An Algorithmic Framework for Visualising and Exploring Multidimensional Data  

Ross, G., PhD thesis, Department of Computing Science, University of Glasgow, Scotland, 2006.

Visualisation techniques for users and designers of layout algorithms 

Visualisation systems consisting of a set of components through which data and interaction commands flow have been explored by a number of researchers. Such hybrid and multistage algorithms can be used to reduce overall computation time, and to provide views of the data that show intermediate results and the outputs of complementary algorithms. In this paper we present work on expanding the range and variety of such components, with two new techniques for analysing and controlling the performance of visualisation processes. While the techniques presented are quite different, they are unified within HIVE: a visualisation system based upon a data-flow model and visual programming. Embodied within this system is a framework for weaving together our visualisation components to better afford insight into data and also deepen understanding of the process of the data's visualisation. We describe the new components and offer short case studies of their application. We demonstrate that both analysts and visualisation designers can benefit from a rich set of components and integrated tools for profiling performance.

Ross, G., Morrison, A.J., Chalmers, M., Proceedings of the 9th International Conference on Information Visualisation 2005 (London, 2005).

Coordinating Views for Data Visualisation and Algorithmic Profiling  

A number of researchers have designed visualisation systems that consist of multiple components, through which data and interaction commands flow. Such multistage (hybrid) models can be used to reduce algorithmic complexity, and to open up intermediate stages of algorithms for inspection and steering. In this paper we present work on aiding the developer and the user of such algorithms through the application of interactive visualisation techniques. We present a set of tools designed to profile the performance of other visualisation components, and provide further functionality for the exploration of high dimensional data sets. Case studies are provided, illustrating the application of the profiling modules to a number of data sets. Through this work we are exploring ways in which techniques traditionally used to prepare for visualisation runs, and to retrospectively analyse them, can find new uses within the context of a multi-component visualisation system.

Ross, G., Morrison, A.J., Chalmers, M., Coordinated and Multiple Views in Exploratory Visualization 2004 (London, 2004).

A Visual Workspace for Constructing Hybrid MDS Algorithms and Coordinating Multiple Views  

Data can be distinguished according to volume, variable types and distribution, and each of these characteristics imposes constraints upon the choice of applicable algorithms for their visualisation. This has led to an abundance of often disparate algorithmic techniques. Previous work has shown that a hybrid algorithmic approach can be successful in addressing the impact of data volume on the feasibility of multidimensional scaling (MDS). This paper presents a system and framework in which a user can easily explore algorithms as well as their hybrid conjunctions and the data flowing through them. Visual programming and a novel algorithmic architecture let the user semi-automatically define data flows and the co-ordination of multiple views of algorithmic and visualisation components. We propose that our approach has two main benefits: significant improvements in run times of MDS algorithms can be achieved, and intermediate views of the data and the visualisation program structure can provide greater insight and control over the visualisation process.

Ross, G. , Chalmers, M., Information Visualization 2(4) December 2003, pp. 247-257.

A Visual Workspace for Hybrid Multidimensional Scaling Algorithms  

In visualising multidimensional data, it is well known that different types of data require different types of algorithms to process them. Data sets might be distinguished according to volume, variable types and distribution, and each of these characteristics imposes constraints upon the choice of applicable algorithms for their visualisation. Previous work has shown that a hybrid algorithmic approach can be successful in addressing the impact of data volume on the feasibility of multidimensional scaling (MDS). This suggests that hybrid combinations of appropriate algorithms might also successfully address other characteristics of data. This paper presents a system and framework in which a user can easily explore hybrid algorithms and the data flowing through them. Visual programming and a novel algorithmic architecture let the user semi-automatically define data flows and the co-ordination of multiple views.

Ross, G. , Chalmers, M., IEEE Symposium on Information Visualization (Seattle, USA), 2003.

Fast Multidimensional Scaling through Sampling, Springs and Interpolation  

The term 'proximity data' refers to data sets within which it is possible to assess the similarity of pairs of objects. Multidimensional scaling (MDS) is applied to such data and attempts to map high-dimensional objects onto low-dimensional space through the preservation of these similarity relationships. Standard MDS techniques have in the past suffered from high computational complexity and, as such, could not feasibly be applied to data sets over a few thousand objects in size. Through a novel hybrid approach based upon stochastic sampling, interpolation and spring models, we have designed an algorithm running in ο(N√N). Using Chalmers' 1996 ο(N2) spring model as a benchmark for the evaluation of our technique, we compare layout quality and run times using data sets of synthetic and real data. Our algorithm executes significantly faster than Chalmers' 1996 algorithm, whilst producing superior layouts. In reducing complexity and run time, we allow the visualisation of data sets of previously infeasible size. Our results indicate that our method is a solid foundation for interactive and visual exploration of data.

Morrison, A.J., Ross, G., Chalmers, M., Information Visualization 2(1) March 2003, pp. 68-77.

A Hybrid Layout Algorithm for Sub-Quadratic Multidimensional Scaling  

Many clustering and layout techniques have been used for structuring and visualising complex data. This paper is inspired by a number of such contemporary techniques and presents a novel hybrid approach based upon stochastic sampling, interpolation and spring models. We use Chalmers' 1996 ο(N2) spring model as a benchmark when evaluating our technique, comparing layout quality and run times using data sets of synthetic and real data. Our algorithm runs in ο(N√N) and executes significantly faster than Chalmers' 1996 algorithm, whilst producing superior layouts. In reducing complexity and run time, we allow the visualisation of data sets of previously infeasible size. Our results indicate that our method is a solid foundation for interactive and visual exploration of data.

Morrison, A.J., Ross, G., Chalmers, M., IEEE Symposium on Information Visualization (Boston, USA), 2002.

Combining and comparing clustering and layout algorithms  

Many clustering and layout techniques have been used for structuring and visualising complex data. This paper explores a number of combinations and variants of sampling, K-means clustering and spring models in making such layouts, using Chalmers' 1996 linear iteration time spring model as a benchmark. This algorithm runs in ο(N2) time overall, but the run times for the new algorithms we describe reach ο(N√N). We compare their layout quality and run times in laying out two collections of synthetic data, drawing samples from each collection of sizes ranging from 1000 to 20000. Based on these comparisons, we outline a number of avenues for future work that may further reduce time complexity and improve layout quality.

Morrison, A.J., Ross, G., Chalmers, M., Department of Computing Science, University of Glasgow (2002).