A decomposition framework for visualising telecommunications and cyberspace systems

A new technique has been developed to visualise massive amounts of telecommunications and network data. This is achieved by representing the discrete data in the form of a continuous surface map similar to meteorological weather maps to enable local and large scale features or behaviours to be viewed and analysed.

The technique has two steps: (1) The discrete data is interpreted as a set of vectors positioned on a geographical map; (2) The set of vectors are transformed into a 3 dimensional surface called a torque surface.

The transformation utilises the notion of physical torque defined by vector cross product. The torque affect is modified by a gaussian function whose parameter when varied, reveals local and global features on the torque surface. In the definitive version, surface peaks represent the source of data output. Peak heights represent the volume of output. Nadirs which are valleys surrounding peaks, indicate direction of output. Nadir depths represent directional output in relation to peaks.

The torque surface is shown to be a Lipschitz function which can be encoded into binary sequences using a proven efficient technique from the global optimisation discipline. Lipschitz functions are represented by monotone functions by applying a symmetric chain decomposition on an E grid. These binary sequences effectively reduce the data representation to a size that can be managed by a desktop computer.

The peaks and nadirs surface can be viewed as a "meteorological weather" map of telecommunications or cyberspace data. The geographical context of the data is clearly seen as in a weather map. In particular, the shape of the surface gives large-scale information similar to a weather map such as the position and motion of a front. The weather map view allows an unlimited amount of data to be viewed in a limited area such as on a computer monitor. The evolution of a network can be visualised in an animation of a series of torque surface "snapshots" of a network taken at regular time intervals.