Pattern Analysis and Machine Learning
The NCRG has a strong research record in the area of pattern analysis and machine learning. Prior activity has included major theoretical and algorithmic advances and inventions. For example, the GTM (Generative Topographic Mapping), MDN (Mixture Density Network), NeuroScale, and hierarchical GTM - all highly exploited models around the world - were all invented and developed by the NCRG. Novel approaches to algorithm design and implementation have been invented in the group, facilitating new ways to extract information for complex data sources. Part of this work has been embodied in software, known as NetLab, which is widely used. These methods have also been used in a broad range of applications, particularly in the biomedical area. Among the researchers working on the development of pattern analysis techniques and their application are Dr. Dan Cornford, Prof. David Lowe and Prof. Ian Nabney.
The NCRG work in the application of statistical mechanics techniques to complex interacting systems resulted in several significant contributions, in areas linked to the theory of learning, information theory, cryptography and hard computational problems. Activities linking statistical physics and information theory improved existing bounds in coding theory and provided insight that led to the development of new state-of-the-art error-correcting codes. Similar techniques have been employed to investigate multi-user communication, failures in electricity grids and distributed storage of data. Among the researchers working in this area are Dr. Jort van Mourik, Dr. Juan P Neirotti and Prof. David Saad.
The NCRG has developed a generic expertise in the area of complex systems. This activity encompasses both the modelling and understanding of complex dynamical systems, and the development of novel statistical and physical inference methods. The former looks at, for instance, the emergence of collaboration and hierarchy in evolving learning agents and arrays of micromechanical systems (MEMS), the dynamics of econo-systems (the field known as econophysics) and environmental modelling; while the latter focuses on new ways to extract information from complex systems, combining mathematical understanding and novel algorithmic development. A unique expertise developed in the NCRG is the ability to link and exploit methods that have been developed in the statistical physics community to model and analyse complex systems. Among the researchers working in this area are Dr. Sudhir Jain, Prof. David Lowe, Dr. Jort van Mourik, Dr. Juan P Neirotti, Dr. Alexander Stepanenko and Prof. David Saad.
Nonlinear stochastic equations
Another area of the NCRG research is related to the field of nonlinear stochastic systems that are described by stochastic ordinary or partial differential equations. One example of such system is the Nonlinear Schrodinger Equation driven by spatio-temporal Gaussian noise. Such systems describe e.g. propagation of optical solitons in fibre transmission link with noise emitting optical amplifiers. In the study the traditional perturbational approach was applied to render the stochastic PDE to the system of stochastic ODEs (Langeven equations) with multiplicative noise for the parameters of an optical soliton. Then assuming that noise is white in both spatial and time coordinates a series of approaches were used to determine the distribution of the solution (including the Fokker-Planck equation, functional integration, direct Monte Carlo simulations). Among the researchers working in this area are Dr. Stanislav Derevyanko, Dr. Amit Chattopadhyay and Dr. Sotos Generalis.