Using hyperbolic geometry for visualisation of concept spaces for adaptive e-learning

The Concept Space or Domain Ontology is an important part of an adaptive eLearning course. Understanding the structure of a concept space from a traditional concept map is not, however, always straightforward. Hyperbolic trees are one alternative representation which can allow easier comprehension. 1 Traditional Concept Space Visualisation Methods A fundamental part of an Adaptive eLearning system is the Concept Space or Domain Ontology. This provides a conceptual model of the subject matter being studied and allows a pedagogy and adaptivity to be constructed around it. Concept Spaces may be encoded in various formats (commonly XML using a standard such as OWL[9]). Traditionally, however, they have been visualised using a concept map diagram, a downward-branching, heirarchical tree structure. See Figure 1 for XML and tree representation of the same simple map. Fig. 1. A simple Concept Space in XML and Graph format; the two are equivalent. In mathematical terms, a concept space map is essentially a directed acyclical graph[11], a generalization of a tree structure in which certain subtrees can be shared by different parts of the tree. However in practice, cycles are possible in a concept map when different types of relationship are represented. Generally the tools used to create and visualise concept spaces are quite forgiving in mathematical terms and loops or cycles are tolerated. Fig. 2. A graph with multiple root nodes and shared sub-trees. 2 Representing large Concept Spaces This paper concentrates on large concept spaces, such as would be necessary to describe very large software systems. 2.1 Problems with large concept spaces Where a large concept space must be created and maintained, the traditional concept map becomes an unweildy tool for visualisation. Using a traditional concept-space editor it is possible to view the concept space graphically, but the sheer size of a very large concept space means that it is not possible to view the entire concept space on-screen at the one time without zooming out so far that the labels on concepts and relationships are no longer readable. Similarly, the number of relationships makes it extremely difficult to understand the structure of the concept space. The difficulty in interpreting a concept space from a concept map diagram is of particular concern where the course creators are not the same people as the domain experts who created the concept space mapping. 2.2 Case Study: The R-GMA course An adaptive course on R-GMA is being developed at Trinity College. This is part of an ongoing project to provide Adapitve e-Learning training on Grid technologies to Scientists and other Grid users. R-GMA[5][14] is a relational implementation of the Grid Monitoring Architecture (GMA)[12] of the Global Grid Forum (GGF), which is an information and monitoring architecture for Grid Computing Systems. R-GMA was originally developed as part of the European DataGrid (EDG) and is currently being further developed as part of the EU EGEE[4] project. R-GMA consists of a number of services which work together to produce the effect of a distributed virtual database whereby Producers publish information about grid services to the grid and Consumers query and use this information. It is relational in the sense that Producers announce what they have to publish via a SQL CREATE TABLE statement and publish with a SQL INSERT and that Consumers use a SQL SELECT to collect the information they need. The R-GMA adaptive course concept space contains 99 concepts and an impressive 267 relationships. A concept space of this scale is not easily handled by traditional concept space visualisation methods. Fig. 3. The R-GMA Concept Space in ACCT