diff --git a/inst/appdir/reportMultiple.Rmd b/inst/appdir/reportMultiple.Rmd
index f5b3f92..394d3ca 100644
--- a/inst/appdir/reportMultiple.Rmd
+++ b/inst/appdir/reportMultiple.Rmd
@@ -1,565 +1,565 @@
 ---
 params:
   object: NA
   colors: NA
   name: NULL
   consensus: NA
 title: "Benchmarking report for `r params$name` "
 author: "created by challengeR v`r packageVersion('challengeR')`  \nWiesenfarth, Reinke, Landman, Cardoso, Maier-Hein & Kopp-Schneider (2019)"
 date: "`r Sys.setlocale('LC_TIME', 'English'); format(Sys.time(), '%d %B, %Y')`"
 editor_options: 
   chunk_output_type: console
 ---
 
 <!-- This text is outcommented -->
 <!-- R code chunks start with "```{r }" and end with "```" -->
 <!-- Please do not change anything inside of code chunks, otherwise any latex code is allowed -->
 
 <!-- inline code with `r 0` -->
 
 
 ```{r setup, include=FALSE}
 options(width=80)
 out.format <- knitr::opts_knit$get("out.format")
 img_template <- switch( out.format,
                      word = list("img-params"=list(dpi=150,
                                                fig.width=6,
                                                fig.height=6,
                                                out.width="504px",
                                                out.height="504px")),
                      {
                        # default
                        list("img-params"=list( fig.width=7,fig.height = 3,dpi=300))
                      } )
 
 knitr::opts_template$set( img_template )
 
 knitr::opts_chunk$set(echo = F,#fig.width=7,fig.height = 3,dpi=300,
                       fig.align="center")
 theme_set(theme_light())
 
 ```
 
 
 ```{r }
 boot_object = params$object
 ordering_consensus=names(params$consensus)
 color.fun=params$colors
 ```
 
 ```{r }
 challenge_multiple=boot_object$data
 
 ranking.fun=boot_object$FUN
 object=challenge_multiple%>%ranking.fun
 
 cols_numbered=cols=color.fun(length(ordering_consensus))
 names(cols)=ordering_consensus
 names(cols_numbered)= paste(1:length(cols),names(cols))
 
 
 ```
 
 
 This document presents a systematic report on a benchmark study. Input data comprises raw metric values for all algorithms and test cases. Generated plots are:
 
 * Visualization of assessment data: Dot- and boxplots, podium plots and ranking heatmaps
 * Visualization of ranking robustness: Line plots
 * Visualization of ranking stability: Blob plots, violin plots and significance maps
 * Visualization of cross-task insights
 
 
 Ranking of algorithms within tasks according to the following chosen ranking scheme:
 
 ```{r,results='asis'}
 a=(  lapply(object$FUN.list,function(x) {
                  if (!is.character(x)) return(paste0("aggregate using function ",
                                                      paste(gsub("UseMethod","",
                                                                 deparse(functionBody(x))),
                                                            collapse=" ")
                                                      ))
                  else if (x=="rank") return(x)
                  else return(paste0("aggregate using function ",x))
   }))
 cat("&nbsp; &nbsp; *",paste0(a,collapse=" then "),"*",sep="")
 
 if (is.character(object$FUN.list[[1]]) && object$FUN.list[[1]]=="significance") cat("\n\n Column 'prop.sign' is equal to the number of pairwise significant test results for a given algorithm divided by the number of algorithms.")
 ```
 
 
 Ranking list for each task:
 ```{r,results='asis'}
 for (t in 1:length(object$matlist)){
   cat("\n",names(object$matlist)[t],": ")
   n.cases=nrow(challenge_multiple[[t]])/length(unique(challenge_multiple[[t]][[attr(challenge_multiple,"algorithm")]]))
   cat("\nAnalysis based on ", 
       n.cases,
       " test cases which included", 
       sum(is.na(challenge_multiple[[t]][[attr(challenge_multiple,"value")]])),
       " missing values.")
   
   if (n.cases<log2(5000)) warning("Associated figures based on bootstrapping should be treated with caution due to small number of test cases!")
   
   x=object$matlist[[t]]
   print(knitr::kable(x[order(x$rank),]))
 }
 
 ```
 
 \bigskip
 
 Consensus ranking according to chosen method `r attr(params$consensus,"method")`:
 ```{r}
 knitr::kable(data.frame(value=round(params$consensus,3), 
                         rank=rank(params$consensus, 
                                   ties.method="min")))
 ```
 
 
 # Visualization of raw assessment data
 Algorithms are ordered according to chosen ranking scheme for each task.
 
 ## Dot- and boxplots
 
 *Dot- and boxplots* for visualizing raw assessment data separately for each algorithm. Boxplots representing descriptive statistics over all test cases (median, quartiles and outliers) are combined with horizontally jittered dots representing individual test cases.
 
 \bigskip
 
 ```{r boxplots}
 temp=boxplot(object,size=.8)
 temp=lapply(temp,function(x) utils::capture.output(x+xlab("Algorithm")+ylab("Metric value")))
 
 ```
 
 
 
 ## Podium plots
 *Podium plots* (see also Eugster et al, 2008) for visualizing raw assessment data. Upper part (spaghetti plot): Participating algorithms are color-coded, and each colored dot in the plot represents a metric value achieved with the respective algorithm. The actual metric value is encoded by the y-axis. Each podium (here: $p$=`r length(ordering_consensus)`) represents one possible rank, ordered from best (1) to last (here: `r length(ordering_consensus)`). The assignment of metric values (i.e. colored dots) to one of the podiums is based on the rank that the respective algorithm achieved on the corresponding test case. Note that the plot part above each podium place is further subdivided into $p$ "columns", where each column represents one participating algorithm (here: $p=$ `r length(ordering_consensus)`).  Dots corresponding to identical test cases are connected by a line, leading to the shown spaghetti structure. Lower part: Bar charts represent the relative frequency for each algorithm to achieve the rank encoded by the podium place. 
 
 ```{r ,eval=T,fig.width=12, fig.height=6,include=FALSE}
 plot.new()
 algs=ordering_consensus
 l=legend("topright", 
          paste0(1:length(algs),": ",algs), 
          lwd = 1, cex=1.4,seg.len=1.1,
          title="Rank: Alg.",
          plot=F) 
 
 w <- grconvertX(l$rect$w, to='ndc') - grconvertX(0, to='ndc')
 h<- grconvertY(l$rect$h, to='ndc') - grconvertY(0, to='ndc')
 addy=max(grconvertY(l$rect$h,"user","inches"),6)
 ```
 
 
 ```{r podium,eval=T,fig.width=12, fig.height=addy}
 #c(bottom, left, top, right
 op<-par(pin=c(par()$pin[1],6),
         omd=c(0, 1-w, 0, 1),
         mar=c(par('mar')[1:3], 0)+c(-.5,0.5,-.5,0),
         cex.axis=1.5,
         cex.lab=1.5,
         cex.main=1.7)#,mar=c(5, 4, 4, 2) + 0.1)
 
 oh=grconvertY(l$rect$h,"user","lines")-grconvertY(6,"inches","lines")
 if (oh>0) par(oma=c(oh,0,0,0))
 
 
 set.seed(38)
 podium(object,
        col=cols,
        lines.show = T, lines.alpha = .4,
        dots.cex=.9,
        ylab="Metric value",
        layout.heights=c(1,.35),
        legendfn = function(algs, cols) {
                  legend(par('usr')[2], par('usr')[4], 
                  xpd=NA, 
                  paste0(1:length(algs),": ",algs), 
                  lwd = 1, col =  cols, 
                  bg = NA,
                  cex=1.4, seg.len=1.1,
                  title="Rank: Alg.") 
         }
       )
 par(op)
   
 ```
 
 
 ## Ranking heatmaps
 *Ranking heatmaps* for visualizing raw assessment data. Each cell $\left( i, A_j \right)$ shows the absolute frequency of test cases in which algorithm $A_j$ achieved rank $i$.
 
 \bigskip
 
 ```{r rankingHeatmap,fig.width=9, fig.height=9,out.width='70%'}
 temp=utils::capture.output(rankingHeatmap(object))
 ```
 
 
 
 # Visualization of ranking stability
 
 
 
 ## *Blob plot* for visualizing ranking stability 
 based on bootstrap sampling}\label{blobByTask}
 
 Algorithms are color-coded, and the area of each blob at position $\left( A_i, \text{rank } j \right)$ is proportional to the relative frequency $A_i$ achieved rank $j$ across $b=$ `r ncol(boot_object$bootsrappedRanks[[1]])` bootstrap samples. The median rank for each algorithm is indicated by a black cross. 95\% bootstrap intervals across bootstrap samples are indicated by black lines. 
 
 
 \bigskip
 
 ```{r blobplot_bootstrap,fig.width=9, fig.height=9}
 pl=list()
 for (subt in names(boot_object$bootsrappedRanks)){
   a=list(bootsrappedRanks=list(boot_object$bootsrappedRanks[[subt]]),
          matlist=list(boot_object$matlist[[subt]]))
   names(a$bootsrappedRanks)=names(a$matlist)=subt
   class(a)="bootstrap.list"
   r=boot_object$matlist[[subt]]
 
   pl[[subt]]=stabilityByTask(a,
                              max_size =8,
                              ordering=rownames(r[order(r$rank),]),
                              size.ranks=.25*theme_get()$text$size,
                              size=8,
                              shape=4) + scale_color_manual(values=cols)
 
 }
 
 # if (length(boot_object$matlist)<=6 &nrow((boot_object$matlist[[1]]))<=10 ){
 #   ggpubr::ggarrange(plotlist = pl)
 # } else {
   for (i in 1:length(pl)) print(pl[[i]])
 #}
 
 ```
 
 
 ## *Violin plot* for visualizing ranking stability based on bootstrapping \label{violin}
 
 The ranking list based on the full assessment data is pairwisely compared with the ranking lists based on the individual bootstrap samples (here $b=$ `r ncol(boot_object$bootsrappedRanks[[1]])` samples). For each pair of rankings, Kendall's $\tau$ correlation is computed. Kendall’s $\tau$ is a scaled index determining the correlation between the lists. It is computed by evaluating the number of pairwise concordances and discordances between ranking lists and produces values between $-1$ (for inverted order) and $1$ (for identical order). A violin plot, which simultaneously depicts a boxplot and a density plot, is generated from the results.
 
 \bigskip
 
 ```{r violin}
 violin(boot_object)
 ```
 
 
 
 
 
 ## *Significance maps* for visualizing ranking stability based on statistical significance
 
 *Significance maps* depict incidence matrices of
 pairwise significant test results for the one-sided Wilcoxon signed rank test at a 5\% significance level with adjustment for multiple testing according to Holm. Yellow shading indicates that metric values of the algorithm on the x-axis were significantly superior to those from the algorithm on the y-axis, blue color indicates no significant difference.
 
 
 \bigskip
 
 ```{r significancemap,fig.width=6, fig.height=6,out.width='200%'}
 temp=utils::capture.output(significanceMap(object,alpha=0.05,p.adjust.method="holm")
         )
 ```
 
 <!-- \subsubsection{Hasse diagram} -->
 
 <!-- ```{r single_stability_significance_hasse, fig.height=19} -->
 <!-- plot(relensemble) -->
 <!-- ``` -->
 
 
 
 
 ## Ranking robustness to ranking methods
 *Line plots* for visualizing rankings robustness across different ranking methods. Each algorithm is represented by one colored line. For each ranking method encoded on the x-axis, the height of the line represents the corresponding rank. Horizontal lines indicate identical ranks for all methods.
 
 \bigskip
 
 ```{r lineplot,fig.width=7,fig.height = 5}
 if (length(boot_object$matlist)<=6 &
     nrow((boot_object$matlist[[1]]))<=10 ){
   methodsplot(challenge_multiple,
               ordering = ordering_consensus,
               na.treat=object$call[[1]][[1]]$na.treat) + scale_color_manual(values=cols)
 } else {
   x=challenge_multiple
   for (subt in names(challenge_multiple)){
      dd=as.challenge(x[[subt]],
                      value=attr(x,"value"), 
                      algorithm=attr(x,"algorithm") ,
                      case=attr(x,"case"),
                      annotator = attr(x,"annotator"), 
                      by=attr(x,"by"),
                      smallBetter = !attr(x,"largeBetter"),
                      na.treat=object$call[[1]][[1]]$na.treat
                      )
  
     print(methodsplot(dd,
                       ordering = ordering_consensus) + scale_color_manual(values=cols)
           )
   }
 }
 ```
 
 
 
 
 
 # Visualization of cross-task insights
 
 Algorithms are ordered according to consensus ranking.
 
 
 
 
 ## Characterization of algorithms
 
 ### Ranking stability: Variability of achieved rankings across tasks
 <!-- Variability of achieved rankings across tasks: If a -->
 <!-- reasonably large number of tasks is available, a blob plot -->
 <!-- can be drawn, visualizing the distribution -->
 <!-- of ranks each algorithm attained across tasks. -->
 <!-- Displayed are all ranks and their frequencies an algorithm -->
 <!-- achieved in any task. If all tasks would provide the same -->
 <!-- stable ranking, narrow intervals around the diagonal would -->
 <!-- be expected. -->
 blob plot similar to the one shown in Fig.~\ref{blobByTask} substituting rankings based on bootstrap samples with the rankings corresponding to multiple tasks. This way, the distribution of ranks across tasks can be intuitively visualized.
 
 
 \bigskip
 
 ```{r blobplot_raw}
 #stability.ranked.list
 stability(object,ordering=ordering_consensus,max_size=9,size=8,shape=4)+scale_color_manual(values=cols)
 ```
 
 
 ### Ranking stability: Ranking variability via bootstrap approach
 
 Blob plot of bootstrap results over the different tasks separated
 by algorithm allows another perspective on the assessment data. This gives deeper insights into the characteristics
 of tasks and the ranking uncertainty of the algorithms in each
 task. 
 <!-- 1000 bootstrap Rankings were performed for each task. -->
 <!-- Each algorithm is considered separately and for each subtask (x-axis) all observed ranks across bootstrap samples (y-axis) are displayed. Additionally, medians and IQR is shown in black. -->
 
 <!-- We see which algorithm is consistently among best, which is consistently among worst, which vary extremely... -->
 
 
 \bigskip
 
 ```{r blobplot_bootstrap_byAlgorithm,fig.width=7,fig.height = 5}
 #stabilityByAlgorithm.bootstrap.list
 if (length(boot_object$matlist)<=6 &nrow((boot_object$matlist[[1]]))<=10 ){
   stabilityByAlgorithm(boot_object,
                        ordering=ordering_consensus,
                        max_size = 9,
                        size=4,
                        shape=4,
                        single = F) + scale_color_manual(values=cols)
 } else {
   pl=stabilityByAlgorithm(boot_object,
                           ordering=ordering_consensus,
                           max_size = 9,
                           size=4,
                           shape=4,
                           single = T)
   for (i in 1:length(pl)) print(pl[[i]] + 
                                   scale_color_manual(values=cols) +
                                   guides(size = guide_legend(title="%"),color="none")
                                 )
 }
 
 ```
 
 <!-- Stacked frequencies of observed ranks across bootstrap samples are displayed with colouring according to subtask. Vertical lines provide original (non-bootstrap) rankings for each subtask. -->
 
 An alternative representation is provided by a stacked
 frequency plot of the observed ranks, separated by algorithm. Observed ranks across bootstrap samples are
 displayed with colouring according to task. For algorithms that
 achieve the same rank in different tasks for the full assessment
 data set, vertical lines are on top of each other. Vertical lines
 allow to compare the achieved rank of each algorithm over
 different tasks.
 
 \bigskip
 
 
 ```{r stackedFrequencies_bootstrap_byAlgorithm,fig.width=7,fig.height = 5}
 #stabilityByAlgorithmStacked.bootstrap.list
 stabilityByAlgorithmStacked(boot_object,ordering=ordering_consensus)
 ```
 
 
 
 
 ## Characterization of tasks
 
 
 ### Visualizing bootstrap results
 To investigate which
 tasks separate algorithms well (i.e., lead to a stable ranking),
 two visualization methods are recommended.
 
 Bootstrap results can be shown in a blob plot showing one plot for each
 task. In this view, the spread of the blobs for each algorithm
 can be compared across tasks. Deviations from the diagonal indicate deviations
 from the consensus ranking (over tasks). Specifically, if rank
 distribution of an algorithm is consistently below the diagonal,
 the algorithm performed better in this task than on average
 across tasks, while if the rank distribution of an algorithm
 is consistently above the diagonal, the algorithm performed
 worse in this task than on average across tasks. At the bottom
 of each panel, ranks for each algorithm in the tasks is provided.
 
 
 <!-- Shows which subtask leads to stable ranking and in which subtask ranking is more uncertain. -->
 
 
 Same as in Section \ref{blobByTask} but now ordered according to consensus.
 
 \bigskip
 
 ```{r blobplot_bootstrap_byTask,fig.width=9, fig.height=9}
 #stabilityByTask.bootstrap.list
 if (length(boot_object$matlist)<=6 &nrow((boot_object$matlist[[1]]))<=10 ){
   stabilityByTask(boot_object,
                   ordering=ordering_consensus,
                   max_size = 9,
                   size=4,
                   shape=4) + scale_color_manual(values=cols)
 } else {
   pl=list()
   for (subt in names(boot_object$bootsrappedRanks)){
     a=list(bootsrappedRanks=list(boot_object$bootsrappedRanks[[subt]]),
            matlist=list(boot_object$matlist[[subt]]))
     names(a$bootsrappedRanks)=names(a$matlist)=subt
     class(a)="bootstrap.list"
     r=boot_object$matlist[[subt]]
     
     pl[[subt]]=stabilityByTask(a,
                                max_size = 9,
                                ordering=ordering_consensus,
                                size.ranks=.25*theme_get()$text$size,
                                size=4,
                                shape=4) + scale_color_manual(values=cols)
   }
   for (i in 1:length(pl)) print(pl[[i]])
 }
 ```
 
 
 ### Cluster Analysis
 <!-- Quite a different question of interest -->
 <!-- is to investigate the similarity of tasks with respect to their -->
 <!-- rankings, i.e., which tasks lead to similar ranking lists and the -->
 <!-- ranking of which tasks are very different. For this question -->
 <!-- a hierarchical cluster analysis is performed based on the -->
 <!-- distance between ranking lists. Different distance measures -->
 <!-- can be used (here: Spearman's footrule distance) -->
 <!-- as well as different agglomeration methods (here: complete and average).  -->
 
 
-Dendrogram from hierarchical cluster analysis} and \textit{network-type graphs} for assessing the similarity of tasks based on challenge rankings. 
+Dendrogram from hierarchical cluster analysis and \textit{network-type graphs} for assessing the similarity of tasks based on challenge rankings. 
 
 A dendrogram is a visualization approach based on hierarchical clustering. It depicts clusters according to a chosen distance measure (here: Spearman's footrule) as well as a chosen agglomeration method (here: complete and average agglomeration). 
 \bigskip
 
 ```{r , fig.width=6, fig.height=5,out.width='60%'}
 #d=relation_dissimilarity.ranked.list(object,method=kendall)
 
 # use ranking list
   relensemble=as.relation.ranked.list(object)
  
 # # use relations
 #   a=challenge_multi%>%decision.challenge(p.adjust.method="none")
 #   aa=lapply(a,as.relation.challenge.incidence)
 #   names(aa)=names(challenge_multi)
 #   relensemble= do.call(relation_ensemble,args = aa)
 d <- relation_dissimilarity(relensemble, method = "symdiff")
 ```
 
   
 ```{r dendrogram_complete, fig.width=6, fig.height=5,out.width='60%'}
 if (length(relensemble)>2) {
   plot(hclust(d,method="complete")) #,main="Symmetric difference distance - complete"
 } else cat("\nCluster analysis only sensible if there are >2 tasks.\n\n")
 ```
 
 \bigskip
 
 
 ```{r dendrogram_average, fig.width=6, fig.height=5,out.width='60%'}
 if (length(relensemble)>2) plot(hclust(d,method="average")) #,main="Symmetric difference distance - average"
 ```
 
 <!-- An alternative representation of -->
 <!-- distances between tasks (see Eugster et al, 2008) is provided by networktype -->
 <!-- graphs. -->
 <!-- Every task is represented by a node and nodes are connected -->
 <!-- by edges. Distance between nodes increase exponentially with -->
 <!-- the chosen distance measure d (here: distance between nodes -->
 <!-- equal to 1:05d). Thick edges represent smaller distance, i.e., -->
 <!-- the ranking lists of corresponding tasks are similar. Tasks with -->
 <!-- a unique winner are filled to indicate the algorithm. In case -->
 <!-- there are more than one first-ranked algorithm, nodes remain -->
 <!-- uncoloured. -->
 
 
 In network-type graphs (see Eugster et al, 2008), every task is represented by a node and nodes are connected by edges whose length is determined by a chosen distance measure. Here, distances between nodes are chosen to increase exponentially in Spearman's footrule distance with growth rate 0.05 to accentuate large distances.
 Hence, tasks that are similar with respect to their algorithm ranking appear closer together than those that are dissimilar. Nodes representing tasks with a unique winner are colored-coded by the winning algorithm. In case there are more than one first-ranked algorithms in a task, the corresponding node remains uncolored.
 \bigskip
 
 ```{r ,eval=T,fig.width=12, fig.height=6,include=FALSE}
 if (length(relensemble)>2) {
   netw=network(object,
                method = "symdiff", 
                edge.col=grDevices::grey.colors,
                edge.lwd=1,
                rate=1.05,
                cols=cols
                )
   
   plot.new()
   leg=legend("topright",  names(netw$leg.col), lwd = 1, col = netw$leg.col, bg =NA,plot=F,cex=.8)
   w <- grconvertX(leg$rect$w, to='inches')
   addy=6+w
 } else addy=1
 
 ```
 
 ```{r network, fig.width=addy, fig.height=6,out.width='100%'}
 if (length(relensemble)>2) {
   plot(netw,
        layoutType = "neato",
        fixedsize=TRUE,
        # fontsize,
        # width,
        # height,
        shape="ellipse",
        cex=.8
        )
 }
 
 ```
 
 
 # Reference
 
 Wiesenfarth, M., Reinke, A., Landman, B.A., Cardoso, M.J., Maier-Hein, L. and Kopp-Schneider, A. (2019). Methods and open-source toolkit for analyzing and visualizing challenge results. *arXiv preprint arXiv:1910.05121*
 
 M. J. A. Eugster, T. Hothorn, and F. Leisch, “Exploratory
 and inferential analysis of benchmark experiments,”
 Institut fuer Statistik, Ludwig-Maximilians-
 Universitaet Muenchen, Germany, Technical Report 30,
 2008. [Online]. Available: http://epub.ub.uni-muenchen.
 de/4134/.
 
 
 
 
 
 
 
diff --git a/inst/appdir/reportMultipleShort.Rmd b/inst/appdir/reportMultipleShort.Rmd
index f363c6e..a3d0d45 100644
--- a/inst/appdir/reportMultipleShort.Rmd
+++ b/inst/appdir/reportMultipleShort.Rmd
@@ -1,409 +1,409 @@
 ---
 params:
   object: NA
   colors: NA
   name: NULL
   consensus: NA
 title: "Benchmarking report for `r params$name` "
 author: "created by challengeR v`r packageVersion('challengeR')`  \nWiesenfarth, Reinke, Landman, Cardoso, Maier-Hein & Kopp-Schneider (2019)"
 date: "`r Sys.setlocale('LC_TIME', 'English'); format(Sys.time(), '%d %B, %Y')`"
 editor_options: 
   chunk_output_type: console
 ---
 
 <!-- This text is outcommented -->
 <!-- R code chunks start with "```{r }" and end with "```" -->
 <!-- Please do not change anything inside of code chunks, otherwise any latex code is allowed -->
 
 <!-- inline code with `r 0` -->
 
 
 ```{r setup, include=FALSE}
 options(width=80)
 out.format <- knitr::opts_knit$get("out.format")
 img_template <- switch( out.format,
                      word = list("img-params"=list(dpi=150,
                                                fig.width=6,
                                                fig.height=6,
                                                out.width="504px",
                                                out.height="504px")),
                      {
                        # default
                        list("img-params"=list( fig.width=7,fig.height = 3,dpi=300))
                      } )
 
 knitr::opts_template$set( img_template )
 
 knitr::opts_chunk$set(echo = F,#fig.width=7,fig.height = 3,dpi=300,
                       fig.align="center")
 theme_set(theme_light())
 
 ```
 
 
 ```{r }
 object = params$object
 ordering_consensus=names(params$consensus)
 color.fun=params$colors
 
 ```
 
 ```{r }
 challenge_multiple=object$data
 
 ranking.fun=object$FUN
 
 cols_numbered=cols=color.fun(length(ordering_consensus))
 names(cols)=ordering_consensus
 names(cols_numbered)= paste(1:length(cols),names(cols))
 
 ```
 
 
 This document presents a systematic report on a benchmark study. Input data comprises raw metric values for all algorithms and test cases. Generated plots are:
 
 * Visualization of assessment data: Dot- and boxplots, podium plots and ranking heatmaps
 * Visualization of ranking robustness: Line plots
 * Visualization of ranking stability: Significance maps
 * Visualization of cross-task insights
 
 
 Ranking of algorithms within tasks according to the following chosen ranking scheme:
 
 ```{r,results='asis'}
 a=(  lapply(object$FUN.list,function(x) {
                  if (!is.character(x)) return(paste0("aggregate using function ",
                                                      paste(gsub("UseMethod","",
                                                                 deparse(functionBody(x))),
                                                            collapse=" ")
                                                      ))
                  else if (x=="rank") return(x)
                  else return(paste0("aggregate using function ",x))
   }))
 cat("&nbsp; &nbsp; *",paste0(a,collapse=" then "),"*",sep="")
 
 if (is.character(object$FUN.list[[1]]) && object$FUN.list[[1]]=="significance") cat("\n\n Column 'prop.sign' is equal to the number of pairwise significant test results for a given algorithm divided by the number of algorithms.")
 ```
 
 
 Ranking list for each task:
 ```{r,results='asis'}
 for (t in 1:length(object$matlist)){
   cat("\n",names(object$matlist)[t],": ")
   n.cases=nrow(challenge_multiple[[t]])/length(unique(challenge_multiple[[t]][[attr(challenge_multiple,"algorithm")]]))
   
   cat("\nAnalysis based on ", 
       n.cases,
       " test cases which included", 
       sum(is.na(challenge_multiple[[t]][[attr(challenge_multiple,"value")]])),
       " missing values.")
   
   x=object$matlist[[t]]
   print(knitr::kable(x[order(x$rank),]))
 }
 
 ```
 
 \bigskip
 
 Consensus ranking according to chosen method `r attr(params$consensus,"method")`:
 ```{r}
 knitr::kable(data.frame(value=round(params$consensus,3), 
                         rank=rank(params$consensus, 
                                   ties.method="min")))
 ```
 
 
 # Visualization of raw assessment data
 Algorithms are ordered according to chosen ranking scheme for each task.
 
 ## Dot- and boxplots
 
 *Dot- and boxplots* for visualizing raw assessment data separately for each algorithm. Boxplots representing descriptive statistics over all test cases (median, quartiles and outliers) are combined with horizontally jittered dots representing individual test cases.
 
 \bigskip
 
 ```{r boxplots}
 temp=boxplot(object, size=.8)
 temp=lapply(temp, function(x) utils::capture.output(x+xlab("Algorithm")+ylab("Metric value")))
 
 ```
 
 
 
 ## Podium plots
 *Podium plots* (see also Eugster et al, 2008) for visualizing raw assessment data. Upper part (spaghetti plot): Participating algorithms are color-coded, and each colored dot in the plot represents a metric value achieved with the respective algorithm. The actual metric value is encoded by the y-axis. Each podium (here: $p$=`r length(ordering_consensus)`) represents one possible rank, ordered from best (1) to last (here: `r length(ordering_consensus)`). The assignment of metric values (i.e. colored dots) to one of the podiums is based on the rank that the respective algorithm achieved on the corresponding test case. Note that the plot part above each podium place is further subdivided into $p$ "columns", where each column represents one participating algorithm (here: $p=$ `r length(ordering_consensus)`).  Dots corresponding to identical test cases are connected by a line, leading to the shown spaghetti structure. Lower part: Bar charts represent the relative frequency for each algorithm to achieve the rank encoded by the podium place. 
 
 ```{r ,eval=T,fig.width=12, fig.height=6,include=FALSE}
 plot.new()
 algs=ordering_consensus
 l=legend("topright", 
          paste0(1:length(algs),": ",algs), 
          lwd = 1, cex=1.4,seg.len=1.1,
          title="Rank: Alg.",
          plot=F) 
 
 w <- grconvertX(l$rect$w, to='ndc') - grconvertX(0, to='ndc')
 h<- grconvertY(l$rect$h, to='ndc') - grconvertY(0, to='ndc')
 addy=max(grconvertY(l$rect$h,"user","inches"),6)
 ```
 
 
 ```{r podium,eval=T,fig.width=12, fig.height=addy}
 #c(bottom, left, top, right
 
 op<-par(pin=c(par()$pin[1],6),
         omd=c(0, 1-w, 0, 1),
         mar=c(par('mar')[1:3], 0)+c(-.5,0.5,-.5,0),
         cex.axis=1.5,
         cex.lab=1.5,
         cex.main=1.7)
 
 oh=grconvertY(l$rect$h,"user","lines")-grconvertY(6,"inches","lines")
 if (oh>0) par(oma=c(oh,0,0,0))
 
 
 set.seed(38)
 podium(object,
        col=cols,
        lines.show = T, lines.alpha = .4,
        dots.cex=.9,
        ylab="Metric value",
        layout.heights=c(1,.35),
        legendfn = function(algs, cols) {
                  legend(par('usr')[2], par('usr')[4], 
                  xpd=NA, 
                  paste0(1:length(algs),": ",algs), 
                  lwd = 1, col =  cols, 
                  bg = NA,
                  cex=1.4, seg.len=1.1,
                  title="Rank: Alg.") 
         }
       )
 par(op)
   
 ```
 
 
 ## Ranking heatmaps
 *Ranking heatmaps* for visualizing raw assessment data. Each cell $\left( i, A_j \right)$ shows the absolute frequency of test cases in which algorithm $A_j$ achieved rank $i$.
 
 \bigskip
 
 ```{r rankingHeatmap,fig.width=9, fig.height=9,out.width='70%'}
 temp=utils::capture.output(rankingHeatmap(object))
 ```
 
 
 
 # Visualization of ranking stability
 
 
 
 
 
 ## *Significance maps* for visualizing ranking stability based on statistical significance
 
 *Significance maps* depict incidence matrices of
 pairwise significant test results for the one-sided Wilcoxon signed rank test at a 5\% significance level with adjustment for multiple testing according to Holm. Yellow shading indicates that metric values of the algorithm on the x-axis were significantly superior to those from the algorithm on the y-axis, blue color indicates no significant difference.
 
 
 \bigskip
 
 ```{r significancemap,fig.width=6, fig.height=6,out.width='200%'}
 temp=utils::capture.output(significanceMap(object,alpha=0.05,p.adjust.method="holm")
         )
 
 ```
 
 <!-- \subsubsection{Hasse diagram} -->
 
 <!-- ```{r single_stability_significance_hasse, fig.height=19} -->
 <!-- plot(relensemble) -->
 <!-- ``` -->
 
 
 
 
 ## Ranking robustness to ranking methods
 *Line plots* for visualizing rankings robustness across different ranking methods. Each algorithm is represented by one colored line. For each ranking method encoded on the x-axis, the height of the line represents the corresponding rank. Horizontal lines indicate identical ranks for all methods.
 
 \bigskip
 
 ```{r lineplot,fig.width=7,fig.height = 5}
 if (length(object$matlist)<=6 &nrow((object$matlist[[1]]))<=10 ){
   methodsplot(challenge_multiple,
               ordering = ordering_consensus,
               na.treat=object$call[[1]][[1]]$na.treat) + scale_color_manual(values=cols)
 } else {
   x=challenge_multiple
   for (subt in names(challenge_multiple)){
      dd=as.challenge(x[[subt]],
                      value=attr(x,"value"), 
                      algorithm=attr(x,"algorithm") ,
                      case=attr(x,"case"),
                      annotator = attr(x,"annotator"), 
                      by=attr(x,"by"),
                      smallBetter = !attr(x,"largeBetter"),
                      na.treat=object$call[[1]][[1]]$na.treat
                      )
  
     print(methodsplot(dd,
                       ordering = ordering_consensus) + scale_color_manual(values=cols)
           )
   }
 }
 ```
 
 
 
 
 
 # Visualization of cross-task insights
 
 Algorithms are ordered according to consensus ranking.
 
 
 
 
 ## Characterization of algorithms
 
 ### Ranking stability: Variability of achieved rankings across tasks
 <!-- Variability of achieved rankings across tasks: If a -->
 <!-- reasonably large number of tasks is available, a blob plot -->
 <!-- can be drawn, visualizing the distribution -->
 <!-- of ranks each algorithm attained across tasks. -->
 <!-- Displayed are all ranks and their frequencies an algorithm -->
 <!-- achieved in any task. If all tasks would provide the same -->
 <!-- stable ranking, narrow intervals around the diagonal would -->
 <!-- be expected. -->
 
 <!-- blob plot similar to the one shown in Fig.~\ref{blobByTask} substituting rankings based on bootstrap samples with the rankings corresponding to multiple tasks. This way, the distribution of ranks across tasks can be intuitively visualized. -->
 
 
 \bigskip
 
 ```{r blobplot_raw}
 #stability.ranked.list
 stability(object,ordering=ordering_consensus,max_size=9,size=8,shape=4)+scale_color_manual(values=cols)
 ```
 
 
 
 
 ## Characterization of tasks
 
 
 
 ### Cluster Analysis
 <!-- Quite a different question of interest -->
 <!-- is to investigate the similarity of tasks with respect to their -->
 <!-- rankings, i.e., which tasks lead to similar ranking lists and the -->
 <!-- ranking of which tasks are very different. For this question -->
 <!-- a hierarchical cluster analysis is performed based on the -->
 <!-- distance between ranking lists. Different distance measures -->
 <!-- can be used (here: Spearman's footrule distance) -->
 <!-- as well as different agglomeration methods (here: complete and average).  -->
 
 
-Dendrogram from hierarchical cluster analysis} and \textit{network-type graphs} for assessing the similarity of tasks based on challenge rankings. 
+Dendrogram from hierarchical cluster analysis and \textit{network-type graphs} for assessing the similarity of tasks based on challenge rankings. 
 
 A dendrogram is a visualization approach based on hierarchical clustering. It depicts clusters according to a chosen distance measure (here: Spearman's footrule) as well as a chosen agglomeration method (here: complete and average agglomeration). 
 \bigskip
 
 ```{r , fig.width=6, fig.height=5,out.width='60%'}
 #d=relation_dissimilarity.ranked.list(object,method=kendall)
 
 # use ranking list
   relensemble=as.relation.ranked.list(object)
  
 # # use relations
 #   a=challenge_multi%>%decision.challenge(p.adjust.method="none")
 #   aa=lapply(a,as.relation.challenge.incidence)
 #   names(aa)=names(challenge_multi)
 #   relensemble= do.call(relation_ensemble,args = aa)
 d <- relation_dissimilarity(relensemble, method = "symdiff")
 ```
 
   
 ```{r dendrogram_complete, fig.width=6, fig.height=5,out.width='60%'}
 if (length(relensemble)>2) {
   plot(hclust(d,method="complete")) #,main="Symmetric difference distance - complete"
 } else cat("\nCluster analysis only sensible if there are >2 tasks.\n\n")
 ```
 
 \bigskip
 
 
 ```{r dendrogram_average, fig.width=6, fig.height=5,out.width='60%'}
 if (length(relensemble)>2) plot(hclust(d,method="average")) #,main="Symmetric difference distance - average"
 ```
 
 <!-- An alternative representation of -->
 <!-- distances between tasks (see Eugster et al, 2008) is provided by networktype -->
 <!-- graphs. -->
 <!-- Every task is represented by a node and nodes are connected -->
 <!-- by edges. Distance between nodes increase exponentially with -->
 <!-- the chosen distance measure d (here: distance between nodes -->
 <!-- equal to 1:05d). Thick edges represent smaller distance, i.e., -->
 <!-- the ranking lists of corresponding tasks are similar. Tasks with -->
 <!-- a unique winner are filled to indicate the algorithm. In case -->
 <!-- there are more than one first-ranked algorithm, nodes remain -->
 <!-- uncoloured. -->
 
 
 In network-type graphs (see Eugster et al, 2008), every task is represented by a node and nodes are connected by edges whose length is determined by a chosen distance measure. Here, distances between nodes are chosen to increase exponentially in Spearman's footrule distance with growth rate 0.05 to accentuate large distances.
 Hence, tasks that are similar with respect to their algorithm ranking appear closer together than those that are dissimilar. Nodes representing tasks with a unique winner are colored-coded by the winning algorithm. In case there are more than one first-ranked algorithms in a task, the corresponding node remains uncolored.
 \bigskip
 
 ```{r ,eval=T,fig.width=12, fig.height=6,include=FALSE}
 if (length(relensemble)>2) {
   netw=network(object,
                method = "symdiff", 
                edge.col=grDevices::grey.colors,
                edge.lwd=1,
                rate=1.05,
                cols=cols
                )
   
   plot.new()
   leg=legend("topright",  names(netw$leg.col), lwd = 1, col = netw$leg.col, bg =NA,plot=F,cex=.8)
   w <- grconvertX(leg$rect$w, to='inches')
   addy=6+w
 } else addy=1
 
 ```
 
 ```{r network, fig.width=addy, fig.height=6,out.width='100%'}
 if (length(relensemble)>2) {
   plot(netw,
        layoutType = "neato",
        fixedsize=TRUE,
        # fontsize,
        # width,
        # height,
        shape="ellipse",
        cex=.8
        )
 }
 
 ```
 
 
 # Reference
 
 Wiesenfarth, M., Reinke, A., Landman, B.A., Cardoso, M.J., Maier-Hein, L. and Kopp-Schneider, A. (2019). Methods and open-source toolkit for analyzing and visualizing challenge results. *arXiv preprint arXiv:1910.05121*
 
 M. J. A. Eugster, T. Hothorn, and F. Leisch, “Exploratory
 and inferential analysis of benchmark experiments,”
 Institut fuer Statistik, Ludwig-Maximilians-
 Universitaet Muenchen, Germany, Technical Report 30,
 2008. [Online]. Available: http://epub.ub.uni-muenchen.
 de/4134/.