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...ting that rows or columns do not belong to the considered bicluster. Categorial cluster annotations and initial membership threshold guesses can be loaded in addition. Further, we provide an R script =-=[40]-=- for exporting FABIA result objects in the CSV file format required by Caleydo. The script can easily be adapted to load results of arbitrary bicluster algorithms from R. Force-directed layout To simp...

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...ata for rows and columns. Examples for additional data defined on biological samples are gender, age, and tumor staging. In gene dimension, analysts can load metadata such as Gene Ontology (GO) terms =-=[37]-=- and the results of a gene set enrichment analysis [38] performed on KEGG pathways [39]. Furthermore, external cluster assignments can be loaded as additional categories to compare multiple clustering...

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...6] and the Dual Analysis framework [17]. For hierarchical clustering results, the clustered heatmap is commonly extended with a dendrogram that represents the similarities between the rows or columns =-=[18]-=-. The Hierarchical Cluster Explorer (HCE) [19] and MultiClusterTree [20] are both approaches that allow interactive analysis of hierarchical clustering results. However, as mentioned at the beginning ...

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...ership values. In order to reduce the number of genes in the cluster, she increases the membership level threshold in gene dimension. By inspecting the result of a gene annotation enrichment analysis =-=[43]-=-, which is provided as an additonal metadata bar, she infers that the strongest bicluster genes seem to stem from prostate tissue. The second interesting bicluster, bicluster6, only consists of lung (...

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...-way clustering, the goal is to determine either clusters in the row or the column dimension. Examples for one-way clustering algorithms are k-means, hierarchical clustering, and affinity propagation =-=[3]-=-. In two-way clustering, the result of two sequentially performed one-way clustering runs - one in the row and one in the column dimension - are combined into one result. Biclustering Biclustering [4]...

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...of nonbinary membership values that describe to what degree rows and columns belong to the clusters. As the assignment of rows and columns to clusters is fuzzy, this is also known as fuzzy clustering =-=[7,8]-=-. Bicluster visualization Let us consider the visualization of hard clustering results first. In order to understand and interpret hard clustering results, it is necessary to visualize the clusters to...

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...ierarchical clustering results, the clustered heatmap is commonly extended with a dendrogram that represents the similarities between the rows or columns [18]. The Hierarchical Cluster Explorer (HCE) =-=[19]-=- and MultiClusterTree [20] are both approaches that allow interactive analysis of hierarchical clustering results. However, as mentioned at the beginning of the Bicluster visualization section, for bi...

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...e gender, age, and tumor staging. In gene dimension, analysts can load metadata such as Gene Ontology (GO) terms [37] and the results of a gene set enrichment analysis [38] performed on KEGG pathways =-=[39]-=-. Furthermore, external cluster assignments can be loaded as additional categories to compare multiple clustering results. In Furby, we visualize contextual data by attaching additional bars to the cl...

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...[3]. In two-way clustering, the result of two sequentially performed one-way clustering runs - one in the row and one in the column dimension - are combined into one result. Biclustering Biclustering =-=[4]-=-, also known as co-clustering or two-mode clustering, is an emerging field of machine learning. In contrast to one-way and two-way clustering, biclustering is a category of algorithms in which the row...

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...lization. The array of available biclustering methods ranges from algorithms that try to find a single bicluster, to algorithms that seek to find multiple overlapping biclusters. Madeira and Oliveira =-=[5]-=- surveyed different biclustering algorithms with respect to the structure of their output. Bicluster algorithms are often used to analyze gene expression data [6]. In the context of gene expression, a...

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...S4 http://www.biomedcentral.com/1471-2105/15/S6/S4 Page 5 of 13 important aspects of a scalable visualization technique, formulated in requirement R IV. To achieve this, we use a combination of stubs =-=[35,36]-=- and fading effects. Stubs are small indicators that replace the bands and point in the direction of the connected cluster, resulting in a significant reduction of visual clutter. While Figure 4(a) sh...

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...s into clusters such that the clusters themselves are as homogenous as possible and as dissimilar as possible to other clusters. Clustering is often applied to, for instance, gene expression matrices =-=[1,2]-=-, consisting of genes (rows) and samples (columns). We need to differentiate between one-way, two-way, and biclustering. In one-way clustering, the goal is to determine either clusters in the row or t...

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...nly a small number of articles on visualizing fuzzy clustering results have been published. Most of them propose extensions to classical clustering visualizations, including parallel coordinate plots =-=[27]-=-, heatmaps [28], and RadVis [29] - a radial visualization technique, in which membership values are projected to polar coordinates. A similar approach was developed by Rueda and Zhang [30], which maps...

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...clustering is the clustered heatmap, where rows and/or columns are reordered to reflect the similarities. Examples for visual analysis tools that provide interactive heatmaps are Mayday [14], Caleydo =-=[15,16]-=- and the Dual Analysis framework [17]. For hierarchical clustering results, the clustered heatmap is commonly extended with a dendrogram that represents the similarities between the rows or columns [1...

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...preting the clusters. A simple approach to visualizing biclustering results is to create a separate plot for each bicluster, as implemented, for instance, in the Biclustering Analysis Toolbox (BicAT) =-=[21]-=-, the BiClust R toolbox [21] and the BiVisu tool [22]. Showing every cluster as a separate plot allows analysts to inspect the clusters individually, which addresses requirement R I. However, this mak...

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...g biclustering results is to create a separate plot for each bicluster, as implemented, for instance, in the Biclustering Analysis Toolbox (BicAT) [21], the BiClust R toolbox [21] and the BiVisu tool =-=[22]-=-. Showing every cluster as a separate plot allows analysts to inspect the clusters individually, which addresses requirement R I. However, this makes it impossible to see which rows and columns they s...

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...coordinates. A similar approach was developed by Rueda and Zhang [30], which maps membership values to a hypertetrahedron in the 2D or 3D space representing three or four fuzzy clusters. clusterMaker =-=[31]-=- takes a different approach by representing a one-way fuzzy clustering result as a force-directed graph where the clustered entities are shown as nodes and color is used to encode the cluster membersh...

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...s into clusters such that the clusters themselves are as homogenous as possible and as dissimilar as possible to other clusters. Clustering is often applied to, for instance, gene expression matrices =-=[1,2]-=-, consisting of genes (rows) and samples (columns). We need to differentiate between one-way, two-way, and biclustering. In one-way clustering, the goal is to determine either clusters in the row or t...

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...esearch problem that cannot be addressed by any of the existing tools. We will first elaborate on how biclustering results can be represented and then introduce the FABIA fuzzy biclustering algorithm =-=[9]-=-. We use FABIA to demonstrate the proposed technique; however, note that any other biclustering algorithm that produces overlapping clusters can be used in the same way. We continue by introducing gen...

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...he number of duplicates. As this can, however, still result in very large matrices, scalability is limited (see R IV). The work that is probably related most closely to ours is the BicOverlapper tool =-=[26]-=-, which presents the biclustering result in a multiple-coordinated view setup. A parallel coordinates view and a heatmap show the individual biclusters, realizing R I. The overlapper view visualizes t...

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...defined on biological samples are gender, age, and tumor staging. In gene dimension, analysts can load metadata such as Gene Ontology (GO) terms [37] and the results of a gene set enrichment analysis =-=[38]-=- performed on KEGG pathways [39]. Furthermore, external cluster assignments can be loaded as additional categories to compare multiple clustering results. In Furby, we visualize contextual data by att...

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...clustering is the clustered heatmap, where rows and/or columns are reordered to reflect the similarities. Examples for visual analysis tools that provide interactive heatmaps are Mayday [14], Caleydo =-=[15,16]-=- and the Dual Analysis framework [17]. For hierarchical clustering results, the clustered heatmap is commonly extended with a dendrogram that represents the similarities between the rows or columns [1...

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...neand two-way clustering is the clustered heatmap, where rows and/or columns are reordered to reflect the similarities. Examples for visual analysis tools that provide interactive heatmaps are Mayday =-=[14]-=-, Caleydo [15,16] and the Dual Analysis framework [17]. For hierarchical clustering results, the clustered heatmap is commonly extended with a dendrogram that represents the similarities between the r...

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...exploiting analogies to the hypergraph vertex ordering problem. Grothaus et al. [24] propose to duplicate rows and columns to resolve situations where reordering is not possible. The BiCluster viewer =-=[25]-=- follows the same approach, but additionally allows analysts to interactively decide which clusters to show contiguously in order to minimize the number of duplicates. As this can, however, still resu...

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...S4 http://www.biomedcentral.com/1471-2105/15/S6/S4 Page 5 of 13 important aspects of a scalable visualization technique, formulated in requirement R IV. To achieve this, we use a combination of stubs =-=[35,36]-=- and fading effects. Stubs are small indicators that replace the bands and point in the direction of the connected cluster, resulting in a significant reduction of visual clutter. While Figure 4(a) sh...

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...users to maintain their mental map. Results We demonstrate the application and usefulness of Furby by a representative analysis of the multiple tissue types dataset [41] as provided by Hoshida et al. =-=[42]-=- using a soft biclustering result created by the FABIA algorithm. The dataset contains the gene expression values of 5,565 genes for 102 samples extracted from various types of tissue. In addition, we...

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... R II. Jin et al. [23] formulated the reordering issue as an optimization problem and proposed a reordering approach by exploiting analogies to the hypergraph vertex ordering problem. Grothaus et al. =-=[24]-=- propose to duplicate rows and columns to resolve situations where reordering is not possible. The BiCluster viewer [25] follows the same approach, but additionally allows analysts to interactively de...

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...n visualizing fuzzy clustering results have been published. Most of them propose extensions to classical clustering visualizations, including parallel coordinate plots [27], heatmaps [28], and RadVis =-=[29]-=- - a radial visualization technique, in which membership values are projected to polar coordinates. A similar approach was developed by Rueda and Zhang [30], which maps membership values to a hypertet...

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...ange and refine the color mapping on the fly during the analysis. The overlaps between biclusters are encoded using bands connecting the biclusters, which satisfies requirement R II. In previous work =-=[33,34]-=-, we have already made use of bands to visualize the relationships between clusters represented as heatmaps in the context of one-way clustering. In Furby, the same approach is applied in both dimensi...

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...inate plots [27], heatmaps [28], and RadVis [29] - a radial visualization technique, in which membership values are projected to polar coordinates. A similar approach was developed by Rueda and Zhang =-=[30]-=-, which maps membership values to a hypertetrahedron in the 2D or 3D space representing three or four fuzzy clusters. clusterMaker [31] takes a different approach by representing a one-way fuzzy clust...

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...ange and refine the color mapping on the fly during the analysis. The overlaps between biclusters are encoded using bands connecting the biclusters, which satisfies requirement R II. In previous work =-=[33,34]-=-, we have already made use of bands to visualize the relationships between clusters represented as heatmaps in the context of one-way clustering. In Furby, the same approach is applied in both dimensi...

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...ping biclusters. Madeira and Oliveira [5] surveyed different biclustering algorithms with respect to the structure of their output. Bicluster algorithms are often used to analyze gene expression data =-=[6]-=-. In the context of gene expression, a bicluster may correspond to a pathway that is activated in particular samples (the column members) and that contains certain genes (the row members). Each gene* ...

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...re rows and/or columns are reordered to reflect the similarities. Examples for visual analysis tools that provide interactive heatmaps are Mayday [14], Caleydo [15,16] and the Dual Analysis framework =-=[17]-=-. For hierarchical clustering results, the clustered heatmap is commonly extended with a dendrogram that represents the similarities between the rows or columns [18]. The Hierarchical Cluster Explorer...

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...ults, the clustered heatmap is commonly extended with a dendrogram that represents the similarities between the rows or columns [18]. The Hierarchical Cluster Explorer (HCE) [19] and MultiClusterTree =-=[20]-=- are both approaches that allow interactive analysis of hierarchical clustering results. However, as mentioned at the beginning of the Bicluster visualization section, for biclustering results it is o...

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...plot allows analysts to inspect the clusters individually, which addresses requirement R I. However, this makes it impossible to see which rows and columns they share, which violates R II. Jin et al. =-=[23]-=- formulated the reordering issue as an optimization problem and proposed a reordering approach by exploiting analogies to the hypergraph vertex ordering problem. Grothaus et al. [24] propose to duplic...

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...ber of articles on visualizing fuzzy clustering results have been published. Most of them propose extensions to classical clustering visualizations, including parallel coordinate plots [27], heatmaps =-=[28]-=-, and RadVis [29] - a radial visualization technique, in which membership values are projected to polar coordinates. A similar approach was developed by Rueda and Zhang [30], which maps membership val...

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... user study in order to formally evaluate the effectiveness of the presented approach. We also believe that the proposed visualization technique could be applied in the context of subspace clustering =-=[44,45]-=-. Another interesting avenue for future research is the comparison of multiple biclustering results. Additional information A video, demonstrating the interaction with Furby, is available at [46]. Com...

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... user study in order to formally evaluate the effectiveness of the presented approach. We also believe that the proposed visualization technique could be applied in the context of subspace clustering =-=[44,45]-=-. Another interesting avenue for future research is the comparison of multiple biclustering results. Additional information A video, demonstrating the interaction with Furby, is available at [46]. Com...

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...g [44,45]. Another interesting avenue for future research is the comparison of multiple biclustering results. Additional information A video, demonstrating the interaction with Furby, is available at =-=[46]-=-. Competing interests The authors declare that they have no competing interests. Authors’ contributions Marc Streit conceived the project and designed the technique. Marc Streit and Samuel Gratzl wrot...