we scan all groups of genes that have functional enrichments , greedily starting from the one that provides the strongest annotation score . a cluster is not considered if any of its child or parent clusters is already a dense cluster .
dense clusters are shown in the final output.second , we detect sparse clusters , i.e. groups of genes that have poor or no functional enrichments .
we start the analysis from the root of the dendrogram and pass it recursively , compressing all clusters except the ones that contain dense clusters as child nodes .
sparse clusters are cut - off from the dendrogram and corresponding expression profiles are hidden in the heatmap .
first , we look for dense clusters , i.e. clusters with a high annotation score q , or alternatively , the term with the strongest p - value m. we scan all groups of genes that have functional enrichments , greedily starting from the one that provides the strongest annotation score . a cluster is not considered if any of its child or parent clusters is already a dense cluster .
second , we detect sparse clusters , i.e. groups of genes that have poor or no functional enrichments .
we start the analysis from the root of the dendrogram and pass it recursively , compressing all clusters except the ones that contain dense clusters as child nodes .
sparse clusters are cut - off from the dendrogram and corresponding expression profiles are hidden in the heatmap .
our annotation - driven clustering algorithm is fully automated and does not depend on user - defined cut - offs .
vishic excludes small ( < 5 genes ) and large ( > 1000 genes ) clusters from enrichment analysis for optimal running time .
the user may choose a different range of cluster sizes , or disable all compression to view the full expression matrix with all related enrichments .
all functional terms that remain significant after multiple testing correction are used for computing the optimal clustering .
however , one may apply a more stringent p - value threshold to reduce the number of contributing enrichments and compress the matrix to a greater extent .
the resulting expression matrix is presented as a heatmap of gene activation and repression patterns , complete with a dendrogram that highlights functional groups of coexpressed genes .
colour - coded rectangles in the dendrogram denote dense clusters and related functional categories ( go , kegg , reactome , regulatory motifs , microrna target sites ) .
cluster - specific functional annotations are additionally presented in a table and also appear when hovering over the dendrogram .
the main window displays the compact heatmap with all highlighted clusters , while one may also  zoom in to view any cluster separately .
in compact view , vertical branch stumps of the dendrogram mark places where sparse clusters are compressed . the user may search for genes of interest , or conduct further analysis via hyperlinks to external resources , e.g. browse - related functional categories via the go web site or g : profiler .
we present a case study to demonstrate the use of vishic in biological analyses ( figure 1 ) .
the example comprises a microarray dataset of myocardial remodelling , including 38 samples from 3 clinical groups of patients with ischemic , non - ischemic and myocardial infarction , taken before and after left ventricular assist device implantation [ available in geo as part of the series gse974 ( 35 ) ] .
we clustered the dataset , detected optimal clusters with best enrichments and visualized the resulting expression matrix ( figure 1a ) .
we used a custom stringent p - value threshold ( p < 10 ) and  best annotation cluster selection strategy with pearson correlation measure to compress the matrix into a reasonable publication - sized format .
the best scoring clusters are related to mitochondrion ( figure 1b ) , muscle tissue ( figure 1c ) and extracellular matrix , all of which are expected to be present in heart tissue expression profiles .
a recent publication underlines the importance of mitochondria in the heart and relates its mutations to heart disorders ( 36 ) .
the cluster with muscle tissue enrichments ( id:36899 , see figure 1e for expression profiles and figure 1f for functional annotations ) contains 420 probesets for 251 genes and has several strong enrichments ( contractile fibre : p < 10 , muscle system process : p < 10 , cytoskeletal protein binding : p < 10 ) . in addition , our analysis reveals an enrichment for the binding site of serum response factor ( srf ) ( transfac m01007 , p < 10 ) .
srf is a known heart transcription factor which increased expression in congestive heart failure ( 37 ) .
the case study shows that vishic successfully extracts relevant functional aspects of a dataset , and compresses it into an easily perceivable compact format that fits well on screen and paper .
vishic ( http://biit.cs.ut.ee/vishic/ ) is a public web server for clustering and interpreting gene expression data .
the tool is designed to extract the most significant biological features of a microarray dataset in a single run .
the main output is a compact global view of the expression matrix with only the most significant clusters shown and less pronounced patterns hidden away , as its interactive format leaves open ends for more detailed analyses .
vishic provides stability to otherwise ambiguous clustering and performs the labour - intensive task of evaluating hundreds of redundant clusters in a rapid automated manner . the approximate hierarchical clustering and rapid functional analysis guarantee meaningful results even if the datasets are large .
functional assessment of microarray datasets is an immediate application of vishic analysis , as annotations of highlighted clusters should relate to proposed hypotheses .
our approach is likely to be useful for large expression data warehouses , so that first broad overviews could be offered to users who are routinely browsing hundreds of datasets .
one may use vishic to compare different datasets in the context of experimental conditions , global expression patterns and functional aspects . integrating expression clusters with other types of experimental data like protein 
dna and protein  protein interactions may provide researchers with additional clues about gene regulation .
eu fp6 grants ( enfin lshg - ct-2005 - 518254 and cobred lshb - ct-2007 - 037730 ) . funding for open access charge : erdf through the estonian centre of excellence in computer science project .
 measuring gene expression levels with microarrays is one of the key technologies of modern genomics . 
 clustering of microarray data is an important application , as genes with similar expression profiles may be regulated by common pathways and involved in related functions . 
 gene ontology ( go ) analysis and visualization allows researchers to study the biological context of discovered clusters and characterize genes with previously unknown functions . 
 we present vishic ( visualization of hierarchical clustering ) , a web server for clustering and compact visualization of gene expression data combined with automated function enrichment analysis . 
 the main output of the analysis is a dendrogram and visual heatmap of the expression matrix that highlights biologically relevant clusters based on enriched go terms , pathways and regulatory motifs 
 . clusters with most significant enrichments are contracted in the final visualization , while less relevant parts are hidden altogether . 
 such a dense representation of microarray data gives a quick global overview of thousands of transcripts in many conditions and provides a good starting point for further analysis . 
 vishic is freely available at http://biit.cs.ut.ee/vishic . 
INTRODUCTION
THE VisHiC SERVER
Novel approximate algorithm allows rapid hierarchical clustering of gene expression data
Functional enrichment analysis reveals optimal gene clusters of biological relevance
Enrichment-driven pruning of clustering dendrogram creates a compact view of expression data
Results: expression profiles of heart tissue of cardiovascular patients contain clusters related to muscle, mitochondria and extracellular matrix
DISCUSSION AND CONCLUSION
FUNDING