Guiding local regression using visualisation

Solving many scientific problems requires effective regression and/or classification models for large high-dimensional datasets. Experts from these problem domains (e.g. biologists, chemists, financial analysts) have insights into the domain which can be helpful in developing powerful models but they need a modelling framework that helps them to use these insights. Data visualisation is an effective technique for presenting data and requiring feedback from the experts. A single global regression model can rarely capture the full behavioural variability of a huge multi-dimensional dataset. Instead, local regression models, each focused on a separate area of input space, often work better since the behaviour of different areas may vary. Classical local models such as Mixture of Experts segment the input space automatically, which is not always effective and it also lacks involvement of the domain experts to guide a meaningful segmentation of the input space. In this paper we addresses this issue by allowing domain experts to interactively segment the input space using data visualisation. The segmentation output obtained is then further used to develop effective local regression models.

Developments of the generative topographic mapping

The generative topographic mapping (GTM) model was introduced by Bishop et al. (1998, Neural Comput. 10(1), 215-234) as a probabilistic re- formulation of the self-organizing map (SOM). It offers a number of advantages compared with the standard SOM, and has already been used in a variety of applications. In this paper we report on several extensions of the GTM, including an incremental version of the EM algorithm for estimating the model parameters, the use of local subspace models, extensions to mixed discrete and continuous data, semi-linear models which permit the use of high-dimensional manifolds whilst avoiding computational intractability, Bayesian inference applied to hyper-parameters, and an alternative framework for the GTM based on Gaussian processes. All of these developments directly exploit the probabilistic structure of the GTM, thereby allowing the underlying modelling assumptions to be made explicit. They also highlight the advantages of adopting a consistent probabilistic framework for the formulation of pattern recognition algorithms.

GTM: the generative topographic mapping

This thesis describes the Generative Topographic Mapping (GTM) --- a non-linear latent variable model, intended for modelling continuous, intrinsically low-dimensional probability distributions, embedded in high-dimensional spaces. It can be seen as a non-linear form of principal component analysis or factor analysis. It also provides a principled alternative to the self-organizing map --- a widely established neural network model for unsupervised learning --- resolving many of its associated theoretical problems. An important, potential application of the GTM is visualization of high-dimensional data. Since the GTM is non-linear, the relationship between data and its visual representation may be far from trivial, but a better understanding of this relationship can be gained by computing the so-called magnification factor. In essence, the magnification factor relates the distances between data points, as they appear when visualized, to the actual distances between those data points. There are two principal limitations of the basic GTM model. The computational effort required will grow exponentially with the intrinsic dimensionality of the density model. However, if the intended application is visualization, this will typically not be a problem. The other limitation is the inherent structure of the GTM, which makes it most suitable for modelling moderately curved probability distributions of approximately rectangular shape. When the target distribution is very different to that, theaim of maintaining an `interpretable' structure, suitable for visualizing data, may come in conflict with the aim of providing a good density model. The fact that the GTM is a probabilistic model means that results from probability theory and statistics can be used to address problems such as model complexity. Furthermore, this framework provides solid ground for extending the GTM to wider contexts than that of this thesis.

On the annealed VC entropy for margin classifiers: A statistical mechanics study

Using techniques from Statistical Physics, the annealed VC entropy for hyperplanes in high dimensional spaces is calculated as a function of the margin for a spherical Gaussian distribution of inputs.

Artefactual structure from least squares multidimensional scaling

We consider the problem of illusory or artefactual structure from the visualisation of high-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SSTRESs measure) gives rise to an annular structure when the input data is drawn from a high-dimensional isotropic distribution, and we provide a theoretical justification for this observation.

Visual data mining: integrating machine learning with information visualization

Today, the data available to tackle many scientific challenges is vast in quantity and diverse in nature. The exploration of heterogeneous information spaces requires suitable mining algorithms as well as effective visual interfaces. Most existing systems concentrate either on mining algorithms or on visualization techniques. Though visual methods developed in information visualization have been helpful, for improved understanding of a complex large high-dimensional dataset, there is a need for an effective projection of such a dataset onto a lower-dimension (2D or 3D) manifold. This paper introduces a flexible visual data mining framework which combines advanced projection algorithms developed in the machine learning domain and visual techniques developed in the information visualization domain. The framework follows Shneiderman’s mantra to provide an effective user interface. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection methods, such as Generative Topographic Mapping (GTM) and Hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates, billboarding, and user interaction facilities, to provide an integrated visual data mining framework. Results on a real life high-dimensional dataset from the chemoinformatics domain are also reported and discussed. Projection results of GTM are analytically compared with the projection results from other traditional projection methods, and it is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework.

Novel visualization methods for protein data

Visualization of high-dimensional data has always been a challenging task. Here we discuss and propose variants of non-linear data projection methods (Generative Topographic Mapping (GTM) and GTM with simultaneous feature saliency (GTM-FS)) that are adapted to be effective on very high-dimensional data. The adaptations use log space values at certain steps of the Expectation Maximization (EM) algorithm and during the visualization process. We have tested the proposed algorithms by visualizing electrostatic potential data for Major Histocompatibility Complex (MHC) class-I proteins. The experiments show that the variation in the original version of GTM and GTM-FS worked successfully with data of more than 2000 dimensions and we compare the results with other linear/nonlinear projection methods: Principal Component Analysis (PCA), Neuroscale (NSC) and Gaussian Process Latent Variable Model (GPLVM).

Data visualisation and exploration with prior knowledge

Visualising data for exploratory analysis is a major challenge in many applications. Visualisation allows scientists to gain insight into the structure and distribution of the data, for example finding common patterns and relationships between samples as well as variables. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are employed. These methods are favoured because of their simplicity, but they cannot cope with missing data and it is difficult to incorporate prior knowledge about properties of the variable space into the analysis; this is particularly important in the high-dimensional, sparse datasets typical in geochemistry. In this paper we show how to utilise a block-structured correlation matrix using a modification of a well known non-linear probabilistic visualisation model, the Generative Topographic Mapping (GTM), which can cope with missing data. The block structure supports direct modelling of strongly correlated variables. We show that including prior structural information it is possible to improve both the data visualisation and the model fit. These benefits are demonstrated on artificial data as well as a real geochemical dataset used for oil exploration, where the proposed modifications improved the missing data imputation results by 3 to 13%.

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'.

Non-linear hierarchical visualisation

This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. High Throughput Screening (HTS) is an important tool in the pharmaceutical industry for discovering leads which can be optimised and further developed into candidate drugs. Since the development of new robotic technologies, the ability to test the activities of compounds has considerably increased in recent years. Traditional methods, looking at tables and graphical plots for analysing relationships between measured activities and the structure of compounds, have not been feasible when facing a large HTS dataset. Instead, data visualisation provides a method for analysing such large datasets, especially with high dimensions. So far, a few visualisation techniques for drug design have been developed, but most of them just cope with several properties of compounds at one time. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine the distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of t.he hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E- and M-step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model. In this thesis we also demonstrate the applicability of the hierarchy of latent trait models in the field of document data mining.

Uncertainty and topographic visualisations

This thesis is a study of low-dimensional visualisation methods for data visualisation under certainty of the input data. It focuses on the two main feed-forward neural network algorithms which are NeuroScale and Generative Topographic Mapping (GTM) by trying to make both algorithms able to accommodate the uncertainty. The two models are shown not to work well under high levels of noise within the data and need to be modified. The modification of both models, NeuroScale and GTM, are verified by using synthetic data to show their ability to accommodate the noise. The thesis is interested in the controversy surrounding the non-uniqueness of predictive gene lists (PGL) of predicting prognosis outcome of breast cancer patients as available in DNA microarray experiments. Many of these studies have ignored the uncertainty issue resulting in random correlations of sparse model selection in high dimensional spaces. The visualisation techniques are used to confirm that the patients involved in such medical studies are intrinsically unclassifiable on the basis of provided PGL evidence. This additional category of ‘unclassifiable’ should be accommodated within medical decision support systems if serious errors and unnecessary adjuvant therapy are to be avoided.

Predictive gene lists for breast cancer prognosis: a topographic visualisation study

Background: The controversy surrounding the non-uniqueness of predictive gene lists (PGL) of small selected subsets of genes from very large potential candidates as available in DNA microarray experiments is now widely acknowledged 1. Many of these studies have focused on constructing discriminative semi-parametric models and as such are also subject to the issue of random correlations of sparse model selection in high dimensional spaces. In this work we outline a different approach based around an unsupervised patient-specific nonlinear topographic projection in predictive gene lists. Methods: We construct nonlinear topographic projection maps based on inter-patient gene-list relative dissimilarities. The Neuroscale, the Stochastic Neighbor Embedding(SNE) and the Locally Linear Embedding(LLE) techniques have been used to construct two-dimensional projective visualisation plots of 70 dimensional PGLs per patient, classifiers are also constructed to identify the prognosis indicator of each patient using the resulting projections from those visualisation techniques and investigate whether a-posteriori two prognosis groups are separable on the evidence of the gene lists. A literature-proposed predictive gene list for breast cancer is benchmarked against a separate gene list using the above methods. Generalisation ability is investigated by using the mapping capability of Neuroscale to visualise the follow-up study, but based on the projections derived from the original dataset. Results: The results indicate that small subsets of patient-specific PGLs have insufficient prognostic dissimilarity to permit a distinction between two prognosis patients. Uncertainty and diversity across multiple gene expressions prevents unambiguous or even confident patient grouping. Comparative projections across different PGLs provide similar results. Conclusion: The random correlation effect to an arbitrary outcome induced by small subset selection from very high dimensional interrelated gene expression profiles leads to an outcome with associated uncertainty. This continuum and uncertainty precludes any attempts at constructing discriminative classifiers. However a patient's gene expression profile could possibly be used in treatment planning, based on knowledge of other patients' responses. We conclude that many of the patients involved in such medical studies are intrinsically unclassifiable on the basis of provided PGL evidence. This additional category of 'unclassifiable' should be accommodated within medical decision support systems if serious errors and unnecessary adjuvant therapy are to be avoided.

Comparing dissimilarity measures for content-based image retrieval

Dissimilarity measurement plays a crucial role in content-based image retrieval, where data objects and queries are represented as vectors in high-dimensional content feature spaces. Given the large number of dissimilarity measures that exist in many fields, a crucial research question arises: Is there a dependency, if yes, what is the dependency, of a dissimilarity measure’s retrieval performance, on different feature spaces? In this paper, we summarize fourteen core dissimilarity measures and classify them into three categories. A systematic performance comparison is carried out to test the effectiveness of these dissimilarity measures with six different feature spaces and some of their combinations on the Corel image collection. From our experimental results, we have drawn a number of observations and insights on dissimilarity measurement in content-based image retrieval, which will lay a foundation for developing more effective image search technologies.

Multi-level visualisation using Gaussian process latent variable models

Projection of a high-dimensional dataset onto a two-dimensional space is a useful tool to visualise structures and relationships in the dataset. However, a single two-dimensional visualisation may not display all the intrinsic structure. Therefore, hierarchical/multi-level visualisation methods have been used to extract more detailed understanding of the data. Here we propose a multi-level Gaussian process latent variable model (MLGPLVM). MLGPLVM works by segmenting data (with e.g. K-means, Gaussian mixture model or interactive clustering) in the visualisation space and then fitting a visualisation model to each subset. To measure the quality of multi-level visualisation (with respect to parent and child models), metrics such as trustworthiness, continuity, mean relative rank errors, visualisation distance distortion and the negative log-likelihood per point are used. We evaluate the MLGPLVM approach on the ‘Oil Flow’ dataset and a dataset of protein electrostatic potentials for the ‘Major Histocompatibility Complex (MHC) class I’ of humans. In both cases, visual observation and the quantitative quality measures have shown better visualisation at lower levels.

Discovering properties of new DNA-binding activity of proteins

Protein-DNA interactions are an essential feature in the genetic activities of life, and the ability to predict and manipulate such interactions has applications in a wide range of fields. This Thesis presents the methods of modelling the properties of protein-DNA interactions. In particular, it investigates the methods of visualising and predicting the specificity of DNA-binding Cys2His2 zinc finger interaction. The Cys2His2 zinc finger proteins interact via their individual fingers to base pair subsites on the target DNA. Four key residue positions on the a- helix of the zinc fingers make non-covalent interactions with the DNA with sequence specificity. Mutating these key residues generates combinatorial possibilities that could potentially bind to any DNA segment of interest. Many attempts have been made to predict the binding interaction using structural and chemical information, but with only limited success. The most important contribution of the thesis is that the developed model allows for the binding properties of a given protein-DNA binding to be visualised in relation to other protein-DNA combinations without having to explicitly physically model the specific protein molecule and specific DNA sequence. To prove this, various databases were generated, including a synthetic database which includes all possible combinations of the DNA-binding Cys2His2 zinc finger interactions. NeuroScale, a topographic visualisation technique, is exploited to represent the geometric structures of the protein-DNA interactions by measuring dissimilarity between the data points. In order to verify the effect of visualisation on understanding the binding properties of the DNA-binding Cys2His2 zinc finger interaction, various prediction models are constructed by using both the high dimensional original data and the represented data in low dimensional feature space. Finally, novel data sets are studied through the selected visualisation models based on the experimental DNA-zinc finger protein database. The result of the NeuroScale projection shows that different dissimilarity representations give distinctive structural groupings, but clustering in biologically-interesting ways. This method can be used to forecast the physiochemical properties of the novel proteins which may be beneficial for therapeutic purposes involving genome targeting in general.