This paper combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these structures using the tools of category theory to provide a general framework for understanding visualization in practice, including: Relationships between systems, data collected from those systems, renderings of those data in the form of representations, the reading of those representations to create visualizations, and the use of those visualizations to create knowledge and understanding of the system under inspection. The resulting framework is validated by demonstrating how familiar information visualization concepts (such as literalness, sensitivity, redundancy, ambiguity, generalizability, and chart junk) arise naturally from it and can be defined formally and precisely. This paper generalizes previous work on the formal characterization of visualization by, inter alia, Ziemkiewicz and Kosara and allows us to formally distinguish properties of the visualization process that previous work does not.

Small-world networks are a very commonly occurring type of graph in the real-world, which exhibit a clustered structure that is not well represented by current graph layout algorithms. In many cases we also have information about the nodes in such graphs, which are typically depicted on the graph as node colour, shape or size. Here we demonstrate that these attributes can instead be used to layout the graph in high-dimensional data space. Then using a dimension reduction technique, targeted projection pursuit, the graph layout can be optimised for displaying clustering. The technique out-performs force-directed layout methods in cluster separation when applied to a sample, artificially generated, small-world network.

High-dimensional data is, by its nature, difficult to visualise. Many current techniques involve reducing the dimensionality of the data, which results in a loss of information. Targeted Projection Pursuit is a novel method for visualising high-dimensional datasets which allows the user to interactively explore the space of possible views to find those that meet their requirements. A prototype tool that utilises this method is introduced, and is shown to allow users to explore data through an interface that is transparent and efficient. The tool and underlying technique are general purpose - applicable to any high-dimensional numeric data, and supporting a wide range of exploratory data analysis activities - but are evaluated on three particular tasks using gene expression data: identifying discriminatory genes, visualising diagnostic classes, and detecting misdiagnosed samples. It is found to perform well in comparison with standard techniques.

UNLABELLED: We present a novel method for finding low-dimensional views of high-dimensional data: Targeted Projection Pursuit. The method proceeds by finding projections of the data that best approximate a target view. Two versions of the method are introduced; one version based on Procrustes analysis and one based on an artificial neural network. These versions are capable of finding orthogonal or non-orthogonal projections, respectively. The method is quantitatively and qualitatively compared with other dimension reduction techniques. It is shown to find 2D views that display the classification of cancers from gene expression data with a visual separation equal to, or better than, existing dimension reduction techniques. AVAILABILITY: source code, additional diagrams, and original data are available from http://computing.unn.ac.uk/staff/CGJF1/tpp/bioinf.html