Parallel coordinates

Abstract: As microbial ecologists take advantage of high-throughput sequencing technologies to describe microbial communities across ever-increasing numbers of samples, new analysis tools are required to relate the distribution of microbes among larger numbers of communities, and to use increasingly rich and standards-compliant metadata to understand the biological factors driving these relationships. In particular, the Earth Microbiome Project drives these needs by profiling the genomic content of tens of thousands of samples across multiple environment types. Features of EMPeror include: ability to visualize gradients and categorical data, visualize different principal coordinates axes, present the data in the form of parallel coordinates, show taxa as well as environmental samples, dynamically adjust the size and transparency of the spheres representing the communities on a per-category basis, dynamically scale the axes according to the fraction of variance each explains, show, hide or recolor points according to arbitrary metadata including that compliant with the MIxS family of standards developed by the Genomic Standards Consortium, display jackknifed-resampled data to assess statistical confidence in clustering, perform coordinate comparisons (useful for procrustes analysis plots), and greatly reduce loading times and overall memory footprint compared with existing approaches. Additionally, ease of sharing, given EMPeror’s small output file size, enables agile collaboration by allowing users to embed these visualizations via emails or web pages without the need for extra plugins. Here we present EMPeror, an open source and web browser enabled tool with a versatile command line interface that allows researchers to perform rapid exploratory investigations of 3D visualizations of microbial community data, such as the widely used principal coordinates plots. EMPeror includes a rich set of controllers to modify features as a function of the metadata. By being specifically tailored to the requirements of microbial ecologists, EMPeror thus increases the speed with which insight can be gained from large microbiome datasets.

Abstract: This article presents the basic results of using the parallel coordinate representation as a high-dimensional data analysis tool. Several alternatives are reviewed. The basic algorithm for parallel coordinates is laid out and a discussion of its properties as a projective transformation is given. Several duality results are discussed along with their interpretations as data analysis tools. Permutations of the parallel coordinate axes are discussed, and some examples are given. Some extensions of the parallel coordinate idea are given. The article closes with a discussion of implementation and some of my experiences.

Abstract: This book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving process, and focusing on parallel coordinates. The barrier, imposed by our three-dimensional habitation and perceptual experience, has been breached by this innovative and versatile methodology. The accurate visualization of multidimensional problems and multivariate data unlocks insights into the role of dimensionality. Beginning with an introductory chapter on geometry, the mathematical foundations are intuitively developed, interlaced with applications to data mining, information visualization, computer vision, geometric modeling,collision avoidance for air traffic and process-control. Many results appear for the first time.Multidimensional lines, planes, proximities, surfaces and their properties are unambiguously recognized (i.e. convexity viewed in any dimension) enabling powerful construction algorithms (for intersections, interior-points, linear-programming). Key features of Parallel Coordinates: * An easy-to-read self-contained chapter on data mining and information visualization * Numerous exercises with solutions, from basic to advanced topics, course projects and research directions * "Fast Track" markers throughout provide a quick grasp of essential material. * Interactive Learning Module (ILM) CD: designed for classroom demonstration and fun experimentation for mastering key topics and examples cross-referenced in the text * Extensive bibliography, index, and a chapter containing a collection of recent results (i.e. visualizing large networks,complex-valued functions and more) Parallel Coordinates requires only an elementary knowledge of linear algebra. It is well-suited for self-study and as a textbook (or companion) for courses on information visualization, data mining, mathematics, statistics, computer science, engineering, finance, management,manufacturing, in scientific disciplines and even the arts

Abstract: Evolutionary multicriteria optimization has traditionally concentrated on problems comprising 2 or 3 objectives. While engineering design problems can often be conveniently formulated as multiobjective optimization problems, these often comprise a relatively large number of objectives. Such problems pose new challenges for algorithm design, visualisation and implementation. Each of these three topics is addressed. Progressive articulation of design preferences is demonstrated to assist in reducing the region of interest for the search and, thereby, simplified the problem. Parallel coordinates have proved a useful tool for visualising many objectives in a two-dimensional graph and the computational grid and wireless Personal Digital Assistants offer technological solutions to implementation difficulties arising in complex system design.