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.

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).

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.

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.

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.

Distribution of A4 protein and neurofibrillary change in the hippocampus in Alzheimer's disease

The principal components of classical senile plaques (SP) in Alzheimer's disease (AD) appear to be A4/beta protein and paired helical filaments (PHF). A4 deposits may evolve into classical SP in brain regions vulnerable to the formation of PHF. We have investigated the diatribution of A4 deposits using an immunostain and the neurofibrillary change using the Gallyas stain in various regions of the hippocampus. This region is particularly affected in AD and also has relatively restricted inputs and outputs. In 6 patients we found a significant preponderance of A4 deposits in the adjacent parahippocampal gyrus (PHG) compared with all regions of the hippocampus. However, plaque-like clusters of PHF (Gallyas plaques) were more abundant in the subiculum while neurofibrillary tangles (NFT) were more abundant in the subiculum and region CA1 compared with the PHG and other hippocampal regions. Hence, A4 deposits appear to be concentrated in the region providing a major input into the hippocampus while the neurofibrillary changes are characteristic of the major output areas (subiculum and CA1). Hence, the data suggest that A4 formation and the neurofibrillary changes may occur in regions of the hippocampus that are connected anatomically.

Exploratory database visualisation: the application and assessment of data and dimensionality reduction

This thesis describes the development of a complete data visualisation system for large tabular databases, such as those commonly found in a business environment. A state-of-the-art 'cyberspace cell' data visualisation technique was investigated and a powerful visualisation system using it was implemented. Although allowing databases to be explored and conclusions drawn, it had several drawbacks, the majority of which were due to the three-dimensional nature of the visualisation. A novel two-dimensional generic visualisation system, known as MADEN, was then developed and implemented, based upon a 2-D matrix of 'density plots'. MADEN allows an entire high-dimensional database to be visualised in one window, while permitting close analysis in 'enlargement' windows. Selections of records can be made and examined, and dependencies between fields can be investigated in detail. MADEN was used as a tool for investigating and assessing many data processing algorithms, firstly data-reducing (clustering) methods, then dimensionality-reducing techniques. These included a new 'directed' form of principal components analysis, several novel applications of artificial neural networks, and discriminant analysis techniques which illustrated how groups within a database can be separated. To illustrate the power of the system, MADEN was used to explore customer databases from two financial institutions, resulting in a number of discoveries which would be of interest to a marketing manager. Finally, the database of results from the 1992 UK Research Assessment Exercise was analysed. Using MADEN allowed both universities and disciplines to be graphically compared, and supplied some startling revelations, including empirical evidence of the 'Oxbridge factor'.

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’.

The West Midlands road transport industry

The object of this project was to identify those elements of management practice which characterised firms in the West Midlands Road Transport Industry. The object being to establish the contents of what might be termed a management policy portfolio for growth. The First Phase was the review of those factors which were generally accepted as having an influence on the success rate of transport firms in order to ascertain if they explained observed patterns. Secondly, if this were not the case, to instigate a field work study to isolate those policies which were associated with growth organizations. Investigation of the vehicle movements for the entire West Midlands Fleet over a complete licence cycle suggested that conventional explanations could not fully account for the observed patterns. To carry out the second phase of the study a sample of growth firms were visited in order to measure their attitudes on a range of factors hypothesised to affect growth. Field data were analysed to establish management activities over a wide range of areas and the results further investigated through a Principal Components and Cluster Analysis programme. The outcome of the study indicates that some past attitudes on the skills and attitudes of transport managers may have to be re-examined. As a result, the project produced a new classification of road transport firms based not on the conventional categories of long and short haul, or the types of traffics carried, but on the marketing policies and management skills employed within the organization.

The use of spot simulation imagery for forestry mapping and management

SPOT simulation imagery was acquired for a test site in the Forest of Dean in Gloucestershire, U.K. This data was qualitatively and quantitatively evaluated for its potential application in forest resource mapping and management. A variety of techniques are described for enhancing the image with the aim of providing species level discrimination within the forest. Visual interpretation of the imagery was more successful than automated classification. The heterogeneity within the forest classes, and in particular between the forest and urban class, resulted in poor discrimination using traditional `per-pixel' automated methods of classification. Different means of assessing classification accuracy are proposed. Two techniques for measuring textural variation were investigated in an attempt to improve classification accuracy. The first of these, a sequential segmentation method, was found to be beneficial. The second, a parallel segmentation method, resulted in little improvement though this may be related to a combination of resolution in size of the texture extraction area. The effect on classification accuracy of combining the SPOT simulation imagery with other data types is investigated. A grid cell encoding technique was selected as most appropriate for storing digitised topographic (elevation, slope) and ground truth data. Topographic data were shown to improve species-level classification, though with sixteen classes overall accuracies were consistently below 50%. Neither sub-division into age groups or the incorporation of principal components and a band ratio significantly improved classification accuracy. It is concluded that SPOT imagery will not permit species level classification within forested areas as diverse as the Forest of Dean. The imagery will be most useful as part of a multi-stage sampling scheme. The use of texture analysis is highly recommended for extracting maximum information content from the data. Incorporation of the imagery into a GIS will both aid discrimination and provide a useful management tool.