GTM-based data visualisation with incomplete data

We analyse how the Generative Topographic Mapping (GTM) can be modified to cope with missing values in the training data. Our approach is based on an Expectation -Maximisation (EM) method which estimates the parameters of the mixture components and at the same time deals with the missing values. We incorporate this algorithm into a hierarchical GTM. We verify the method on a toy data set (using a single GTM) and a realistic data set (using a hierarchical GTM). The results show our algorithm can help to construct informative visualisation plots, even when some of the training points are corrupted with missing values.

Semi-supervised learning of hierarchical latent trait models for data visualisation

An interactive hierarchical Generative Topographic Mapping (HGTM) ¸iteH_GTM has been developed to visualise complex data sets. In this paper, we build a more general visualisation system by extending the HGTM visualisation system in 3 directions: bf (1) We generalize HGTM to noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM) developed in ¸iteKaban_pami. bf (2) We give the user a choice of initializing the child plots of the current plot in either em interactive, or em automatic mode. In the interactive mode the user interactively selects ``regions of interest'' as in ¸iteH_GTM, whereas in the automatic mode an unsupervised minimum message length (MML)-driven construction of a mixture of LTMs is employed. bf (3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualisation plots, since they can highlight the boundaries between data clusters. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. We illustrate our approach on a toy example and apply our system to three more complex real data sets.

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.

Block GTM: Incorporating prior knowledge of covariance structure in data visualisation

Visualising data for exploratory analysis is a big challenge in scientific and engineering domains where there is a need to gain insight into the structure and distribution of the data. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are used, but it is difficult to incorporate prior knowledge about structure of the data into the analysis. In this technical report we discuss a complementary approach based on an extension of a well known non-linear probabilistic model, the Generative Topographic Mapping. We show that by including prior information of the covariance structure into the model, we are able to improve both the data visualisation and the model fit.

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%.

Helicopter vibration sensor selection using data visualisation

The main objective of the project is to enhance the already effective health-monitoring system (HUMS) for helicopters by analysing structural vibrations to recognise different flight conditions directly from sensor information. The goal of this paper is to develop a new method to select those sensors and frequency bands that are best for detecting changes in flight conditions. We projected frequency information to a 2-dimensional space in order to visualise flight-condition transitions using the Generative Topographic Mapping (GTM) and a variant which supports simultaneous feature selection. We created an objective measure of the separation between different flight conditions in the visualisation space by calculating the Kullback-Leibler (KL) divergence between Gaussian mixture models (GMMs) fitted to each class: the higher the KL-divergence, the better the interclass separation. To find the optimal combination of sensors, they were considered in pairs, triples and groups of four sensors. The sensor triples provided the best result in terms of KL-divergence. We also found that the use of a variational training algorithm for the GMMs gave more reliable results.

Improved data visualisation through multiple dissimilarity modelling

Popular dimension reduction and visualisation algorithms rely on the assumption that input dissimilarities are typically Euclidean, for instance Metric Multidimensional Scaling, t-distributed Stochastic Neighbour Embedding and the Gaussian Process Latent Variable Model. It is well known that this assumption does not hold for most datasets and often high-dimensional data sits upon a manifold of unknown global geometry. We present a method for improving the manifold charting process, coupled with Elastic MDS, such that we no longer assume that the manifold is Euclidean, or of any particular structure. We draw on the benefits of different dissimilarity measures allowing for the relative responsibilities, under a linear combination, to drive the visualisation process.

Advanced data driven visualisation for geo-spatial data

Most current 3D landscape visualisation systems either use bespoke hardware solutions, or offer a limited amount of interaction and detail when used in realtime mode. We are developing a modular, data driven 3D visualisation system that can be readily customised to specific requirements. By utilising the latest software engineering methods and bringing a dynamic data driven approach to geo-spatial data visualisation we will deliver an unparalleled level of customisation in near-photo realistic, realtime 3D landscape visualisation. In this paper we show the system framework and describe how this employs data driven techniques. In particular we discuss how data driven approaches are applied to the spatiotemporal management aspect of the application framework, and describe the advantages these convey.

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'.

Advanced data driven visualisation for geo-spatial data

Most current 3D landscape visualisation systems either use bespoke hardware solutions, or offer a limited amount of interaction and detail when used in realtime mode. We are developing a modular, data driven 3D visualisation system that can be readily customised to specific requirements. By utilising the latest software engineering methods and bringing a dynamic data driven approach to geo-spatial data visualisation we will deliver an unparalleled level of customisation in near-photo realistic, realtime 3D landscape visualisation. In this paper we show the system framework and describe how this employs data driven techniques. In particular we discuss how data driven approaches are applied to the spatiotemporal management aspect of the application framework, and describe the advantages these convey. © Springer-Verlag Berlin Heidelberg 2006.

A novel neural network technique for exploratory data analysis

This paper surveys the context of feature extraction by neural network approaches, and compares and contrasts their behaviour as prospective data visualisation tools in a real world problem. We also introduce and discuss a hybrid approach which allows us to control the degree of discriminatory and topographic information in the extracted feature space.

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.

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.

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.

Visualisation of bioinformatics datasets

Analysing the molecular polymorphism and interactions of DNA, RNA and proteins is of fundamental importance in biology. Predicting functions of polymorphic molecules is important in order to design more effective medicines. Analysing major histocompatibility complex (MHC) polymorphism is important for mate choice, epitope-based vaccine design and transplantation rejection etc. Most of the existing exploratory approaches cannot analyse these datasets because of the large number of molecules with a high number of descriptors per molecule. This thesis develops novel methods for data projection in order to explore high dimensional biological dataset by visualising them in a low-dimensional space. With increasing dimensionality, some existing data visualisation methods such as generative topographic mapping (GTM) become computationally intractable. We propose variants of these methods, where we use log-transformations at certain steps of expectation maximisation (EM) based parameter learning process, to make them tractable for high-dimensional datasets. We demonstrate these proposed variants both for synthetic and electrostatic potential dataset of MHC class-I. We also propose to extend a latent trait model (LTM), suitable for visualising high dimensional discrete data, to simultaneously estimate feature saliency as an integrated part of the parameter learning process of a visualisation model. This LTM variant not only gives better visualisation by modifying the project map based on feature relevance, but also helps users to assess the significance of each feature. Another problem which is not addressed much in the literature is the visualisation of mixed-type data. We propose to combine GTM and LTM in a principled way where appropriate noise models are used for each type of data in order to visualise mixed-type data in a single plot. We call this model a generalised GTM (GGTM). We also propose to extend GGTM model to estimate feature saliencies while training a visualisation model and this is called GGTM with feature saliency (GGTM-FS). We demonstrate effectiveness of these proposed models both for synthetic and real datasets. We evaluate visualisation quality using quality metrics such as distance distortion measure and rank based measures: trustworthiness, continuity, mean relative rank errors with respect to data space and latent space. In cases where the labels are known we also use quality metrics of KL divergence and nearest neighbour classifications error in order to determine the separation between classes. We demonstrate the efficacy of these proposed models both for synthetic and real biological datasets with a main focus on the MHC class-I dataset.