Topographic mappings and feed-forward neural networks

This thesis is a study of the generation of topographic mappings - dimension reducing transformations of data that preserve some element of geometric structure - with feed-forward neural networks. As an alternative to established methods, a transformational variant of Sammon's method is proposed, where the projection is effected by a radial basis function neural network. This approach is related to the statistical field of multidimensional scaling, and from that the concept of a 'subjective metric' is defined, which permits the exploitation of additional prior knowledge concerning the data in the mapping process. This then enables the generation of more appropriate feature spaces for the purposes of enhanced visualisation or subsequent classification. A comparison with established methods for feature extraction is given for data taken from the 1992 Research Assessment Exercise for higher educational institutions in the United Kingdom. This is a difficult high-dimensional dataset, and illustrates well the benefit of the new topographic technique. A generalisation of the proposed model is considered for implementation of the classical multidimensional scaling (¸mds}) routine. This is related to Oja's principal subspace neural network, whose learning rule is shown to descend the error surface of the proposed ¸mds model. Some of the technical issues concerning the design and training of topographic neural networks are investigated. It is shown that neural network models can be less sensitive to entrapment in the sub-optimal global minima that badly affect the standard Sammon algorithm, and tend to exhibit good generalisation as a result of implicit weight decay in the training process. It is further argued that for ideal structure retention, the network transformation should be perfectly smooth for all inter-data directions in input space. Finally, there is a critique of optimisation techniques for topographic mappings, and a new training algorithm is proposed. A convergence proof is given, and the method is shown to produce lower-error mappings more rapidly than previous algorithms

Feed-forward neural networks and topographic mappings for exploratory data analysis

A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feed-forward neural network is utilised to effect a topographic, structure-preserving, dimension-reducing transformation of the data, with an additional facility to incorporate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established techniques for feature extraction, and related to topographic mappings, the Sammon projection and the statistical field of multidimensional scaling

A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images

Probabilistic principal component analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA

Hierarchies Everywhere -- Managing & Measuring Uncertainty in Hierarchical Time Series

We examine the problem of making reconciled forecasts of large collections of related time series through a behavioural/Bayesian lens. Our approach explicitly acknowledges and exploits the 'connectedness' of the series in terms of time-series characteristics and forecast accuracy as well as hierarchical structure. By making maximal use of the available information, and by significantly reducing the dimensionality of the hierarchical forecasting problem, we show how to improve the accuracy of the reconciled forecasts. In contrast to existing approaches, our structure allows the analysis and assessment of the forecast value added at each hierarchical level. Our reconciled forecasts are inherently probabilistic, whether probabilistic base forecasts are used or not

Impact of the earthworm Lumbricus terrestris (L.) on As, Cu, Pb and Zn mobility and speciation in contaminated soils

To assess the risks that contaminated soils pose to the environment properly a greater understanding of how soil biota influence the mobility of metal(loid)s in soils is required. Lumbricus terrestris L. were incubated in three soils contaminated with As, Cu, Pb and Zn. The concentration and speciation of metal(loid)s in pore waters and the mobility and partitioning in casts were compared with earthworm-free soil. Generally the concentrations of water extractable metal(loid)s in earthworm casts were greater than in earthworm-free soil. The impact of the earthworms on concentration and speciation in pore waters was soil and metal specific and could be explained either by earthworm induced changes in soil pH or soluble organic carbon. The mobilisation of metal(loid)s in the environment by earthworm activity may allow for leaching or uptake into biota

Contrasting vulnerability of drained tropical and high-latitude peatlands to fluvial loss of stored carbon

Carbon sequestration and storage in peatlands rely on consistently highwater tables. Anthropogenic pressures including drainage, burning, land conversion for agriculture, timber, and biofuel production, cause loss of peat-forming vegetation and exposure of previously anaerobic peat to aerobic decomposition. This can shift peatlands from net CO2 sinks to large CO2 sources, releasing carbon held for millennia. Peatlands also export significant quantities of carbon via fluvial pathways, mainly as dissolved organic carbon (DOC). We analyzed radiocarbon (14C) levels of DOC in drainage water from multiple peatlands in Europe and Southeast Asia, to infer differences in the age of carbon lost from intact and drained systems. In most cases, drainage led to increased release of older carbon from the peat profile but withmarked differences related to peat type. Very low DOC-14C levels in runoff from drained tropical peatlands indicate loss of very old (centuries to millennia) stored peat carbon. High-latitude peatlands appear more resilient to drainage; 14C measurements from UK blanket bogs suggest that exported DOC remains young (500 year) carbon in high-latitude systems. Rewetting at least partially offsets drainage effects on DOC age

Plasmacytoid dendritic cells appear inactive during sub-microscopic Plasmodium falciparum blood-stage infection, yet retain their ability to respond to TLR stimulation

Plasmacytoid dendritic cells (pDC) are activators of innate and adaptive immune responses that express HLA-DR, toll-like receptor (TLR) 7, TLR9 and produce type I interferons. The role of human pDC in malaria remains poorly characterised. pDC activation and cytokine production were assessed in 59 malaria-naive volunteers during experimental infection with 150 or 1,800 P. falciparum-parasitized red blood cells. Using RNA sequencing, longitudinal changes in pDC gene expression were examined in five adults before and at peak-infection. pDC responsiveness to TLR7 and TLR9 stimulation was assessed in-vitro. Circulating pDC remained transcriptionally stable with gene expression altered for 8 genes (FDR < 0.07). There was no upregulation of co-stimulatory molecules CD86, CD80, CD40, and reduced surface expression of HLA-DR and CD123 (IL-3R-α). pDC loss from the circulation was associated with active caspase-3, suggesting pDC apoptosis during primary infection. pDC remained responsive to TLR stimulation, producing IFN-α and upregulating HLA-DR, CD86, CD123 at peak-infection. In clinical malaria, pDC retained HLA-DR but reduced CD123 expression compared to convalescence. These data demonstrate pDC retain function during a first blood-stage P. falciparum exposure despite sub-microscopic parasitaemia downregulating HLA-DR. The lack of evident pDC activation in both early infection and malaria suggests little response of circulating pDC to infection