Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

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 review of non-pharmacological and pharmacological management of seasonal and perennial allergic conjunctivitis

Allergic eye disease encompasses a group of hypersensitivity disorders which primarily affect the conjunctiva and its prevalence is increasing. It is estimated to affect 8% of patients attending optometric practice but is poorly managed and rarely involves ophthalmic assessment. Seasonal allergic conjunctivitis (SAC) is the most common form of allergic eye disease (90%), followed by perennial allergic conjunctivitis (PAC; 5%). Both are type 1 IgE mediated hypersensitivity reactions where mast cells play an important role in pathophysiology. The signs and symptoms are similar but SAC occurs periodically whereas PAC occurs year round. Despite being a relatively mild condition, the effects on the quality of life can be profound and therefore they demand attention. Primary management of SAC and PAC involves avoidance strategies depending on the responsible allergen(s) to prevent the hypersensitivity reaction. Cooled tear supplements and cold compresses may help bring relief. Pharmacological agents may become necessary as it is not possible to completely avoid the allergen(s). There are a wide range of anti-allergic medications available, such as mast cell stabilisers, antihistamines and dual-action agents. Severe cases refractory to conventional treatment require anti-inflammatories, immunomodulators or immunotherapy. Additional qualifications are required to gain access to these medications, but entry-level optometrists must offer advice and supportive therapy. Based on current evidence, the efficacy of anti-allergic medications appears equivocal so prescribing should relate to patient preference, dosing and cost. More studies with standardised methodologies are necessary elicit the most effective anti-allergic medications but those with dual-actions are likely to be first line agents.

Non-invasive phakometric measurement of corneal and crystalline lens alignment in human eyes

We describe a non-invasive phakometric method for determining corneal axis rotation relative to the visual axis (β) together with crystalline lens axis tilt (α) and decentration (d) relative to the corneal axis. This does not require corneal contact A-scan ultrasonography for the measurement of intraocular surface separations. Theoretical inherent errors of the method, evaluated by ray tracing through schematic eyes incorporating the full range of human ocular component variations, were found to be larger than the measurement errors (β < 0.67°, α < 0.72° and d < 0.08 mm) observed in nine human eyes with known ocular component dimensions. Intersubject variations (mean ± S.D.: β = 6.2 ± 3.4° temporal, α = 0.2 ± 1.8° temporal and d = 0.1 ± 0.1 mm temporal) and repeatability (1.96 × S.D. of difference between repeat readings: β ± 2.0°, α ± 1.8° and d ± 0.2 mm) were studied by measuring the left eyes of 45 subjects (aged 18-42 years, 29 females and 16 males, 15 Caucasians, 29 Indian Asians, one African, refractive error range -7.25 to +1.25 D mean spherical equivalent) on two occasions. © 2005 The College of Optometrists.

Automated mapping of environmental variables from a SEIS or SISE perspective

The INTAMAP FP6 project has developed an interoperable framework for real-time automatic mapping of critical environmental variables by extending spatial statistical methods and employing open, web-based, data exchange protocols and visualisation tools. This paper will give an overview of the underlying problem, of the project, and discuss which problems it has solved and which open problems seem to be most relevant to deal with next. The interpolation problem that INTAMAP solves is the generic problem of spatial interpolation of environmental variables without user interaction, based on measurements of e.g. PM10, rainfall or gamma dose rate, at arbitrary locations or over a regular grid covering the area of interest. It deals with problems of varying spatial resolution of measurements, the interpolation of averages over larger areas, and with providing information on the interpolation error to the end-user. In addition, monitoring network optimisation is addressed in a non-automatic context.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.

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.

Effect of contact surfaces on the thermal and photoxidation of dehydrated castor oil

The effect of stainless steel, glass, zirconium and titanium enamel surfaces on the thermal and photooxidative toughening mechanism of dehydrated castor oil films deposited on these surfaces was investigated using different analytical and spectroscopic methods. The conjugated and non-conjugated double bonds were identified and quantified using both Raman spectroscopy and 1D and 2D NMR spectroscopy. The disappearance of the double bonds in thermally oxidised oil-on-surface films was shown to be concomitant with the formation of hydroperoxides (determined by iodometric titration). The type of the surface had a major effect on the rate of thermal oxidation of the oil, but all of the surfaces examined had resulted in a significantly higher rate of oxidation compared to that of the neat oil. The highest effect was exhibited by the stainless steel surface followed by zirconium enamel, titanium enamel and glass. The rate of thermal oxidation of the oil-on-steel surface (at 100 °C, based on peroxide values) was more than five times faster than that of oil-on-glass and more than 21 times faster than the neat oil when compared under similar thermal oxidative conditions. The rate of photooxidation at 60 °C of oil-on-steel films was found to be about one and half times faster than their rate of thermal oxidation at the same temperature. Results from absorbance reflectance infrared microscopy with line scans taken across the depth of thermally oxidised oil-on-steel films suggest that the thermal oxidative toughening mechanism of the oil occurs by two different reaction pathways with the film outermost layers, i.e. furthest away from the steel surface, oxidising through a traditional free radical oxidation process involving the formation of various oxygenated products formed from the decomposition of allylic hydroperoxides, whereas, in the deeper layers closer to the steel surface, crosslinking reactions predominate.

Addressing missing data in geochemistry: a non-linear approach

Exploratory analysis of petroleum geochemical data seeks to find common patterns to help distinguish between different source rocks, oils and gases, and to explain their source, maturity and any intra-reservoir alteration. However, at the outset, one is typically faced with (a) a large matrix of samples, each with a range of molecular and isotopic properties, (b) a spatially and temporally unrepresentative sampling pattern, (c) noisy data and (d) often, a large number of missing values. This inhibits analysis using conventional statistical methods. 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 paper we introduce a complementary approach based on a non-linear probabilistic model. Generative topographic mapping enables the visualisation of the effects of very many variables on a single plot, while also dealing with missing data. We show how using generative topographic mapping also provides an optimal method with which to replace missing values in two geochemical datasets, particularly where a large proportion of the data is missing.

Predicting success with silicone-hydrogel contact lenses in new wearers

Purpose: to evaluate changes in tear metrics and ocular signs induced by six months of silicone-hydrogel contact lens wear and the difference in baseline characteristics between those who successfully continued in contact lens wear compared to those that did not. Methods: Non-invasive Keratograph, Tearscope and fluorescein tear break-up times (TBUTs), tear meniscus height, bulbar and limbal hyperaemia, lid-parallel conjunctival folds (LIPCOF), phenol red thread, fluorescein and lissamine-green staining, and lid wiper epitheliopathy were measured on 60 new contact lens wearers fitted with monthly silicone-hydrogels (average age 36 ± 14 years, 40 females). Symptoms were evaluated by the Ocular Surface Disease Index (OSDI). After six months full time contact lens wear the above metrics were re-measured on those patients still in contact lens wear (n= 33). The initial measurements were also compared between the group still wearing lenses after six months and those who had ceased lens wear (n= 27). Results: There were significant changes in tear meniscus height (p= 0.031), bulbar hyperaemia (p= 0.011), fluorescein TBUT (p= 0.027), corneal (p= 0.007) and conjunctival (p= 0.009) staining, LIPCOF (p= 0.011) and lid wiper epitheliopathy (p= 0.002) after six months of silicone-hydrogel wear. Successful wearers had a higher non-invasive (17.0 ± 8.2. s vs 12.0 ± 5.6. s; p= 0.001) and fluorescein (10.7 ± 6.4. s vs 7.5 ± 4.7. s; p= 0.001) TBUT than drop-outs, although OSDI (cut-off 4.2) was also a strong predictor of success. Conclusion: Silicone-hydrogel lenses induced significant changes in the tear film and ocular surface as well as lid margin staining. Wettability of the ocular surface is the main factor affecting contact lens drop-out. © 2013 British Contact Lens Association.

The predictive ability of clinical tests for contact lens induced dry eye

Approximately half of current contact lens wearers suffer from dryness and discomfort, particularly towards the end of the day. Contact lens practitioners have a number of dry eye tests available to help them to predict which of their patients may be at risk of contact lens drop out and advise them accordingly. This thesis set out to rationalize them to see if any are of more diagnostic significance than others. This doctorate has found: (1) The Keratograph, a device which permits an automated, examiner independent technique for measuring non invasive tear break up time (NITBUT) measured NITBUT consistently shorter than measurements recorded with the Tearscope. When measuring central corneal curvature the spherical equivalent power of the cornea was measured as being significantly flatter than with a validated automated keratometer. (2) Non-invasive and invasive tear break-up times significantly correlated to each other, but not the other tear metrics. Symptomology, assessed using the OSDI questionnaire, correlated more with those tests indicating possible damage to the ocular surface (including LWE, LIPCOF and conjunctival staining) than with tests of either tear volume or stability. Cluster analysis showed some statistically significant groups of patients with different sign and symptom profiles. The largest cluster demonstrated poor tear quality with both non-invasive and invasive tests, low tear volume and more symptoms. (3) Care should be taken in fitting patients new to contact lenses if they have a NITBUT less than 10s or an OSDI comfort rating greater than 4.2 as they are more likely to drop-out within the first 6 months. Cluster analysis was not found to be beneficial in predicting which patients will succeed with lenses and which will not. A combination of the OSDI questionnaire and a NITBUT measurement was most useful both in diagnosing dry eye and in predicting contact lens drop out.

Specialist contact lens fitting

What is meant by the term ‘specialist contact lens fitting’? Or put another way, what would be considered non-specialist contact lens fitting? Is there such a thing as routine contact lens fitting? Soft or silicone hydrogel fitting for daily wear would probably be considered as routine contact lens fitting, but would extended or flexible wear remain in the same category or would they be considered a specialist fit? Different eras will classify different products as being ‘specialist’. Certainly twenty years ago soft toric contact lenses were considered as being speciality lenses but today would be thought of as routine lenses. Conversely, gas permeable lenses were thought of as mainstream twenty years ago but now are considered as speciality lenses. Although this would not be the same globally, as in some countries (such as Netherlands, France and Japan) gas permeable lens fitting remains popular and is not on the decline as in other countries (Canada, Australia and Sweden) [1]. Bandage soft lenses applied after surface laser refractive procedures would be considered as therapeutic lenses but in reality they are just plano thin hydrogel lenses worn constantly for 3–4 days to allow the underlying epithelium to convalesce and are then removed [2]. Some patients find that wearing hydrogel lenses during periods when they suffer from seasonal allergies actually improves their ocular comfort as the contact lens acts as a barrier to the allergen [3] and [4]. Scleral lenses have long been considered speciality lenses, apart from a time when they were the only lenses available but at that time all contact lens work would have been considered speciality practice! Nowadays we see the advent of mini-scleral designs and we see large diameter gas permeable lenses too. It is possible that these lenses increase the popularity of gas permeable lenses again and they become more main stream. So it would seem that the lines between routine and speciality contact lens fitting are not clear. Whether a lens is classed a specialist fit or not would depend on the lens type, why it was fitted, where in the world the fitting was being done and even the era in which it was fitted. This begs the question as to what would be considered entry level knowledge in contact lens fitting. This may not be an issue for most BCLA members or CLAE readers but certainly would be for bodies such as the College of Optometrists (UK) or the Association of British Dispensing Opticians when they are planning the final registration examinations for budding practitioners or when planning the level of higher level qualifications such as College Certificates or Diplomas. Similarly for training institutions when they are planning their course content. This becomes even trickier when trying to devise a qualification that spans across many countries, like the European Diploma in Optometry and Optics. How do we know if the training and examination level is correct? One way would be to analyse things when they go wrong and if patterns of malpractice are seen then maybe that could be used as an indicator to more training being needed. There were 162 Fitness to Practice Hearing at the General Optical Council between 2001 and 2010. Forty-seven of these were clinically related case, 39 fraud related, and 76 others. Of the clinical ones only 3 were contact lens related. So it would appear that as whole, in the profession, contact lens clinical skills are not being questioned too often (although it seems a few of us can’t keep our hands out the cookie jar!).

The Aston Medication Adherence Study:mapping the adherence patterns of an inner-city population

Background: The Aston Medication Adherence Study was designed to examine non-adherence to prescribed medicines within an inner-city population using general practice (GP) prescribing data. Objective: To examine non-adherence patterns to prescribed oralmedications within three chronic disease states and to compare differences in adherence levels between various patient groups to assist the routine identification of low adherence amongst patients within the Heart of Birmingham teaching Primary Care Trust (HoBtPCT). Setting: Patients within the area covered by HoBtPCT (England) prescribed medication for dyslipidaemia, type-2 diabetes and hypothyroidism, between 2000 and 2010 inclusively. HoBtPCT's population was disproportionately young,with seventy per cent of residents fromBlack and Minority Ethnic groups. Method: Systematic computational analysis of all medication issue data from 76 GP surgeries dichotomised patients into two groups (adherent and non-adherent) for each pharmacotherapeutic agent within the treatment groups. Dichotomised groupings were further analysed by recorded patient demographics to identify predictors of lower adherence levels. Results were compared to an analysis of a self-reportmeasure of adherence [using the Modified Morisky Scale© (MMAS-8)] and clinical value data (cholesterol values) from GP surgery records. Main outcome: Adherence levels for different patient demographics, for patients within specific longterm treatment groups. Results: Analysis within all three groups showed that for patients with the following characteristics, adherence levels were statistically lower than for others; patients: younger than 60 years of age; whose religion is coded as "Islam"; whose ethnicity is coded as one of the Asian groupings or as "Caribbean", "Other Black" and "African"; whose primary language is coded as "Urdu" or "Bengali"; and whose postcodes indicate that they live within the most socioeconomically deprived areas of HoBtPCT. Statistically significant correlations between adherence status and results from the selfreport measure of adherence and of clinical value data analysis were found. Conclusion: Using data fromGP prescribing systems, a computerised tool to calculate individual adherence levels for oral pharmacotherapy for the treatment of diabetes, dyslipidaemia and hypothyroidism has been developed.The tool has been used to establish nonadherence levels within the three treatment groups and the demographic characteristics indicative of lower adherence levels, which in turn will enable the targeting of interventional support within HoBtPCT. © Koninklijke Nederlandse Maatschappij ter bevordering der Pharmacie 2013.

A review of non-pharmacological and pharmacological management of seasonal and perennial allergic conjunctivitis

Allergic eye disease encompasses a group of hypersensitivity disorders which primarily affect the conjunctiva and its prevalence is increasing. It is estimated to affect 8% of patients attending optometric practice but is poorly managed and rarely involves ophthalmic assessment. Seasonal allergic conjunctivitis (SAC) is the most common form of allergic eye disease (90%), followed by perennial allergic conjunctivitis (PAC; 5%). Both are type 1 IgE mediated hypersensitivity reactions where mast cells play an important role in pathophysiology. The signs and symptoms are similar but SAC occurs periodically whereas PAC occurs year round. Despite being a relatively mild condition, the effects on the quality of life can be profound and therefore they demand attention. Primary management of SAC and PAC involves avoidance strategies depending on the responsible allergen(s) to prevent the hypersensitivity reaction. Cooled tear supplements and cold compresses may help bring relief. Pharmacological agents may become necessary as it is not possible to completely avoid the allergen(s). There are a wide range of anti-allergic medications available, such as mast cell stabilisers, antihistamines and dual-action agents. Severe cases refractory to conventional treatment require anti-inflammatories, immunomodulators or immunotherapy. Additional qualifications are required to gain access to these medications, but entry-level optometrists must offer advice and supportive therapy. Based on current evidence, the efficacy of anti-allergic medications appears equivocal so prescribing should relate to patient preference, dosing and cost. More studies with standardised methodologies are necessary elicit the most effective anti-allergic medications but those with dual-actions are likely to be first line agents. © 2011 British Contact Lens Association.