Visualisation of heterogeneous data with simultaneous feature saliency using Generalised Generative Topographic Mapping

Most machine-learning algorithms are designed for datasets with features of a single type whereas very little attention has been given to datasets with mixed-type features. We recently proposed a model to handle mixed types with a probabilistic latent variable formalism. This proposed model describes the data by type-specific distributions that are conditionally independent given the latent space and is called generalised generative topographic mapping (GGTM). It has often been observed that visualisations of high-dimensional datasets can be poor in the presence of noisy features. In this paper we therefore propose to extend the GGTM to estimate feature saliency values (GGTMFS) as an integrated part of the parameter learning process with an expectation-maximisation (EM) algorithm. The efficacy of the proposed GGTMFS model is demonstrated both for synthetic and real datasets.

Projected sequential Gaussian processes:a C++ tool for interpolation of large datasets with heterogeneous noise

Heterogeneous datasets arise naturally in most applications due to the use of a variety of sensors and measuring platforms. Such datasets can be heterogeneous in terms of the error characteristics and sensor models. Treating such data is most naturally accomplished using a Bayesian or model-based geostatistical approach; however, such methods generally scale rather badly with the size of dataset, and require computationally expensive Monte Carlo based inference. Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential Bayesian framework for inference in such projected processes is presented. The observations are considered one at a time which avoids the need for high dimensional integrals typically required in a Bayesian approach. A C++ library, gptk, which is part of the INTAMAP web service, is introduced which implements projected, sequential estimation and adds several novel features. In particular the library includes the ability to use a generic observation operator, or sensor model, to permit data fusion. It is also possible to cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the covariance parameters is explored, including the impact of the projected process approximation on likelihood profiles. We illustrate the projected sequential method in application to synthetic and real datasets. Limitations and extensions are discussed. © 2010 Elsevier Ltd.

Visualisation and browsing of image databases

In this chapter we provide a comprehensive overview of the emerging field of visualising and browsing image databases. We start with a brief introduction to content-based image retrieval and the traditional query-by-example search paradigm that many retrieval systems employ. We specify the problems associated with this type of interface, such as users not being able to formulate a query due to not having a target image or concept in mind. The idea of browsing systems is then introduced as a means to combat these issues, harnessing the cognitive power of the human mind in order to speed up image retrieval.We detail common methods in which the often high-dimensional feature data extracted from images can be used to visualise image databases in an intuitive way. Systems using dimensionality reduction techniques, such as multi-dimensional scaling, are reviewed along with those that cluster images using either divisive or agglomerative techniques as well as graph-based visualisations. While visualisation of an image collection is useful for providing an overview of the contained images, it forms only part of an image database navigation system. We therefore also present various methods provided by these systems to allow for interactive browsing of these datasets. A further area we explore are user studies of systems and visualisations where we look at the different evaluations undertaken in order to test usability and compare systems, and highlight the key findings from these studies. We conclude the chapter with several recommendations for future work in this area. © 2011 Springer-Verlag Berlin Heidelberg.

Machine learning for large-scale wearable sensor data in Parkinson disease:concepts, promises, pitfalls, and futures

For the treatment and monitoring of Parkinson's disease (PD) to be scientific, a key requirement is that measurement of disease stages and severity is quantitative, reliable, and repeatable. The last 50 years in PD research have been dominated by qualitative, subjective ratings obtained by human interpretation of the presentation of disease signs and symptoms at clinical visits. More recently, “wearable,” sensor-based, quantitative, objective, and easy-to-use systems for quantifying PD signs for large numbers of participants over extended durations have been developed. This technology has the potential to significantly improve both clinical diagnosis and management in PD and the conduct of clinical studies. However, the large-scale, high-dimensional character of the data captured by these wearable sensors requires sophisticated signal processing and machine-learning algorithms to transform it into scientifically and clinically meaningful information. Such algorithms that “learn” from data have shown remarkable success in making accurate predictions for complex problems in which human skill has been required to date, but they are challenging to evaluate and apply without a basic understanding of the underlying logic on which they are based. This article contains a nontechnical tutorial review of relevant machine-learning algorithms, also describing their limitations and how these can be overcome. It discusses implications of this technology and a practical road map for realizing the full potential of this technology in PD research and practice. © 2016 International Parkinson and Movement Disorder Society.

Generalized KPCA by adaptive rules in feature space

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. © 2010 Taylor & Francis.

The influence of cutting tool geometry upon aspects of chip flow and tool wear:a theoretical, three dimensional examination of the cutting geometry and the shape of the twist drill

This work is undertaken in the attempt to understand the processes at work at the cutting edge of the twist drill. Extensive drill life testing performed by the University has reinforced a survey of previously published information. This work demonstrated that there are two specific aspects of drilling which have not previously been explained comprehensively. The first concerns the interrelating of process data between differing drilling situations, There is no method currently available which allows the cutting geometry of drilling to be defined numerically so that such comparisons, where made, are purely subjective. Section one examines this problem by taking as an example a 4.5mm drill suitable for use with aluminium. This drill is examined using a prototype solid modelling program to explore how the required numerical information may be generated. The second aspect is the analysis of drill stiffness. What aspects of drill stiffness provide the very great difference in performance between short flute length, medium flute length and long flute length drills? These differences exist between drills of identical point geometry and the practical superiority of short drills has been known to shop floor drilling operatives since drilling was first introduced. This problem has been dismissed repeatedly as over complicated but section two provides a first approximation and shows that at least for smaller drills of 4. 5mm the effects are highly significant. Once the cutting action of the twist drill is defined geometrically there is a huge body of machinability data that becomes applicable to the drilling process. Work remains to interpret the very high inclination angles of the drill cutting process in terms of cutting forces and tool wear but aspects of drill design may already be looked at in new ways with the prospect of a more analytical approach rather than the present mix of experience and trial and error. Other problems are specific to the twist drill, such as the behaviour of the chips in the flute. It is now possible to predict the initial direction of chip flow leaving the drill cutting edge. For the future the parameters of further chip behaviour may also be explored within this geometric model.

Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.