Some Unpublished Work

I have decided to upload some of my unpublished work to the arXiv:

1. Adaptive Cluster Expansion (ACE): A Multilayer Network for Estimating Probability Density Functions
   
   We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach, based on a multilayer topographic mapping network, that adaptively estimates the joint probability density function of the pixel values of an image, and presents this result as a "probability image". We apply this to the problem of identifying statistically anomalous regions in otherwise statistically homogeneous images.


2. Stochastic Vector Quantisers
   
   In this paper a stochastic generalisation of the standard Linde-Buzo-Gray (LBG) approach to vector quantiser (VQ) design is presented, in which the encoder is implemented as the sampling of a vector of code indices from a probability distribution derived from the input vector, and the decoder is implemented as a superposition of reconstruction vectors, and the stochastic VQ is optimised using a minimum mean Euclidean reconstruction distortion criterion, as in the LBG case. Numerical simulations are used to demonstrate how this leads to self-organisation of the stochastic VQ, where different stochastically sampled code indices become associated with different input subspaces. This property may be used to automate the process of splitting high-dimensional input vectors into low-dimensional blocks before encoding them.


3. The Development of Dominance Stripes and Orientation Maps in a Self-Organising Visual Cortex Network (VICON)
   
   A self-organising neural network is presented that is based on a rigorous Bayesian analysis of the information contained in individual neural firing events. This leads to a visual cortex network (VICON) that has many of the properties emerge when a mammalian visual cortex is exposed to data arriving from two imaging sensors (i.e. the two retinae), such as dominance stripes and orientation maps.