Christopher J. Brignell

Factored principal components analysis, with applications to face recognition

A dimension reduction technique is proposed for matrix data, with applications to face recognition from images. In particular, we propose a factored covariance model for the data under study, estimate the parameters using maximum likelihood, and then carry out eigendecompositions of the estimated covariance matrix. We call the resulting method factored principal components analysis. We also develop a method for classification using a likelihood ratio criterion, which has previously been used for evaluating the strength of forensic evidence. The methodology is illustrated with applications in face recognition.

Magnetic Resonance Spectroscopy discriminates the response to microglial stimulation of wild type and Alzheimer’s disease models

Microglia activation has emerged as a potential key factor in the pathogenesis of Alzheimer’s disease. Metabolite levels assessed by magnetic resonance spectroscopy (MRS) are used as markers of neuroinflammation in neurodegenerative diseases, but how they relate to microglial activation in health and chronic disease is incompletely understood. Using MRS, we monitored the brain metabolic response to lipopolysaccharides (LPS)-induced microglia activation in vivo in a transgenic mouse model of Alzheimer’s disease (APP/PS1) and healthy controls (wild-type (WT) littermates) over 4 hours. We assessed reactive gliosis by immunohistochemistry and correlated metabolic and histological measures. In WT mice, LPS induced a microglial phenotype consistent with activation, associated with a sustained increase in macromolecule and lipid levels (ML9). This effect was not seen in APP/PS1 mice, where LPS did not lead to a microglial response measured by histology, but induced a late increase in the putative inflammation marker myoinositol (mI) and metabolic changes in total creatine and taurine previously reported to be associated with amyloid load. We argue that ML9 and mI distinguish the response of WT and APP/PS1 mice to immune mediators. Lipid and macromolecule levels may represent a biomarker of activation of healthy microglia, while mI may not be a glial marker.

Surface shape analysis with an application to brain surface asymmetry in schizophrenia

Some methods for the statistical analysis of surface shapes and asymmetry are introduced. We focus on a case study where magnetic resonance images of the brain are available from groups of 30 schizophrenia patients and 38 controls, and we investigate large-scale brain surface shape differences. Key aspects of shape analysis are to remove nuisance transformations by registration and to identify which parts of one object correspond with the parts of another object. We introduce maximum likelihood and Bayesian methods for registering brain images and providing large-scale correspondences of the brain surfaces. Brain surface size-and-shape analysis is considered using random field theory, and also dimension reduction is carried out using principal and independent components analysis. Some small but significant differences are observed between the the patient and control groups. We then investigate a particular type of asymmetry called torque. Differences in asymmetry are observed between the control and patient groups, which add strength to other observations in the literature. Further investigations of the midline plane location in the 2 groups and the fitting of nonplanar curved midlines are also considered.

Bayesian matching of unlabeled marked point sets using random fields, with an application to molecular alignment

Statistical methodology is proposed for comparing unlabeled marked point sets, with an application to aligning steroid molecules in chemoinformatics. Methods from statistical shape analysis are combined with techniques for predicting random fields in spatial statistics in order to define a suitable measure of similarity between two marked point sets. Bayesian modeling of the predicted field overlap between pairs of point sets is proposed, and posterior inference of the alignment is carried out using Markov chain Monte Carlo simulation. By representing the fields in reproducing kernel Hilbert spaces, the degree of overlap can be computed without expensive numerical integration. Superimposing entire fields rather than the configuration matrices of point coordinates thereby avoids the problem that there is usually no clear one-to-one correspondence between the points. In addition, mask parameters are introduced in the model, so that partial matching of the marked point sets can be carried out. We also propose an adaptation of the generalized Procrustes analysis algorithm for the simultaneous alignment of multiple point sets. The methodology is illustrated with a simulation study and then applied to a data set of 31 steroid molecules, where the relationship between shape and binding activity to the corticosteroid binding globulin receptor is explored.

Area of hock hair loss in dairy cows: Risk factors and correlation with a categorical scale

Data from 3691 dairy cows from 76 farms were used to investigate the risk factors associated with the area of hair loss over the lateral aspect of the hock and the correlation between the area of hair loss (as calculated using a hock map) and hock lesion scores determined using a pre-existing categorical scale. Six factors were associated with a greater area of hair loss, including cows with locomotion score 3, a cleanliness score (10/28 to 18/28), high daily milk yield (25.1-58.1 kg), poor body condition score (1-1.5), duration of winter housing (≥41 days) and some combinations of cubicle base and bedding materials. Compared with cows housed in cubicles with a concrete base and whole straw or rape straw bedding, cows housed in cubicles with concrete bases with sand or chopped straw bedding had smaller areas of hair loss and cows housed on a mattress base with whole straw or rape straw bedding had larger areas of hair loss. Area of hair loss, as measured on hock maps, was not significantly different between cows with score 1 (median 23.6 cm(2)) and score 2 (median 20.3 cm(2)) on the categorical scale for hock lesions. This suggests that the categorical scale was not reflecting the extent of hair loss and that hock maps are a good alternative for studying the dynamics of hock lesions over time.

Covariance Weighted Procrustes Analysis

We revisit the popular Procrustes matching procedure of landmark shape analysis and consider the situation where the landmark coordinates have a completely general covariance matrix, extending previous approaches based on factored covariance structures. Procrustes matching is used to compute the Riemannian metric in shape space and is used more widely for carrying out inference such as estimation of mean shape and covariance structure. Rather than matching using the Euclidean distance we consider a general Mahalanobis distance. This approach allows us to consider different variances at each landmark, as well as covariance structure between the landmark coordinates, and more general covariance structures. Explicit expressions are given for the optimal translation and rotation in two dimensions and numerical procedures are used for higher dimensions. Simultaneous estimation of both mean shape and covariance structure is difficult due to the inherent non-identifiability. The method requires the specification of constraints to carry out inference, and we discuss some possible practical choices. We illustrate the methodology using data from fish silhouettes and mouse vertebra images.