Julian Heinrich

State of the Art of Parallel Coordinates

This work presents a survey of the current state of the art of visualization techniques for parallel coordinates. It covers geometric models for constructing parallel coordinates and reviews methods for creating and understanding visual representations of parallel coordinates. The classification of these methods is based on a taxonomy that was established from the literature and is aimed at guiding researchers to find existing techniques and identifying white spots that require further research. The techniques covered in this survey are further related to an established taxonomy of knowledge-discovery tasks to support users of parallel coordinates in choosing a technique for their problem at hand. Finally, we discuss the challenges in constructing and understanding parallel-coordinates plots and provide some examples from different application domains.

Continuous Parallel Coordinates

Typical scientific data is represented on a grid with appropriate interpolation or approximation schemes,defined on a continuous domain. The visualization of such data in parallel coordinates may reveal patterns latently contained in the data and thus can improve the understanding of multidimensional relations. In this paper, we adopt the concept of continuous scatterplots for the visualization of spatially continuous input data to derive a density model for parallel coordinates. Based on the point-line duality between scatterplots and parallel coordinates, we propose a mathematical model that maps density from a continuous scatterplot to parallel coordinates and present different algorithms for both numerical and analytical computation of the resulting density field. In addition, we show how the 2-D model can be used to successively construct continuous parallel coordinates with an arbitrary number of dimensions. Since continuous parallel coordinates interpolate data values within grid cells, a scalable and dense visualization is achieved, which will be demonstrated for typical multi-variate scientific data.

Unexpected features of the dark proteome

Significance A key remaining frontier in our understanding of biological systems is the “dark proteome”—that is, the regions of proteins where molecular conformation is completely unknown. We systematically surveyed these regions, finding that nearly half of the proteome in eukaryotes is dark and that, surprisingly, most of the darkness cannot be accounted for. We also found that the dark proteome has unexpected features, including an association with secretory tissues, disulfide bonding, low evolutionary conservation, and very few known interactions with other proteins. This work will help future research shed light on the remaining dark proteome, thus revealing molecular processes of life that are currently unknown. We surveyed the “dark” proteome–that is, regions of proteins never observed by experimental structure determination and inaccessible to homology modeling. For 546,000 Swiss-Prot proteins, we found that 44–54% of the proteome in eukaryotes and viruses was dark, compared with only ∼14% in archaea and bacteria. Surprisingly, most of the dark proteome could not be accounted for by conventional explanations, such as intrinsic disorder or transmembrane regions. Nearly half of the dark proteome comprised dark proteins, in which the entire sequence lacked similarity to any known structure. Dark proteins fulfill a wide variety of functions, but a subset showed distinct and largely unexpected features, such as association with secretion, specific tissues, the endoplasmic reticulum, disulfide bonding, and proteolytic cleavage. Dark proteins also had short sequence length, low evolutionary reuse, and few known interactions with other proteins. These results suggest new research directions in structural and computational biology.

Progressive splatting of continuous scatterplots and parallel coordinates

Continuous scatterplots and parallel coordinates are used to visualize multivariate data defined on a continuous domain. With the existing techniques, rendering such plots becomes prohibitively slow, especially for large scientific datasets. This paper presents a scalable and progressive rendering algorithm for continuous data plots that allows exploratory analysis of large datasets at interactive framerates. The algorithm employs splatting to produce a series of plots that are combined using alpha blending to achieve a progressively improving image. For each individual frame, splats are obtained by transforming Gaussian density kernels from the 3‐D domain of the input dataset to the respective data domain. A closed‐form analytic description of the resulting splat footprints is derived to allow pre‐computation of splat textures for efficient GPU rendering. The plotting method is versatile because it supports arbitrary reconstruction or interpolation schemes for the input data and the splatting technique is scalable because it chooses splat samples independently from the size of the input dataset. Finally, the effectiveness of the method is compared to existing techniques regarding rendering performance and quality.

Aquaria: simplifying discovery and insight from protein structures

To the Editor: Since the discovery of the DNA double helix, biologists have been aware that atomic-scale three-dimensional (3D) structures can provide significant insight. The Protein Data Bank1 (PDB) contains a wealth of structural information, but few biologists take full advantage of it2. Thus, we developed Aquaria (http://aquaria. ws), a publicly available web resource that streamlines and simplifies the process of gleaning insight from protein structures. In contrast to most molecular graphics tools (for example, Astex3 or Chimera4), the user interface of Aquaria is organized primarily by protein sequence, not structure (Fig. 1). A user starts by specifying a protein of interest by name and organism (Supplementary Fig. 1), by identifier or by URL (for example, http://aquaria.ws/ P04637); Aquaria then generates a concise visual summary of all related PDB structures (Fig. 1 and Supplementary Methods), using a precalculated all-against-all comparison of Swiss-Prot5 and PDB1 sequences (updated monthly). The related structures are grouped first by alignment to the specified sequence and second by oligomeric state. Structures are then ranked—in both groupings—by sequence similarity to the specified protein. Users can quickly review all known structural information for a protein and find the structures most relevant to them (Supplementary Video 1). Initially, 3D structures are colored to highlight amino acid differences from the specified protein sequence, with bright, saturated colors indicating identical residues and with slightly dark and very dark coloring indicating conserved and nonconserved substitutions, respectively (Fig. 1). Aquaria also allows mapping of InterPro6 and UniProt5 sequence features (for example, domains, single-nucleotide polymorphisms or posttranslational modifications) onto 3D structures: a simple yet effective way to gain insight into molecular function2 (Supplementary Figs. 2 and 3). Aquaria is designed for biologists; its user interface creates clear and useful default views that show only the most relevant structural information tightly integrated with sequence, features and text that provide biological context. Aquaria uses a minimal set of mouse-based controls that are intuitive yet powerful7. For example, its “Autofocus” feature allows exploration of large complexes by focusing on one molecule at a time. Aquaria can also be controlled via hand gestures using the Leap Motion8. Currently, Aquaria contains 46 million precalculated sequenceto-structure alignments, resulting in at least one matching structure for 87% of Swiss-Prot proteins and a median of 35 structures per protein; this provides a depth of sequence-to-structure information currently not available from other resources.

SpRay: A visual analytics approach for gene expression data

We present a new application, SpRay, designed for the visual exploration of gene expression data. It is based on an extension and adaption of parallel coordinates to support the visual exploration of large and high-dimensional datasets. In particular, we investigate the visual analysis of gene expression data as generated by micro-array experiments; We combine refined visual exploration with statistical methods to a visual analytics approach that proved to be particularly successful in this application domain. We will demonstrate the usefulness on several multidimensional gene expression datasets from different bioinformatics applications.

BiCluster viewer: a visualization tool for analyzing gene expression data

Exploring data sets by applying biclustering algorithms was first introduced in gene expression analysis. While the generated biclustered data grows with increasing rates due to the technological progress in measuring gene expression data, the visualization of the computed biclusters still remains an open issue. For efficiently analyzing the vast amount of gene expression data, we propose an algorithm to generate and layout biclusters with a minimal number of row and column duplications on the one hand and a visualization tool for interactively exploring the uncovered biclusters on the other hand. In this paper, we illustrate how the BiCluster Viewer may be applied to highlight detected biclusters generated from the original data set by using heatmaps and parallel coordinate plots. Many interactive features are provided such as ordering functions, color codings, zooming, details-on-demand, and the like. We illustrate the usefulness of our tool in a case study where yeast data is analyzed. Furthermore, we conducted a small user study with 4 participants to demonstrate that researchers are able to learn und use our tool to find insights in gene expression data very rapidly.

The Parallel Coordinates Matrix

We introduce the parallel coordinates matrix (PCM) as the counterpart to the scatterplot matrix (SPLOM). Using a graph-theoretic approach, we determine a list of axis orderings such that all pairwise relations can be displayed without redundancy while each parallel-coordinates plot can be used independently to visualize all variables of the dataset. Therefore, existing axis-ordering algorithms, rendering techniques, and interaction methods can easily be applied to the individual parallel-coordinates plots. We demonstrate the value of the PCM in two case studies and show how it can serve as an overview visualization for parallel coordinates. Finally, we apply existing focus-and-context techniques in an interactive setup to support a detailed analysis of multivariate data.

iHAT: interactive Hierarchical Aggregation Table for Genetic Association Data

In the search for single-nucleotide polymorphisms which influence the observable phenotype, genome wide association studies have become an important technique for the identification of associations between genotype and phenotype of a diverse set of sequence-based data. We present a methodology for the visual assessment of single-nucleotide polymorphisms using interactive hierarchical aggregation techniques combined with methods known from traditional sequence browsers and cluster heatmaps. Our tool, the interactive Hierarchical Aggregation Table (iHAT), facilitates the visualization of multiple sequence alignments, associated metadata, and hierarchical clusterings. Different color maps and aggregation strategies as well as filtering options support the user in finding correlations between sequences and metadata. Similar to other visualizations such as parallel coordinates or heatmaps, iHAT relies on the human pattern-recognition ability for spotting patterns that might indicate correlation or anticorrelation. We demonstrate iHAT using artificial and real-world datasets for DNA and protein association studies as well as expression Quantitative Trait Locus data.

Visual Analysis of Trajectories in Multi-Dimensional State Spaces

Multi‐dimensional data originate from many different sources and are relevant for many applications. One specific sub‐type of such data is continuous trajectory data in multi‐dimensional state spaces of complex systems. We adapt the concept of spatially continuous scatterplots and spatially continuous parallel coordinate plots to such trajectory data, leading to continuous‐time scatterplots and continuous‐time parallel coordinates. Together with a temporal heat map representation, we design coordinated views for visual analysis and interactive exploration. We demonstrate the usefulness of our visualization approach for three case studies that cover examples of complex dynamic systems: cyber‐physical systems consisting of heterogeneous sensors and actuators networks (the collection of time‐dependent sensor network data of an exemplary smart home environment), the dynamics of robot arm movement and motion characteristics of humanoids.