Exploratory data analysis with non-linear and missing data in geochemistry

Exploratory analysis of data seeks to find common patterns to gain insights into the structure and distribution of the data. In geochemistry it is a valuable means to gain insights into the complicated processes making up a petroleum system. Typically linear visualisation methods like principal components analysis, linked plots, or brushing are used. These methods can not directly be employed when dealing with missing data and they struggle to capture global non-linear structures in the data, however they can do so locally. This thesis discusses a complementary approach based on a non-linear probabilistic model. The generative topographic mapping (GTM) enables the visualisation of the effects of very many variables on a single plot, which is able to incorporate more structure than a two dimensional principal components plot. The model can deal with uncertainty, missing data and allows for the exploration of the non-linear structure in the data. In this thesis a novel approach to initialise the GTM with arbitrary projections is developed. This makes it possible to combine GTM with algorithms like Isomap and fit complex non-linear structure like the Swiss-roll. Another novel extension is the incorporation of prior knowledge about the structure of the covariance matrix. This extension greatly enhances the modelling capabilities of the algorithm resulting in better fit to the data and better imputation capabilities for missing data. Additionally an extensive benchmark study of the missing data imputation capabilities of GTM is performed. Further a novel approach, based on missing data, will be introduced to benchmark the fit of probabilistic visualisation algorithms on unlabelled data. Finally the work is complemented by evaluating the algorithms on real-life datasets from geochemical projects.

Quantifying the pathology of neurodegenerative disorders:Quantitative measurements, sampling strategies and data analysis

The use of quantitative methods has become increasingly important in the study of neurodegenerative disease. Disorders such as Alzheimer's disease (AD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This article reviews the advantages and limitations of the different methods of quantifying the abundance of pathological lesions in histological sections, including estimates of density, frequency, coverage, and the use of semiquantitative scores. The major sampling methods by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are also described. In addition, the data analysis methods commonly used to analyse quantitative data in neuropathology, including analyses of variance (ANOVA) and principal components analysis (PCA), are discussed. These methods are illustrated with reference to particular problems in the pathological diagnosis of AD and dementia with Lewy bodies (DLB).

Analysis of plasmid profiles of Aeromonas salmonicida isolates by pulsed field gel electrophoresis

Plasmid constitutions of Aeromonas salmonicida isolates were characterised by flat-bed and pulsed field gel electrophoresis. Resolution of plasmids by pulsed field gel electrophoresis was greater and more consistent than that achieved by flat-bed gel electrophoresis. The number of plasmids separated by pulsed field gel electrophoresis varied between A. salmonicida isolates, with five being the most common number present in the isolates used in this study. Plasmid profiles were diverse and the reproducibility of the distances migrated facilitated the use of principal components analysis for the characterisation of the isolates. Isolates were grouped according to the number of plasmids supported. Further principal components analysis of groups of isolates supporting five and seven plasmids showed a spatial separation of plasmids based upon distance migrated. Principal components analysis of plasmid profiles and antimicrobial minimum inhibitory concentrations could not be correlated suggesting that resistance to antimicrobial agents is not associated with either one plasmid or a particular plasmid constitution.

Statistical analysis in microbiology:statnotes

This book is aimed primarily at microbiologists who are undertaking research and who require a basic knowledge of statistics to analyse their experimental data. Computer software employing a wide range of data analysis methods is widely available to experimental scientists. The availability of this software, however, makes it essential that investigators understand the basic principles of statistics. Statistical analysis of data can be complex with many different methods of approach, each of which applies in a particular experimental circumstance. Hence, it is possible to apply an incorrect statistical method to data and to draw the wrong conclusions from an experiment. The purpose of this book, which has its origin in a series of articles published in the Society for Applied Microbiology journal ‘The Microbiologist’, is an attempt to present the basic logic of statistics as clearly as possible and therefore, to dispel some of the myths that often surround the subject. The 28 ‘Statnotes’ deal with various topics that are likely to be encountered, including the nature of variables, the comparison of means of two or more groups, non-parametric statistics, analysis of variance, correlating variables, and more complex methods such as multiple linear regression and principal components analysis. In each case, the relevant statistical method is illustrated with examples drawn from experiments in microbiological research. The text incorporates a glossary of the most commonly used statistical terms and there are two appendices designed to aid the investigator in the selection of the most appropriate test.

Statnote 28:Canonical Variate Analysis (CVA)

The pattern of correlation between two sets of variables can be tested using canonical variate analysis (CVA). CVA, like principal components analysis (PCA) and factor analysis (FA) (Statnote 27, Hilton & Armstrong, 2011b), is a multivariate analysis Essentially, as in PCA/FA, the objective is to determine whether the correlations between two sets of variables can be explained by a smaller number of ‘axes of correlation’ or ‘canonical roots’.

Quantitative neuropathology:data collection and statistical analysis

The use of quantitative methods has become increasingly important in the study of neuropathology and especially in neurodegenerative disease. Disorders such as Alzheimer's disease (AD) and the frontotemporal dementias (FTD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This chapter reviews the advantages and limitations of the different methods of quantifying pathological lesions in histological sections including estimates of density, frequency, coverage, and the use of semi-quantitative scores. The sampling strategies by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are described. In addition, data analysis methods commonly used to analysis quantitative data in neuropathology, including analysis of variance (ANOVA), polynomial curve fitting, multiple regression, classification trees, and principal components analysis (PCA), are discussed. These methods are illustrated with reference to quantitative studies of a variety of neurodegenerative disorders.

Properties of intention:component structure and consequences for behavior, information processing and resistance

Three studies tested the impact of properties of behavioral intention on intention-behavior consistency, information processing, and resistance. Principal components analysis showed that properties of intention formed distinct factors. Study 1 demonstrated that temporal stability, but not the other intention attributes, moderated intention-behavior consistency. Study 2 found that greater stability of intention was associated with improved memory performance. In Study 3, participants were confronted with a rating scale manipulation designed to alter their intention scores. Findings showed that stable intentions were able to withstand attack. Overall, the present research findings suggest that different properties of intention are not simply manifestations of a single underlying construct ("intention strength"), and that temporal stability exhibits superior resistance and impact compared to other intention attributes. © 2013 Wiley Periodicals, Inc.

+Psychometric evaluation of the MacDQoL individualised measure of the impact of macular degeneration on quality of life

Background: The MacDQoL is an individualised measure of the impact of macular degeneration (MD) on quality of life (QoL). There is preliminary evidence of its psychometric properties and sensitivity to severity of MD. The aim of this study was to carry out further psychometric evaluation with a larger sample and investigate the measure's sensitivity to MD severity. Methods: Patients with MD (n = 156: 99 women, 57 men, mean age 79 ± 13 years), recruited from eye clinics (one NHS, one private) completed the MacDQoL by telephone interview and later underwent a clinic vision assessment including near and distance visual acuity (VA), comfortable near VA, contrast sensitivity, colour recognition, recovery from glare and presence or absence of distortion or scotoma in the central 10° of the visual field. Results: The completion rate for the MacDQoL items was 99.8%. Of the 26 items, three were dropped from the measure due to redundancy. A fourth was retained in the questionnaire but excluded when computing the scale score. Principal components analysis and Cronbach's alpha (0.944) supported combining the remaining 22 items in a single scale. Lower MacDQoL scores, indicating more negative impact of MD on QoL, were associated with poorer distance VA (better eye r = -0.431 p < 0.001; worse eye r = -0.350 p < 0.001; binocular vision r = -0.419 p < 0.001) and near VA (better eye r -0.326 p < 0.001; worse eye r = -0.226 p < 0.001; binocular vision r = -0.326 p < 0.001). Poorer MacDQoL scores were associated with poorer contrast sensitivity (better eye r = 0.392 p < 0.001; binocular vision r = 0.423 p < 0.001), poorer colour recognition (r = 0.417 p < 0.001) and poorer comfortable near VA (r = -0.283, p < 0.001). The MacDQoL differentiated between those with and without binocular scotoma (U = 1244 p < 0.001). Conclusion: The MacDQoL 22-item scale has excellent internal consistency reliability and a single-factor structure. The measure is acceptable to respondents and the generic QoL item, MD-specific QoL item and average weighted impact score are related to several measures of vision. The MacDQoL demonstrates that MD has considerable negative impact on many aspects of QoL, particularly independence, leisure activities, dealing with personal affairs and mobility. The measure may be valuable for use in clinical trials and routine clinical care. © 2005 Mitchell et al; licensee BioMed Central Ltd.

Data visualisation with missing data: A non-linear approach

Exploratory analysis of data in all sciences seeks to find common patterns to gain insights into the structure and distribution of the data. Typically visualisation methods like principal components analysis are used but these methods are not easily able to deal with missing data nor can they capture non-linear structure in the data. One approach to discovering complex, non-linear structure in the data is through the use of linked plots, or brushing, while ignoring the missing data. In this technical report we discuss a complementary approach based on a non-linear probabilistic model. The generative topographic mapping enables the visualisation of the effects of very many variables on a single plot, which is able to incorporate far more structure than a two dimensional principal components plot could, and deal at the same time with missing data. We show that using the generative topographic mapping provides us with an optimal method to explore the data while being able to replace missing values in a dataset, particularly where a large proportion of the data is missing.

A quantitative study of the pathological lesions in the neocortex and hippocampus of twelve patients with corticobasal degeneration

The density of ballooned neurons (BN), tau-positive neurons with inclusion bodies (tau+ neurons), and tau-positive plaques (tau+ plaques) was determined in sections of the frontal, parietal, and temporal lobe in 12 patients with corticobasal degeneration (CBD). No significant differences in the mean density of BN and tau+ neurons were observed between neocortical regions. In the hippocampus, the densities of BN were significantly lower than in the neocortex, and densities of tau+ neurons were greater in sectors CA1 and CA2, compared with CA3 and CA4. Tau+ plaques were present in one or more brain regions in six patients. Significantly more BN were recorded in the lower (laminae V/VI) compared with the upper cortex (laminae I/II/III) but tau+ neurons were equally frequent in the upper and lower cortex. No significant correlations were observed between the densities of BN and tau+ neurons, but the densities of BN in the superior temporal gyrus and tau+ plaques in the frontal cortex were positively correlated with age. A principal components analysis (PCA) suggested that differences in the density of tau+ neurons in the frontal and motor cortex were the most important sources of variation between patients. In addition, one patient with a particularly high density of tau+ neurons in the hippocampus appeared to be atypical of the patient group studied. The data support the hypothesis that, although clinically heterogeneous, CBD is a pathologically distinct disorder. (C) 2000 Academic Press.

Its in her eyes? A barometer for EU accession through female perceptions of role portrayals in advertising:a cross-cultural study of Ukraine and Turkey?

This article examines female response to gender role portrayals in advertising for Ukraine and Turkey. Being both new potential EU candidates, we argue that gender stereotype could also be used as a \u2018barometer\u2019 of progress and closure towards a more generally accepted EU behaviour against women. While their history remains different, both from a political and society values point of views, constraints are currently being faced that require convergence or justification of practices and understanding. Principal components analysis is employed over 290 questionnaires to identify the underlying dimensions. Results indicate overall similarities in perceptions, fragmentation within groups, but seem to provide divergence regarding thresholds.

Quantitative variations in the pathology of 11 cases of variant Creutzfeldt-Jakob disease (vCJD)

Quantitative variations in the density and distribution of the vacuolation ('spongiform change'), surviving neurons, and prion protein (PrP) deposits were studied in eight brain regions from 11 cases of variant Creutzfeldt-Jakob disease (vCJD). Principal components analysis (PCA) was used to study the similarities and differences between cases and to identify the neuropathological variables which could best account for these variations. Two principal components (PC) were extracted from the data accounting in total for 93.4% of the variance; the majority of the variance (90%) being associated with PC1. Some clustering of the 11 cases in relation to PC1 and PC2 was evident. The densities of the vacuolation in the occipital cortex and the molecular layer of the cerebellum were positively and negatively correlated, respectively, with PC1. No significant variation between cases was associated with PrP deposition. These data suggest that vCJD cases have a consistent neuropathological profile characterised by the presence of vacuolation, neuronal loss and PrP deposition in the form of florid and non-florid deposits. However, there are quantitative variations between cases in the development of the vacuolation especially affecting the occipital cortex and cerebellum. © 2002 Elsevier Science Ireland Ltd. All rights reserved.

Quantification of pathological lesions in the frontal and temporal lobe of ten patients diagnosed with Pick's disease

The densities of Pick bodies (PB), Pick cells (PC), senile plaques (SP) and neurofibrillary tangles (NFT) in the frontal and temporal lobe were determined in ten patients diagnosed with Pick's disease (PD). The density of PB was significantly higher in the dentate gyrus granule cells compared with the cortex and the CA sectors of the hippocampus. Within the hippocampus, the highest densities of PB were observed in sector CA1. PC were absent in the dentate gyrus and no significant differences in PC density were observed in the remaining brain regions. With the exception of two patients, the densities of SP and NFT were low with no significant differences in mean densities between cortical regions. In the hippocampus, the density of NFT was greatest in sector CA1. PB and PC densities were positively correlated in the frontal cortex but no correlations were observed between the PD and AD lesions. A principal components analysis (PCA) of the neuropathological variables suggested that variations in the densities of SP in the frontal cortex, temporal cortex and hippocampus were the most important sources of heterogeneity within the patient group. Variations in the densities of PB and NFT in the temporal cortex and hippocampus were of secondary importance. In addition, the PCA suggested that two of the ten patients were atypical. One patient had a higher than average density of SP and one familial patient had a higher density of NFT but few SP.

Is neuropathological heterogeneity in Alzheimer’s disease related to apolipoprotein genotype?

The abundance of senile plaques (SP) and neurofibrillary tangles (NFT) was studied in cortical and subcortical regions from 30 patients with Alzheimer’s disease (AD) expressing different apolipoprotein E (apoE) genotypes. Principal components analysis (PCA) was used to identify the most important neuropathological variations between individual patients and to determine whether these variations were related to apoE genotype. The first two principal components (PC) accounted for 60% and 40% of the total variance of the SP and NFT data respectively. The abundance of SP in the frontal and occipital cortex and NFT in the frontal cortex, amygdala and substantia nigra were positively correlated with the first principal component (PC1). Analysis of the SP data revealed that the apoE score of the patient (the sum of the two alleles) was positively correlated with PC1 while analysis of the NFT data revealed no significant correlations between apoE score and the PC. The data suggest that apoE genotype was more closely related to variations in the distribution and abundance of SP than of NFT. In addition, a more rapid spread of SP into the frontal and occipital cortex may occur in patients with a high apoE score.

Relationships between morphological types of plaque in Alzheimer’s disease as revealed in silver and immunostained preparations

The objective of this study was to determine the possible relationships between the morphological types of plaque revealed in silver and immunostained sections of Alzheimer’s disease (AD) tissue. The density of cored and uncored senile plaques in Glees and Marsland preparations, and of diffuse, primitive, classic and compact beta/A4 deposits in immunostained preparations were estimated. A principal components analysis (PCA) of the data suggested that three uncorrelated principal components accounted for 80% of the variation in lesion density in the tissues. This suggested that thee processes lead independently to the formation of: (1) the uncored Glees plaques; (2) the primitive beta/A4 deposits and most of the classic beta/A4 deposits and (3) the compact beta/A4 deposits and the remaining classic deposits. Hence, the uncored plaques revealed by the Glees stain and the primitive beta/A4 deposits represented distinct plaque populations. In addition, the classic beta/A4 deposits did not appear to represent a uniform plaque population but to originate from at least two pathological processes. The uncored Glees plaques appeared to the only plaque population closely related to the diffuse beta/A4 deposits.