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.

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.

Independent component analysis for domain independent watermarking

A new principled domain independent watermarking framework is presented. The new approach is based on embedding the message in statistically independent sources of the covertext to mimimise covertext distortion, maximise the information embedding rate and improve the method's robustness against various attacks. Experiments comparing the performance of the new approach, on several standard attacks show the current proposed approach to be competitive with other state of the art domain-specific methods.

Watermarking of audio signals using independent component analysis

A novel approach to watermarking of audio signals using Independent Component Analysis (ICA) is proposed. It exploits the statistical independence of components obtained by practical ICA algorithms to provide a robust watermarking scheme with high information rate and low distortion. Numerical simulations have been performed on audio signals, showing good robustness of the watermark against common attacks with unnoticeable distortion, even for high information rates. An important aspect of the method is its domain independence: it can be used to hide information in other types of data, with minor technical adaptations.

Evaluation of catalytic pyrolysis of cassava rhizome by principal component analysis

Rhizome of cassava plants (Manihot esculenta Crantz) was catalytically pyrolysed at 500 °C using analytical pyrolysis–gas chromatography/mass spectrometry (Py–GC/MS) method in order to investigate the relative effect of various catalysts on pyrolysis products. Selected catalysts expected to affect bio-oil properties were used in this study. These include zeolites and related materials (ZSM-5, Al-MCM-41 and Al-MSU-F type), metal oxides (zinc oxide, zirconium (IV) oxide, cerium (IV) oxide and copper chromite) catalysts, proprietary commercial catalysts (Criterion-534 and alumina-stabilised ceria-MI-575) and natural catalysts (slate, char and ashes derived from char and biomass). The pyrolysis product distributions were monitored using models in principal components analysis (PCA) technique. The results showed that the zeolites, proprietary commercial catalysts, copper chromite and biomass-derived ash were selective to the reduction of most oxygenated lignin derivatives. The use of ZSM-5, Criterion-534 and Al-MSU-F catalysts enhanced the formation of aromatic hydrocarbons and phenols. No single catalyst was found to selectively reduce all carbonyl products. Instead, most of the carbonyl compounds containing hydroxyl group were reduced by zeolite and related materials, proprietary catalysts and copper chromite. The PCA model for carboxylic acids showed that zeolite ZSM-5 and Al-MSU-F tend to produce significant amounts of acetic and formic acids.

Independent component analysis and feature extraction of financial time series

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A Markov switching unobserved component analysis of the CDX index term premium

Using a Markov switching unobserved component model we decompose the term premium of the North American CDX index into a permanent and a stationary component. We establish that the inversion of the CDX term premium is induced by sudden changes in the unobserved stationary component, which represents the evolution of the fundamentals underpinning the probability of default in the economy. We find evidence that the monetary policy response from the Fed during the crisis period was effective in reducing the volatility of the term premium. We also show that equity returns make a substantial contribution to the term premium over the entire sample period.

Salmonella in companion animals

In an increasingly hygiene concerned society, a major barrier to pet ownership is the perceived role of companion animals in contributing to the risk of exposure to zoonotic bacterial pathogens, such as Salmonella. Manifestations of Salmonella can range from acute gastroenteritis to perfuse enteric fever, in both humans and dogs. Dogs are heavily associated with asymptomatic carriage of Salmonella as the microorganism can persist in the lower intestines of this host which can be then excreted into the environment. Studies in to the asymptomatic carriage of Salmonella in dogs are somewhat dated and there is limited UK data. The current UK carriage rate in dogs was investigated in a randomised dog population and it was revealed that the carriage rate in this population was very low with only one household dog positive for the carriage of Salmonella enterica arizonae (0.2%), out of 490 dogs sampled. Salmonella serotypes share phenotypic and genotypic similarities which are captured in epidemiological typing methods. Therefore, in parallel to the epidemiological investigations, a panel of clinical canine (VLA, UK) and human (Aston University, UK) Salmonella isolates were profiled based on their phenotypic and genotypic characteristics; using API 20E, Biolog Microbial ID System, antibiotic sensitivity testing and PFGE, respectively. Antibiotic sensitivity testing revealed a significant difference between the canine and human isolates with the canine group demonstrating a higher resistance to the panel of antibiotics tested. Further metabolic capabilities of the strains were tested using the Biolog Microbial ID System, which reveal no clear association between the two host groups. However, coupled with Principle Component Analysis two canine isolates were discriminated from the entire population on the basis of a high up-regulation of two carbohydrates. API 20E testing revealed no association between the two host groups. A PFGE harmonised protocol was used to genotypically profile the strains. A dendrogram depicting PFGE profiles of the panel of Salmonella isolates was performed where similarities were calculated by Dice coefficient and represented by UPGMA clustering. Clustering of the profiles from canine isolates and human isolates (HPA, UK) was diverse representing a natural heterogeneity of the genus, additionally, no clear clustering of the isolates was observed between host groups. Clustering was observed with isolates from the same serotype, independent of host origin. Host adaption is a common phenomenon in certain Salmonella serotypes, for example S. Typhi in humans and S. Dublin in cattle. It was of interest to investigate potential host adaptive or restricted strains for canine host by performing adhesion and invasion assays on Dog Intestinal Epithelial Cells (DIECs) (WALTHAM®, UK) and human CaCo-2 (HPA, UK) cell lines. Salmonella arizonae and Enteritidis from an asymptomatic dog and clinical isolate, respectively, demonstrated a significantly high proportion of invasion in DIEC in comparison to human CaCo-2 cells and other tested Salmonella serotypes. This may be suggestive of a potential host restrictive strain as their ability to invade the CaCo-2 cell line was significantly lower than the other serotypes. In conclusion to this thesis the investigations carried out suggest that asymptomatic carriage of Salmonella in UK dogs is low however the microorganism remains as a zoonotic and anthroponotic pathogen based on phenotypic and genotypic characterisation however there may be potential for particular serotype to become host restricted as observed in invasion assays

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.

Mixtures of probabilistic principal component analysers

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.

Understanding U.S. regional linguistic variation with Twitter data analysis

We analyze a Big Data set of geo-tagged tweets for a year (Oct. 2013–Oct. 2014) to understand the regional linguistic variation in the U.S. Prior work on regional linguistic variations usually took a long time to collect data and focused on either rural or urban areas. Geo-tagged Twitter data offers an unprecedented database with rich linguistic representation of fine spatiotemporal resolution and continuity. From the one-year Twitter corpus, we extract lexical characteristics for twitter users by summarizing the frequencies of a set of lexical alternations that each user has used. We spatially aggregate and smooth each lexical characteristic to derive county-based linguistic variables, from which orthogonal dimensions are extracted using the principal component analysis (PCA). Finally a regionalization method is used to discover hierarchical dialect regions using the PCA components. The regionalization results reveal interesting linguistic regional variations in the U.S. The discovered regions not only confirm past research findings in the literature but also provide new insights and a more detailed understanding of very recent linguistic patterns in the U.S.