Visualizing dimensionality reduction of systems biology data

One of the challenges in analyzing high-dimensional expression data is the detection of important biological signals. A common approach is to apply a dimension reduction method, such as principal component analysis. Typically, after application of such a method the data is projected and visualized in the new coordinate system, using scatter plots or profile plots. These methods provide good results if the data have certain properties which become visible in the new coordinate system and which were hard to detect in the original coordinate system. Often however, the application of only one method does not suffice to capture all important signals. Therefore several methods addressing different aspects of the data need to be applied. We have developed a framework for linear and non-linear dimension reduction methods within our visual analytics pipeline SpRay. This includes measures that assist the interpretation of the factorization result. Different visualizations of these measures can be combined with functional annotations that support the interpretation of the results. We show an application to high-resolution time series microarray data in the antibiotic-producing organism Streptomyces coelicolor as well as to microarray data measuring expression of cells with normal karyotype and cells with trisomies of human chromosomes 13 and 21

Structuring visual exploratory analysis of skill demand

The analysis of increasingly large and diverse data for meaningful interpretation and question answering is handicapped by human cognitive limitations. Consequently, semi-automatic abstraction of complex data within structured information spaces becomes increasingly important, if its knowledge content is to support intuitive, exploratory discovery. Exploration of skill demand is an area where regularly updated, multi-dimensional data may be exploited to assess capability within the workforce to manage the demands of the modern, technology- and data-driven economy. The knowledge derived may be employed by skilled practitioners in defining career pathways, to identify where, when and how to update their skillsets in line with advancing technology and changing work demands. This same knowledge may also be used to identify the combination of skills essential in recruiting for new roles. To address the challenges inherent in exploring the complex, heterogeneous, dynamic data that feeds into such applications, we investigate the use of an ontology to guide structuring of the information space, to allow individuals and institutions to interactively explore and interpret the dynamic skill demand landscape for their specific needs. As a test case we consider the relatively new and highly dynamic field of Data Science, where insightful, exploratory data analysis and knowledge discovery are critical. We employ context-driven and task-centred scenarios to explore our research questions and guide iterative design, development and formative evaluation of our ontology-driven, visual exploratory discovery and analysis approach, to measure where it adds value to users’ analytical activity. Our findings reinforce the potential in our approach, and point us to future paths to build on

Superposition rules, Lie theorem and partial differential equations

A rigorous geometric proof of the Lie's Theorem on nonlinear superposition rules for solutions of non-autonomous ordinary differential equations is given filling in all the gaps present in the existing literature. The proof is based on an alternative but equivalent definition of a superposition rule: it is considered as a foliation with some suitable properties. The problem of uniqueness of the superposition function is solved, the key point being the codimension of the foliation constructed from the given Lie algebra of vector fields. Finally, as a more convincing argument supporting the use of this alternative definition of superposition rule, it is shown that this definition allows an immediate generalization of Lie's Theorem for the case of systems of partial differential equations.Comment: 22 page

Visualising interactions in bi- and triadditive models for three-way tables

This paper concerns the visualisation of interaction in three-way arrays. It extends some standard ways of visualising biadditive modelling for two-way data to the case of three-way data. Three-way interaction is modelled by the Parafac method as applied to interaction arrays that have main effects and biadditive terms removed. These interactions are visualised in three and two dimensions. We introduce some ideas to reduce visual overload that can occur when the data array has many entries. Details are given on the interpretation of a novel way of representing rank-three interactions accurately in two dimensions. The discussion has implications regarding interpreting the concept of interaction in three-way arrays

Glyphs for exploring crowd-sourced subjective survey classification

The findings drawn from opinion survey responses are usually made by producing summary charts or conducting statistical analysis. Both involve data aggregation and filtering as exploring the unaggregated data has traditionally been impractical or error-prone for large numbers of responses. We propose the use of glyphs with parallel coordinate plots to show all survey responses in a single view and design an interactive visual analytics tool around the representation to explore the data. We use this software for a ‘photo content assessment’ survey, where 359 participants classify 900 images by seven criteria. The proposed approach allows all 8,434 responses (49,285 answers to questions in total) to be represented in a single view and helps analysts to both clean the data and understand the nature of the survey responses. We describe the construction of the survey response glyphs and the interface to the interactive visual analytics software and generalise the design principles that arise from the approach. We apply the tool to two other datasets to evaluate the technique and to confirm its wider applicability for surveys with Likert scale responses

A grid-enabled problem solving environment for parallel computational engineering design

This paper describes the development and application of a piece of engineering software that provides a problem solving environment (PSE) capable of launching, and interfacing with, computational jobs executing on remote resources on a computational grid. In particular it is demonstrated how a complex, serial, engineering optimisation code may be efficiently parallelised, grid-enabled and embedded within a PSE. The environment is highly flexible, allowing remote users from different sites to collaborate, and permitting computational tasks to be executed in parallel across multiple grid resources, each of which may be a parallel architecture. A full working prototype has been built and successfully applied to a computationally demanding engineering optimisation problem. This particular problem stems from elastohydrodynamic lubrication and involves optimising the computational model for a lubricant based on the match between simulation results and experimentally observed data

A Comprehensive Three-Dimensional Model of the Cochlea

The human cochlea is a remarkable device, able to discern extremely small amplitude sound pressure waves, and discriminate between very close frequencies. Simulation of the cochlea is computationally challenging due to its complex geometry, intricate construction and small physical size. We have developed, and are continuing to refine, a detailed three-dimensional computational model based on an accurate cochlear geometry obtained from physical measurements. In the model, the immersed boundary method is used to calculate the fluid-structure interactions produced in response to incoming sound waves. The model includes a detailed and realistic description of the various elastic structures present. In this paper, we describe the computational model and its performance on the latest generation of shared memory servers from Hewlett Packard. Using compiler generated threads and OpenMP directives, we have achieved a high degree of parallelism in the executable, which has made possible several large scale numerical simulation experiments that study the interesting features of the cochlear system. We show several results from these simulations, reproducing some of the basic known characteristics of cochlear mechanics.Comment: 22 pages, 5 figure

Visualization of Time-Series Data in Parameter Space for Understanding Facial Dynamics

Over the past decade, computer scientists and psychologists have made great efforts to collect and analyze facial dynamics data that exhibit different expressions and emotions. Such data is commonly captured as videos and are transformed into feature-based time-series prior to any analysis. However, the analytical tasks, such as expression classification, have been hindered by the lack of understanding of the complex data space and the associated algorithm space. Conventional graph-based time-series visualization is also found inadequate to support such tasks. In this work, we adopt a visual analytics approach by visualizing the correlation between the algorithm space and our goal – classifying facial dynamics. We transform multiple feature-based time-series for each expression in measurement space to a multi-dimensional representation in parameter space. This enables us to utilize parallel coordinates visualization to gain an understanding of the algorithm space, providing a fast and cost-effective means to support the design of analytical algorithms

Computational steering of a multi-objective evolutionary algorithm for engineering design

The execution process of an evolutionary algorithm typically involves some trial and error. This is due to the difficulty in setting the initial parameters of the algorithm—especially when little is known about the problem domain. This problem is magnified when applied to many-objective optimisation, as care is needed to ensure that the final population of candidate solutions is representative of the trade-off surface. We propose a computational steering system that allows the engineer to interact with the optimisation routine during execution. This interaction can be as simple as monitoring the values of some parameters during the execution process, or could involve altering those parameters to influence the quality of the solutions produced by the optimisation process. The implementation of this steering system should provide the ability to tailor the client to the hardware available, for example providing a lightweight steering and visualisation client for use on a PDA