A generalisation of almost-compactness, with an associated generalisation of completeness

' & $ % Information Geometric Measurements of Generalisation Information Geometric Measurements of Generalisation

Neural networks can be regarded as statistical models, and can be analysed in a Bayesian framework. Generalisation is measured by the performance on independent test data drawn from the same distribution as the training data. Such performance can be quantiied by the posterior average of the information divergence between the true and the model distributions. Averaging over the Bayesian posterio...

Contrasting Classification with Generalisation

Exploratory Construction of Generalisation Rules for Landuse Vector Data Generalisation

Landuse vector data generalisation is to derive a new landuse dataset or map from an initial dataset by removing the minor details. The generalised results should delineate the dominant landuse characteristics of important landuse types in a reduced map space or a theme-specific application. The generalisation process are guided and controlled by a set of generalisation rules serving for the re...

A Generalisation of Tverberg's Theorem

The well know theorem of Tverberg states that if n ≥ (d+1)(r − 1)+1 then one can partition any set of n points in R to r disjoint subsets whose convex hulls have a common point. The numbers T (d, r) = (d + 1)(r − 1) + 1 are known as Tverberg numbers. Reay asks the following question: if we add an additional parameter k (2 ≤ k ≤ r) what is the minimal number of points we need in order to guarant...

A generalisation of t-designs

This paper defines a class of designs which generalise t-designs, resolvable designs, and orthogonal arrays. For the parameters t = 2, k = 3 and λ = 1, the designs in the class consist of Steiner triple systems, Latin squares, and 1-factorisations of complete graphs. For other values of t and k, we obtain t-designs, Kirkman systems, large sets of Steiner triple systems, sets of mutually orthogo...