Spatial aspects of MRSA epidemiology:A case study using stochastic simulation, kernel estimation and SaTScan

The identification of disease clusters in space or space-time is of vital importance for public health policy and action. In the case of methicillin-resistant Staphylococcus aureus (MRSA), it is particularly important to distinguish between community and health care-associated infections, and to identify reservoirs of infection. 832 cases of MRSA in the West Midlands (UK) were tested for clustering and evidence of community transmission, after being geo-located to the centroids of UK unit postcodes (postal areas roughly equivalent to Zip+4 zip code areas). An age-stratified analysis was also carried out at the coarser spatial resolution of UK Census Output Areas. Stochastic simulation and kernel density estimation were combined to identify significant local clusters of MRSA (p<0.025), which were supported by SaTScan spatial and spatio-temporal scan. In order to investigate local sampling effort, a spatial 'random labelling' approach was used, with MRSA as cases and MSSA (methicillin-sensitive S. aureus) as controls. Heavy sampling in general was a response to MRSA outbreaks, which in turn appeared to be associated with medical care environments. The significance of clusters identified by kernel estimation was independently supported by information on the locations and client groups of nursing homes, and by preliminary molecular typing of isolates. In the absence of occupational/ lifestyle data on patients, the assumption was made that an individual's location and consequent risk is adequately represented by their residential postcode. The problems of this assumption are discussed, with recommendations for future data collection.

Regularised mixture density networks for modelling wind direction

This technical report contains all technical information and results from experiments where Mixture Density Networks (MDN) using an RBF network and fixed kernel means and variances were used to infer the wind direction from satellite data from the ersII weather satellite. The regularisation is based on the evidence framework and three different approximations were used to estimate the regularisation parameter. The results were compared with the results by `early stopping'.

A quantum Jensen-Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

A quantum Jensen-Shannon graph kernel using the continuous-time quantum walk

In this paper, we use the quantum Jensen-Shannon divergence as a means to establish the similarity between a pair of graphs and to develop a novel graph kernel. In quantum theory, the quantum Jensen-Shannon divergence is defined as a distance measure between quantum states. In order to compute the quantum Jensen-Shannon divergence between a pair of graphs, we first need to associate a density operator with each of them. Hence, we decide to simulate the evolution of a continuous-time quantum walk on each graph and we propose a way to associate a suitable quantum state with it. With the density operator of this quantum state to hand, the graph kernel is defined as a function of the quantum Jensen-Shannon divergence between the graph density operators. We evaluate the performance of our kernel on several standard graph datasets from bioinformatics. We use the Principle Component Analysis (PCA) on the kernel matrix to embed the graphs into a feature space for classification. The experimental results demonstrate the effectiveness of the proposed approach. © 2013 Springer-Verlag.

A continuous-time quantum walk kernel for unattributed graphs

Kernel methods provide a way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. In this paper, we propose a novel kernel on unattributed graphs where the structure is characterized through the evolution of a continuous-time quantum walk. More precisely, given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic. With this new graph to hand, we compute the density operators of the quantum systems representing the evolutions of two suitably defined quantum walks. Finally, we define the kernel between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.