Geometrical complexity of data approximators

There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on. For each type of approximators the measure of the approximator complexity was developed too. These measures are necessary to find the balance between accuracy and complexity and to define the optimal approximations of a given type. We propose a measure of complexity (geometrical complexity) which is applicable to approximators of several types and which allows comparing data approximations of different types.Comment: 10 pages, 3 figures, minor correction and extensio

Choice of models for the analysis and forecasting of hospital beds

There is growing concern that current health care services are not sustainable. The compartmental flow model provides the opportunity for improved decision-making about bed occupancy decisions, particularly those of a strategic nature. This modelling can be applied to complement infrastructure and workforce-planning methods. Discussion about appropriateness of the level of model complexity, the degree of fit and the ability to use compartmental flow models for generalization and forecasting has been lacking. The authors investigated model selection and assessment in relation to hospital bed compartment flow models. A compartment model for a range of scenarios was created. The training and test data related to the 1998 and 1999 calendar years, respectively. The majority of scenarios tested were based upon commonly used periods that describe periods of time. The goodness-of-fit achieved by optimisation was measured against the training and test data. Model fit improved with increasing complexity as expected. The analysis of model fit against the test data showed that increasing model complexity did result in over-fitting, and better prediction was achieved with a relatively simple model. In terms of generalisation, the seasonal models performed best. Single day census type models, which have been used by Millard and his colleagues, were also generated. The performance of these models was similar, but inferior to that of the models generated from a full year of training data. The additional data make the models better able to capture the variation across the year in activity