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1. gt sReorder lt sCompReorder sMap sMap gt visCompReorder sMap sMap sReorder sReorder It is equivalent to sample projection Reordered components are rich in the information both of genes and samples can be visualised but in a single display 5 Comparing Neighborhood Kernels Among various parameters associated with the training by sPipeline the neighborhood kernel is the most important one because it dictates the final topology of the trained map For visualising neighborhood kernels the function visKernels helps to understand their forms see Figure 8 Each kernel is a non increasing functions of i the distance between the hexagon rectangle and the winner and ii the radius 13 Figure 7 Reordered components of trained map Each component illus trates the sample specific map and is placed within a two dimensional rect angular lattice framed in black Within each component genes with the same or similar expression patterns are mapped to the same or nearby map nodes When zooming out to look at between components samples relationships sam ples with the similar expression profiles are placed closer to each other gt pdf supraHex_vignettes kernels pdf width 12 height 6 gt visKernels newpage F gt dev off From the mathematical definitions and curve forms above it is clear that the gamma and gaussian kernels exert more global influence the ep ker nel puts more emphasis on loca2. As aresult of training similar input data are mapped onto neighboring regions of the supra hexagonal map More formally the map ensembles the structure the shape and density of the input data in a topology preserving fashion Each 160 161 Figure 1 A supra hexagonal map It consists of nHex 169 smaller hexagons For easy reference these hexagons are indexed according to firstly how many steps a hexagon is away from the grid centroid 1 for the centroid itself secondly for those hexagons of the same step an anti clock order start ing from the rightmost This map can also be easily described by the grid radius i e the maximum steps away from the centroid r 8 in this case or by the xy dimensions of the map grid i e the maximum number of hexagons horizontally vertically rdim ydim 15 in this case map node is associated with two coordinates one in two dimensional output space just as you have seen the other in high dimensional input space as you can imagine The coordinate in input space is represented as a prototype weight vector with the same dimension as input data vector Prototype vectors in all map nodes collectively form the codebook matrix In essence the supra hexagonal map converts the input data into the codebook matrix In terms of gene activity matrix as input supraHex produces a map wherein i genes with the same or similar activity patterns are spatially located clustered to the same
3. 1 and 2 are illustrated only Radius 5 2 4 wonepnenggsssesansan cree eeose o toe o e te 4 o e o y e e a o s k 4 T e o o 5 o o 2 o b a e 4 S5 a a o o o o5 e O9 4 2 Co Ooy o 00 20000 4 Adddbbbhesesssddssssssssseeeess T T T T T T 0 1 2 3 4 5 Distance dwi between the hexagon i and the winner w are five kernels that are currently Figure 9 Components of trained map with the gaussian kernel e with cutgaussian kernel see Figure 11 gt sMap_cu lt sPipeline data data neighKernel cutgaussian init uniform gt visHexMulComp sMap_cu e with ep kernel see Figure 12 gt sMap_ep lt sPipeline data data neighKernel ep init uniform gt visHexMulComp sMap_ep 15 Figure 10 Components of trained map with the bubble kernel i Figure 11 Components of trained map with the cutgaussian kernel e with gamma kernel see Figure 13 gt sMap_gm lt sPipeline data data neighKernel gamma init uniform gt visHexMulComp sMap_gm 16 Figure 12 Components of trained map with the ep kernel F i Figure 13 Components of trained map with the gamma kernel 6 Applications to Real Cases The most common real cases are applications in studies involving gene expres sion profilings of i clinical patients ii time course processes In this section we aim to showcase the applic
4. 2 2 2 66 17 3 3 59 10 4 4 54 5 5 5 73 14 11 Figure 5 Bar plot of codebook patterns When the pattern involves both positive and negative values the zero horizental line is in the middle of the hexagon otherwise at the top of the hexagon for all negative values and at the bottom for all positive values You will see the first column for your input data ID an integer otherwise the row names of input data matrix the second column for the corresponding index of best matching hexagons i e gene clusters and the third column for the cluster bases i e gene meta clusters 4 4 Get reordered using sCompReorder and visCompReorder Reordering components for trained map can be realised by using a new map grid with sheet shape consisting of a rectangular lattice to train component plane vectors either column wise vectors of codebook data matrix or the covariance matrix thereof As a result similar component planes are placed closer to each other The functions sCompReorder and visCompReorder are respectively to implement this reordering algorithm and to visualise the reordered compments see Figure 7 5Tn order to display colors properly it is important to reset the argument zlim by respect ing the range of input data matrix more precisely codebook matrix 12 Figure 6 Clusters of the trained map Each cluster is filled with the same continuous color The cluster index is marked in the seed node
5. Contents 1 Introduction 1I What is supraeg e asy aa ee a E N 12 Why te use supraHer say sas dw ak Shae eee i Lo How toint rpret siprader sc ao dus hee a ee ee we eS Installation and Citation Quick Overview Main Functionality 4 1 Get trained using sPipeline 4 2 Get visualised using visHexMapping and visHexPattern 4 3 Get clustered using sDmatCluster and visDmatCluster 4 4 Get reordered using sCompReorder and visCompReorder Comparing Neighborhood Kernels Applications to Real Cases 6 1 Leukemia patient dataset from Golub et al 6 2 Human embryo dataset from Fang et al 0 6 3 Arabidopsis embryo dataset from Xiang et al Session Information List of Tables 1 A summary of functions used for training and analysis 2 A summary of functions used for visualisation List of Figures A supra hexagonal map 20 0000 eee Map hit distribution lt s 24 4684 5 be He eee ee E Map distance visualisation 002 0 00000 Line plot of codebook patterns 00 Bar plot of codebook patterns 0 0 4 Clusters of the trained map oe ss seces enara ias wa Reordered components of trained map Neighborhood kernels aana maanhaar Components of trained map with the gaussian kernel Components of trained map with the bubble kernel Components of trained map with the cutgaus
6. and finetune stages If instructed sustain the finetune training until the mean quantization error does get worse 4 sBMH used to identify the best matching hexagons rectangles BMH for the input data and these response data are appended to the resulting object of sMap class Below is its common usage of sPipeline with default setup using gaussian kernel and printing out messages in the screen gt sMap lt sPipeline data data Use sWriteData to write out the best matching hexagons in terms of data equivalent to gene clustering gt it will also write out a file Output txt into your disk gt output lt sWriteData sMap sMap data data filename Qutput txt gt output 1 5 ID Hexagon_index 1 1 148 2 2 66 3 3 59 4 4 54 5 5 73 You will see the first column for your input data ID an integer otherwise the row names of input data matrix and the second column for the corre sponding index of best matching hexagons i e gene clusters On the way how hexagons get indexed please refer to Figure 1 4 2 Get visualised using visHexMapping and visHexPattern The function visHexMapping is used to visualise the single value properties that are associated with the map e map indexes as shown previously in Figure 1 gt visHexMapping sMap mappingType indexes newpage F e map hit distribution which tells how many input data vectors are hitting each hexagon see Figure 2 gt pdf su
7. ations by providing several datasets published previously and a collection of functions together with optimised arguments to analyse them The end users are encouraged to adapt them to fit your dataset 17 run them first then get down to details We do not repeat the explanations for all used commands and output files and figures On the meanings and interpre tations please refer to Section 4 On purpose of easy copying all commands are provided without the gt prefix 6 1 Leukemia patient dataset from Golub et al This dataset the learning set contains a 3051 x 38 matrix of expression lev els involving 3051 genes and two types of leukemia 11 acute myeloid leukemia AML and 27 acute lymphoblastic leukemia ALL These 27 ALL are fur ther subtyped into 19 B cell ALL ALL_B and 8 T cell ALL ALL_T see Figure 14 GHGS GGG se E3 amp q9 Figure 14 Reordered components of map for leukemia classification Each component illustrates a sample specific transcriptome map Geometric locations of components display the relationships between 38 leukemia samples AML acute myeloid leukemia ALL acute lymphoblastic leukemia ALL_B B cell ALL ALL_T T cell ALL import data data Golub data lt Golub Thttp www ncbi nlm nih gov pubmed 10521349 18 get trained sMap lt sPipeline data visHexMulComp sMap title rotate 10 colormap darkgreen lightgreen lightpink darkred sWriteData
8. e package please type one of two commands library help supraHex real time help help start html help follow the links to supraHex To view this vignette source and R code whereof please type browseVignettes supraHex supraHez is free to use under GPL 2 You can get citation information from citation supraHex cite the package Please cite this package as Fang H Gough J 2014 supraHex an R Bioconductor package for tabular omics data analysis using a supra hexagonal map Biochemical and Biophysical Research Communi cations 443 1 285 289 DOI http dx doi org 10 1016 j bbrce 2013 11 103 PMID http www ncbi nlm nih gov pubmed term 24309102 2http bioconductor org packages release bioc htm1 supraHex html 3http bioconductor org packages devel bioc htm1 supraHex html 3 Quick Overview The functions in the package supraHezx are divided into two categories one for training and analysis see Table 1 the other for visualisation see Table 2 Table 1 A summary of functions used for training and analysis Function Description sHexGrid Define a supra hexagonal grid return a list sTopology Define the topology of a map grid return a sTopol object sHexGrid Define a supra hexagonal grid return a list sInitial Initialise a sMap object given a topology and input data return a sMap object sTrainology Define trainology training environment return a sTrain object sTrainSeq Impleme
9. gt visHexPattern sMap plotType lines customized color rep c red green each 3 newpage F gt dev off e using bar plots see Figure 5 gt pdf supraHex_vignettes bar pdf width 6 height 6 gt visHexPattern sMap plotType bars customized color rep c red green each 3 newpage F gt dev off Both functions also support the visualisation of user customised data On this advanced usage please refer to specifications of functions by gt visHexMapping gt visHexPattern 4 3 Get clustered using sDmatCluster and visDmatCluster Partition the trained map into clusters using region growing algorithm to ensure each cluster is continuous see Figure 6 gt sBase lt sDmatCluster sMap sMap which_neigh 1 distMeasure median clusterLinkage average 10 Figure 4 Line plot of codebook patterns If multple colors are given the points are also plotted When the pattern involves both positive and negative values zero horizental line is also shown gt pdf supraHex_vignettes cluster pdf width 6 height 6 gt visDmatCluster sMap sBase newpage F gt dev off It is equivalent to gene meta clustering Write out results into a tab delimited text file using sWriteData gt it will also write out a file Output_base txt into your disk gt output lt sWriteData sMap data sBase filename Qutput_base txt gt output 1 5 ID Hexagon_index Cluster_base 1 1 148
10. l 3 gt colnames data lt c S1 S1 S1 S2 S2 S2 The first 5 rows of this data gt data 1 5 S1 S1 S1 S2 S2 S2 1 0 04637505 1 5331183 0 4571943 1 4867335 0 29145199 1 7896765 2 0 12146664 1 4618621 0 4696756 0 1062753 0 61200805 0 8049917 3 1 43196516 0 8075947 1 0812769 0 5381012 0 47702965 1 7736551 4 0 05503947 0 3613781 1 1981018 0 4531657 0 02479884 0 4235951 5 0 58916751 0 5537234 1 6807673 0 8336744 0 67680705 0 7072746 4nttp bioconductor org packages devel bioc html supraHex htm1 You can prepare your own data a tab delimited text file Similarly as shown above this file should contain the first row intended for sample names the first column for gene names and the top left entry being left empty You can import it using the R built in function read table gt data lt read table file you_input_data_file header T row names 1 sep t 4 1 Get trained using sPipeline The function sPipeline setups the pipeline for completing ab initio training given the input data only It sequentially consists of 1 sTopology used to define the topology of a grid with suprahex shape by default according to the input data 2 sInitial used to initialise the codebook matrix given the pre defined topology and the input data by default using uniform initialisation method 3 sTrainology and sTrainSeq used to get the grid map trained at both rough
11. l topological relationships and the other two cutgaussian and bubble keep the relative balance It becomes much clearer when using the function visHexMulComp to visualise trained maps using the same data input and the same trainology but choosing different kernels see Figure 9 Figure 10 Figure 11 Figure 12 and Figure 13 e with gaussian kernel see Figure 9 gt sMap_ga lt sPipeline data data neighKernel gaussian init uniform gt visHexMulComp sMap_ga e with bubble kernel see Figure 10 gt sMap_bu lt sPipeline data data neighKernel bubble init uniform gt visHexMulComp sMap_bu 6In order to display colors properly it is important to reset the argument zlim by respect ing the range of input data matrix more precisely codebook matrix 14 Neighborhood kernel hwi t 0 2 1 0 0 8 0 6 0 4 0 0 Radius amp 1 ol pi e o gaussian n o 2 ep hyi t 1 p lt i A bubble hwi t dwi lt amp d tgaussian hy t exp dyi lt outgaussian na eHp Mdu lt dai e gamma hy t 1 mgt T 0 1 Distance dwi between the hexagon i and the winner w Neighborhood kernel hwi t 0 2 1 0 0 8 0 6 0 4 0 0 Figure 8 Neighborhood kernels There supported in the package supraHex These kernels are displayed within a plot for each fixed radius two different radii i e
12. mbryo dataset from Xiang et al This dataset contains gene expression levels 3625 genes and 7 embryo stages see Figure 16 import data data Xiang data lt Xiang Shttp www ncbi nlm nih gov pubmed 20643359 nttp www ncbi nlm nih gov pubmed 21402797 19 9R o1 oF RI SARP ok aR OSE gt AA sig gis gt gt gio R sgh i q gt x gio _R so wa 4 b t q m i a ae R ei sit R aom Bs RS i F 0 Figure 15 Reordered components of map during early human organo genesis Each component illustrates a sample specific transcriptome map Geometric locations of components display the relationships between the six developmental stages S9 514 each with three replicates R1 R3 get trained sMap lt sPipeline data visHexMulComp sMap title rotate 10 colormap darkblue white darkorange sWriteData sMap data filename Output_Xiang txt get visualised visHexMapping sMap mappingType indexes visHexMapping sMap mappingType hits visHexMapping sMap mappingType dist visHexPattern sMap plotType lines visHexPattern sMap plotType bars get clustered sBase lt sDmatCluster sMap visDmatCluster sMap sBase sWriteData sMap data sBase filename Qutput_base_Xiang txt get reordered sReorder lt sCompReorder sMap metric pearson visCompReorder sMap sReorder title rotate 10 colormap darkblue white darkorange 20 Figure 16 Reordered components of map during e
13. mbryo development in Arabidopsis Geometric locations of sample specific transcriptome map char acterise the relationships between the seven developmental stages zygote quad rant globular heart torpedo bent and mature 7 Session Information All of the output in this vignette was produced under the following conditions gt sessionInfo R version 3 2 1 2015 06 18 Platform x86_64 apple darwinl0 8 0 64 bit Running under OS X 10 10 3 Yosemite locale 1 en_GB UTF 8 en_GB UTF 8 en_GB UTF 8 C en_GB UTF 8 en_GB UTF 8 attached base packages 21 1 grid tools stats graphics grDevices utils datasets 8 methods base other attached packages 1 supraHex_1 7 3 hexbin_1 27 0 staticdocs_0 1 crayon_1 3 1 5 digest_0 6 8 devtools_1 8 0 markdown_0 7 7 highlight_0 4 7 9 whisker_0 3 2 evaluate_0 5 5 testthat_0 10 0 stringr_1 0 0 loaded via a namespace and not attached 1 roxygen2_4 1 1 Rcpp_0 12 0 ape_3 3 lattice_0 20 31 5 MASS_7 3 40 nlme_3 1 120 git2r_0 10 1 magrittr_1 5 9 stringi_0 5 5 curl_0 9 1 xml2_0 1 1 rversions_1 0 2 13 memoise_0 2 1 References Hai Fang and Julian Gough supraHex an R Bioconductor package for tab ular omics data analysis using a supra hexagonal map Biochemical and Biophysical Research Communications 443 1 285 289 2014 ISSN 0006 291X doi 10 1016 j bbre 2013 11 103 URL http dx doi org 10 1016 J pbre 2013 11 108 3 22
14. ndexes newpage F gt dev off 1 2 Why to use supraHex Biologists are far often confronted with ever increasing amounts of omics data that are tabulated in the form of matrix measuring levels activities of genomic coordinates e g genes against experimental samples The matrix usually in volves tens of thousands of genes but a much smaller number of samples at most hundreds known as small sample but large gene The atypical struc ture requires easy to interpret models Unsupervised learning algorithm model such as self organising map is popular for its unique way in capturing input data patterns this is simultaneously performing vector quantisation but regularised by vector projection The supraHez borrows this learning algorithm to produce a supra hexagonal map two dimensional output space from input omics data high dimensional input space In this map geographically close locations are indicative of patterns that are similar in terms of the input space Thanks to the prevalence in nature and symmetric beauty this supra hexagonal map is proba bly suited for analysing such input data with approximately perfect symmetry We argue that omics data tend to be symmetric due to unbiased measurements of gene levels activities on a global scale Even when priori knowledge of the data symmetry is unknown we also argue that at least the supra hexagonal map can provide the ease with visualisation 1 3 How to interpret supraHex
15. nt training via sequential algorithm return a sMap object sTrainBatch Implement training via batch algorithm return a sMap object sBMH Identify the best matching hexagons for the input data return a list sPipeline Setup the pipeline for completing ab initio training given the input data return a sMap object sNeighDirect Calculate direct neighbors for each hexagon in a grid return a matrix sNeighAny Calculate any neighbors for each hexagon in a grid return a matrix sHexDist Calculate distances between hexagons in a 2D grid return a matrix sDistance Compute the pairwise distance for a given data matrix return a matrix sDmat Calculate distance matrix in high dimensional input space but ac cording to neighborhood relationships in 2D output space return a vector sDmatMinima Identify local minima in 2D output space of distance matrix in high dimensional input space return a vector sDmatCluster Partition a grid map into clusters return a list sCompReorder Reorder component planes return a sReorder object sWriteData Write out the best matching hexagons and or cluster bases in terms of data return a data frame sMapOverlay Overlay additional data onto the trained map return a sMap object Table 2 A summary of functions used for visualisation Function Description visHexGrid Visualise a supra hexagonal grid visHexMapping Visualise various mapping items within a supra hexagonal grid visHexComp Visuali
16. or nearby map nodes ii the density of genes mapped onto this map i e what we can see is an equivalent to the data density in high dimensional input space i e what we can only imagine and iii when all map nodes are color coded according to values in a specific component for all prototype vectors i e a specific column of codebook matrix a color coded component map can be used to illustrate sample specific gene activities and thus multiple components illustrate changes across all samples in subject Owing to these unique features the supra hexagonal map can be used for gene clustering and sample representation 2 Installation and Citation supraHex is a package for the R computing environment and it is assumed that you have already installed the latest version of R gt 3 0 2 You can install the package following step by step guidelines in http suprahex r forge r v v project org Briefly you can install it from Bioconductor or R Forge Using the release version officially released on 15 10 2013 source http bioconductor org biocLite R biocLite supraHex library supraHex load the package Using the latest development version prefer it for the benefit of latest improvements install packages hexbin repos http www stats bris ac uk R install packages supraHex repos http R Forge R project org type source library supraHex load the package To get help information for th
17. praHex_vignettes hit pdf width 6 height 6 gt visHexMapping sMap mappingType hits newpage F gt dev off DOOBDOOOS SOOO O80 oF CEES a aS oe O66 OoOO D awe CROC ooro Oa oO ONPE e s om a SES 7 gt a 2 gt lt gt Oe Oe OONO eQ 3 e g Figure 2 Map hit distribution The number represents how many input data vectors are hitting each hexagon The size of each hexagon is proportional to the number of hits e map distance visualisation which tells how far each hexagon is away from its neighbors see Figure 3 gt pdf supraHex_vignettes distance pdf width 6 height 6 gt visHexMapping sMap mappingType dist newpage F gt dev off The function visHexPattern is used to visualise the vector based patterns that are associated with the map e using line plots see Figure 4 818 619 8106 O QOO 6 s o cc o QO ae oo 0 Ul QO o o O OO Oo QO C o oO Oo o o 0o oQ0Qo 00 o O0O0OQaeoQoo OQ OC O C o O o ALA ie x O o A OOOO os soo o TEE o O ee Figure 3 Map distance visualisation For each hexagon its median dis tances in high dimensional input space to its neighbors defined in 2D output space is calculated The size of each hexagon is proportional to this distance gt pdf supraHex_vignettes line pdf width 6 height 6
18. sMap data filename Output_Golub txt get visualised visHexMapping sMap mappingType indexes visHexMapping sMap mappingType hits visHexMapping sMap mappingType dist get reordered sReorder lt sCompReorder data metric pearson visCompReorder sMap sReorder title rotate 15 colormap darkgreen lightgreen lightpink darkred 6 2 Human embryo dataset from Fang et al This dataset involves six successive developmental stages with three replicates for each stage see Figure 15 including e Fang a 5441 x 18 matrix of expression levels e Fang geneinfo a 5441 x 3 matrix of gene information e Fang sampleinfo a 5441 x 3 matrix of sample information import data data Fang transform data by row gene centering data lt Fang matrix rep apply Fang 1 mean ncol Fang ncol ncol Fang get trained sMap lt sPipeline data visHexMulComp sMap title rotate 10 sWriteData sMap data filename Output_Fang txt get visualised visHexMapping sMap mappingType indexes visHexMapping sMap mappingType hits visHexMapping sMap mappingType dist visHexPattern sMap plotType lines visHexPattern sMap plotType bars get clustered sBase lt sDmatCluster sMap visDmatCluster sMap sBase sWriteData sMap data sBase filename Output_base_Fang txt get reordered sReorder lt sCompReorder data metric euclidean visCompReorder sMap sReorder title rotate 15 6 3 Arabidopsis e
19. se a component plane of a supra hexagonal grid visColormap Define a colormap visColorbar Define a colorbar visVp Create viewports for multiple supra hexagonal grids visHexMulComp Visualise multiple component planes of a supra hexagonal grid visCompReorder Visualise multiple component planes reorded within a sheet shape rectangle grid visHexPattern Visualise codebook matrix or input patterns within a supra hexagonal grid visDmatCluster Visualise clusters bases partitioned from a supra hexagonal grid visKernels Visualize neighborhood kernels 4 Main Functionality This vignette aims to demonstrate the functionality of the package supraHex in utilising the supra hexagonal map to train analyse and visualise a high dimensional omics data To simplify the descriptions it deals with the gene expression data But it can also be applied in any other omics data a tabular matrix usually containing thousands of genes but with at most hundreds of samples Assumedly we have a gene expression matrix of 1000 x6 measuring the expression levels of 1000 genes across 6 samples These samples come from two different normal distributions S1 and 2 and each i e a matrix of 1000 x 3 is randomly generated from the same normal distribution All examples below are based on the latest development version gt data lt cbind matrix rnorm 1000 3 mean 0 5 sd 1 nrow 1000 ncol 3 matrix rnorm 1000 3 mean 0 5 sd 1 nrow 1000 nco
20. sian kernel Components of trained map with the ep kernel Components of trained map with the gamma kernel Reordered components of map for leukemia classification Reordered components of map during early human organogenesis Reordered components of map during embryo development in ArADIdOPS S 640 a a an o acr Bm SO le Be Ree a RS OANaw kwnr el oo Ooo rwnrr www w or m NOOON m 17 18 19 19 21 10 11 12 13 14 15 15 16 16 17 17 18 20 1 Introduction 1 1 What is supraHex The supraHex package Fang and Gough 2014 devises a supra hexagonal map This map consists of smaller hexagonal lattices on a regular 2 dimensional 2D grid these smaller hexagons collectively form a giant hexagon see Figure 1 As seen it has symmetric beauty around the center from which individual hexagons radiate outwards To ensure that a supra hexagon is forme dexactly inherent relationships must be met between the total number nHex of hexagons in the grid the grid radius r and the xy dimensions zdim and ydim e nHex 14 6 xr x r 1 2 e rdim ydim 2 r 1 The codes used to produce this example are assumedly the package has been successfully installed see Section 2 gt library supraHex gt pdf supraHex_vignettes suprahex pdf width 6 height 6 gt sTopol lt sTopology xdim 15 ydim 15 lattice hexa shape suprahex gt visHexMapping sTopol mappingType i
21. supraHex an R Bioconductor package for tabular omics data analysis using a supra hexagonal map Hai Fang Julian Gough Department of Computer Science University of Bristol UK Abstract We introduce an R Bioconductor package called supraHex It names af ter a supra hexagon that is a giant hexagon on a 2 dimensional 2D map grid seamlessly consisting of smaller hexagons This 2D giant hexagon is intended to train analyse and visualise a high dimensional omics data which usually involves a large number of genomic coordinates e g genes but a much smaller number of samples The resulting supra hexagon en sembles the structure of the input data in a topology preserving fashion With the supraHex users are able to easily and intuitively carry out inte grated tasks such as simultaneous analysis of gene clustering and sample correlation and the overlaying of additional data if any onto the map for multilayer omics data comparisons In this vignette guide we give a tutorial style introduction into how the functions contained in the package supraHez can be used to better understand the input omics data This vignette assumes some basic familiarity with the R language and environ ment It only provides a task oriented description of the package function ality and compliments the accompanying manual supraHex manual pdf that gives a full description of all functions hfang well ox ac uk lhttp suprahex r forge r project org
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