Following the Guidon (With Table of Contents & List of Illustrations that are Interactive)
These values are the results of an aggregation function that can be different for every internal node. The aggregation function depends on several factors, including the scale type of the aggregated items, their distribution, or the degrees of freedom for the visual representation of an aggregate area, color, texture, etc.
Choosing the appropriate aggregation function therefore is an important part of the design choices to be made for the problem at hand and will be discussed for iHAT in the next section. Another aspect to consider is the choice of color maps applied to the values of all nodes in the tree. One might use different mappings for leaf-nodes and for internal aggregated nodes to distinguish between both types and to provide a visual hint of where the user is currently navigating within the hierarchy. Depending on the underlying data type, internal nodes might carry information about the local properties of the tree, such as the number of immediate children, the number of leaf-nodes, the height in the tree, etc.
As described in the previous section, aggregation of rows and columns into hierarchies requires several design choices to be made, as there are many different approaches to realize the general principle. In this section, we therefore provide the design choices made for our implementation iHAT. The motivation for iHAT was to join sequence views with heatmaps to provide a visualization for association studies. To communicate this separation, we decided to split the general table layout into two aligned views: the sequence view containing biological sequences with a fixed alphabet represented as nominal data and a separate heatmap view for the mostly ratio-scaled metadata, usually representing the corresponding phenotypes.
Since the appropriate color map greatly depends on the data that is visualized [ 24 ], we adopted general design principles from the visualization literature [ 25 , 26 ] for the different scale types. In the heatmap view, ratio-scaled values are colored using a single-hue color map with varying saturation. For nominal columns, we adapt the number of different hues to the number of classes contained in the respective column and map the relative frequency of the consensus the most frequent child item to saturation.
In this way, the color scheme is used to visualize the un- certainty of the consensus. Nucleic and amino acid sequences are interpreted as nominal variables for which iHAT offers color maps used by tools like ClustalX [ 18 ], Jalview [ 14 ], Lesk [ 27 ], or the Nucleic Acid Database [ 28 ].
Based on these properties and their intersections, the Venn diagram divides amino acids into seven groups. Amino acids are thus colored with respect to the group to which they belong, where each group is assigned a color. This newly developed color scheme helps the user with getting an immediate impression of the biochemical properties of amino acids within the sequences.
Color scheme. Left: Venn diagram grouping of amino acids based on the biochemical properties: hydrophobicity, size and polarity. Colors for the intersection groups are derived by additive blending of the colors of respective properties. Right, top: Alternative color schemes for amino acids note that the scheme labeled ClustalW is based on the default coloring without color parameter file with N, D, Q, E, A and C mapped to purple.
Right, bottom: Alternative color schemes for nucleic acids. Although aggregation of columns is possible in general, we decided to allow hierarchies only for metadata columns, as there was no practical implication for column aggregation in the sequence view. Furthermore, we do not render dendrograms for columns in order to better use the given screen real estate. For multivariate data without existing hierarchy, we create a tree of height one, where every sample is a child node of the root and a leaf node of the tree.
Internal nodes of the hierarchy can be collapsed resulting in consensus rows which are assigned unique numerical labels starting with a capital 'A'. For nominal values, the relative frequency of the character in the consensus is mapped to saturation of the respective color. For ratio-scaled values, the mean is used instead. The row-hierarchy has been created using the automatic aggregation feature: A internal nodes at depth one correspond to rows with the same symptoms with children grouped by mortality.
B Collapsing internal nodes at level 2 show the consensus of rows with the same value for symptoms. Hiding labels improves the visual pattern matching due to uncluttering, as we can discover columns with the same trend of saturation. Several consensus rows internal nodes can also be joined into a new consensus row. Interactively constructed trees can be exported in Newick format and imported again for further investigation.
The dendrogram itself is visualized as left-to-right node link diagram. To reduce the number of rows and to compare subclasses of the hierarchy, internal nodes can be collapsed to show a consensus row or expanded to show all underlying samples of the aggregate individually. Given the tabular layout of visual items and visual aggregates, we use color to convey information about the distribution of items.
Depending on the color space, color can be split into further variables such as hue, saturation, and value or red, green, and blue, which gives more degrees of freedom for the design of visual aggregates.
However, as a simple mapping of aggregate variables to these color changes very likely interferes with the coloring principles outlined in the previous section, we use the following data-type dependent strategies to assign aggregate values to colors. For nominal data, we use multi-hue bivariate color maps to indicate class membership and map saturation with constant value to the relative frequency of the consensus.
We use the HSV color space [ 30 ] to choose the final color: The hues required to distinguish classes can be chosen by distributing all classes over the range of available hues. This strategy enables one to use saturation as an indication for the uncertainty of the most frequent child item. While this approach can easily be automated, it does not scale well for a large number of classes. For instance, the color scheme used for amino acids as introduced in the previous section allows the user to differentiate between groups of amino acids, whereas differences within a group are less prominent.
Ordinal data is treated similarly to nominal data with respect to aggregation strategies and color mapping because color maps for ordered data highly depend on the semantics of the data. We use a discrete color table for the ordinal value and represent uncertainty equivalently to nominal values. Following the design principles for ratio and interval data [ 26 ], we are interested in conveying quantitative information using the color channel.
Data on a ratio scale is aggregated by computing the mean value of all children. Different color maps exist that ensure that the equivalence of distances of ratios and intervals is perceived correctly. We map ratio values to a univariate single-hue color map, where the ratio value determines saturation. For interval data, we found that it was most useful to convert it to a ratio scale, as this allows for the computation of the mean value and for using the same color mappings as for ratio-scaled data.
Considering that the color of the initial data can be distributed equally over a range of saturations on a single-hue colormap, in-between values as computed by the mean are easier to identify by the viewer as for ratio-scaled data. In addition to the design choices presented in the previous sections, iHAT supports sorting and filtering of rows and columns as well as automatic aggregation of rows.
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As the case studies in this paper make use of these features, a short description thereof is given in the following sections. Rows can be sorted with respect to selected metadata columns.
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- iHAT: interactive Hierarchical Aggregation Table for Genetic Association Data!
If several metadata items are used for sorting, this results in a nested sorting, which is a useful feature to interactively construct a hierarchy of samples. Columns can be filtered to hide uninteresting information. Reasonable filtering options should always be based on the underlying data.
Since our application targets sequences of nucleic acids or amino acids as samples , current filtering options were designed to hide columns that are too homogeneous or too noisy.
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This supports the process of revealing associations between genotype and phenotype. Interactive hierarchical aggregation for amino acid sequences. Using iHAT to find sequence positions correlated with virulence in 15 sequences of the neuraminidase protein of H5N1 influenza virus samples. A the unfiltered alignment using the color map based on Venn diagram grouping; B after removing uninformative columns parameters shown in the dialog window below the alignment , only ten positions remain.
C sequences were sorted by virulence and internal nodes were added aggregating by 2 levels of virulence ; D after aggregation on collapsing the internal tree nodes, the final alignment of the two aggregated sequences labeled with unique numerical identifiers starting with 'A' clearly shows positions correlated with virulence.
Columns that contain mostly gaps resulting from the alignment do not contain any information that helps the user find correlations with the phenotype metadata and can therefore be hidden. While unique insertions or deletions may convey a difference in phenotype, they should at least occur in a certain percentage of the underlying population to allow statistically meaningful conclusions.
By using a row-order dependent noise filter, we aim at hiding columns that violate this assumption, i. Using iHAT, we found that a common task is to sort rows by one or more metadata columns and aggregate rows with common metadata values. With automatic aggregation , iHAT uses selected metadata columns to automatically build the aggregation tree. This is achieved by successively aggregating rows with the same metadata value for all selected columns, in the order of selection.
To demonstrate the functionality and usefulness of iHAT, we used it for the analysis of nucleic acid sequences and amino acid sequences with associated metadata. Here, rows represent sequences, columns represent alignment positions, and cells contain nucleic acids amino acids , or metadata of scale type ratio, interval, nominal, or ordinal.
In the matrix view, each position is colored either by nucleic acid or amino acid or attribute value. Depending on the scale type, different color schemes are used. One of the main features of iHAT is the aggregation of rows here sequences. As sequences are of nominal type, the nucleic acid amino acid of the aggregated consensus sequence at position i is chosen as the one with largest frequency i.
The frequency of the nucleic acid or amino acid in the consensus i. For ratio values within metadata , the mean value is taken as the consensus.
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When using filtering of columns and sorting and aggregation of rows based on some metadata in combination with colormapping, column specific patterns emerge that facilitate the detailed analysis of correlation between nucleic acid amino acid sequences and metadata e. For the analysis of nucleic acid data, our general approach is to associate genotype sequence with phenotype data metadata with the help of the matrix-based alignment view.
The dataset consists of 58 sequences with nucleic acids each. For every sequence, a set of five attributes describing the associated phenotype is given. Four of these are of scale type ordinal symptoms , mortality , complications , at risk vulnerability and one of type nominal drug resistance. For a detailed explanation of the metadata types and their values, we refer to [ 20 ]. Based on the ratio values, we computed a score by aggregating over all metadata columns.
The resulting column is computed as the average of all phenotypes, which is a good representation of the "overall virulence" in this application. Note that in our previous work [ 22 ], the same score was computed with an external tool before loading the data into iHAT. The sorted table shows "overall virulence" in the rightmost column, indicated by the increasing saturation of red with increasing values.
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However, it is difficult to find columns in the sequence where this pattern is reflected. The automatic aggregation feature of iHAT allows us to aggregate rows by a user-defined metadata column. Using this feature results in a condensed view where the high variation in different colors is replaced with a high variation of saturation in the individual columns. Here, column seems to express an inverse pattern to the "overall virulence", with decreasing saturation from top to bottom.
After an additional row-aggregation step, averaging two levels of "overall virulence", more columns with the same or the inverse pattern can be seen. Column shows the same pattern, while columns , , , and show the inverse pattern. With this information, we can go back and look at the fully expanded table again. Here, we see that column has an increasing number of cytosine yellow from top to bottom, but that most of it occurs at low levels of "overall virulence".
Column , in contrast, appears to have an equal distribution of cytosine at the bottom-half of the table, indicating that this mutation occurs with the same frequency for either low or high virulence and that there is nothing in between. Set Osomatsu's Hitotsumatsu pine Parker vol. III Ausf. Carol, 32 sm. Elemental Evil Bosses. Collector's Edition. Millions of patients throughout the United States suffer from chronic wounds associated with diabetes, vascular disease, obesity and other health concerns.
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Thesis and Dissertation