Semi-supervised construction of general visualization hierarchies

We have recently developed a principled approach to interactive non-linear hierarchical visualization [8] based on the Generative Topographic Mapping (GTM). Hierarchical plots are needed when a single visualization plot is not sufficient (e.g. when dealing with large quantities of data). In this paper we extend our system by giving the user a choice of initializing the child plots of the current plot in either interactive, or automatic mode. In the interactive mode the user interactively selects ``regions of interest'' as in [8], whereas in the automatic mode an unsupervised minimum message length (MML)-driven construction of a mixture of GTMs is used. The latter is particularly useful when the 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 data set of 2300 18-dimensional points and mention extension of our system to accommodate discrete data types.

DVMS 1.5: A user manual (the data visualization and modeling system)

The data available during the drug discovery process is vast in amount and diverse in nature. To gain useful information from such data, an effective visualisation tool is required. To provide better visualisation facilities to the domain experts (screening scientist, biologist, chemist, etc.),we developed a software which is based on recently developed principled visualisation algorithms such as Generative Topographic Mapping (GTM) and Hierarchical Generative Topographic Mapping (HGTM). The software also supports conventional visualisation techniques such as Principal Component Analysis, NeuroScale, PhiVis, and Locally Linear Embedding (LLE). The software also provides global and local regression facilities . It supports regression algorithms such as Multilayer Perceptron (MLP), Radial Basis Functions network (RBF), Generalised Linear Models (GLM), Mixture of Experts (MoE), and newly developed Guided Mixture of Experts (GME). This user manual gives an overview of the purpose of the software tool, highlights some of the issues to be taken care while creating a new model, and provides information about how to install & use the tool. The user manual does not require the readers to have familiarity with the algorithms it implements. Basic computing skills are enough to operate the software.

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.

EM algorithm for GTM-FS

We propose a generative topographic mapping (GTM) based data visualization with simultaneous feature selection (GTM-FS) approach which not only provides a better visualization by modeling irrelevant features ("noise") using a separate shared distribution but also gives a saliency value for each feature which helps the user to assess their significance. This technical report presents a varient of the Expectation-Maximization (EM) algorithm for GTM-FS.

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.

miniDVMS v1.8 : A user manual(The data visualization and modeling system)

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. miniDVMS v1.8 provides a flexible visual data mining framework which combines advanced projection algorithms developed in the machine learning domain and visual techniques developed in the information visualisation domain. The advantage of this interface is that the user is directly involved in the data mining process. Principled projection methods, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), are integrated with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates, and user interaction facilities, to provide this integrated visual data mining framework. The software also supports conventional visualisation techniques such as principal component analysis (PCA), Neuroscale, and PhiVis. This user manual gives an overview of the purpose of the software tool, highlights some of the issues to be taken care while creating a new model, and provides information about how to install and use the tool. The user manual does not require the readers to have familiarity with the algorithms it implements. Basic computing skills are enough to operate the software.

Data visualization with simultaneous feature selection

Data visualization algorithms and feature selection techniques are both widely used in bioinformatics but as distinct analytical approaches. Until now there has been no method of measuring feature saliency while training a data visualization model. We derive a generative topographic mapping (GTM) based data visualization approach which estimates feature saliency simultaneously with the training of the visualization model. The approach not only provides a better projection by modeling irrelevant features with a separate noise model but also gives feature saliency values which help the user to assess the significance of each feature. We compare the quality of projection obtained using the new approach with the projections from traditional GTM and self-organizing maps (SOM) algorithms. The results obtained on a synthetic and a real-life chemoinformatics dataset demonstrate that the proposed approach successfully identifies feature significance and provides coherent (compact) projections. © 2006 IEEE.

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.

Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

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).

The interplay between microscopic and mesoscopic structures in complex networks

Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database. © 2011 Reichardt et al.

Outlier detection in scatterometer data:Neural network approaches

Satellite-borne scatterometers are used to measure backscattered micro-wave radiation from the ocean surface. This data may be used to infer surface wind vectors where no direct measurements exist. Inherent in this data are outliers owing to aberrations on the water surface and measurement errors within the equipment. We present two techniques for identifying outliers using neural networks; the outliers may then be removed to improve models derived from the data. Firstly the generative topographic mapping (GTM) is used to create a probability density model; data with low probability under the model may be classed as outliers. In the second part of the paper, a sensor model with input-dependent noise is used and outliers are identified based on their probability under this model. GTM was successfully modified to incorporate prior knowledge of the shape of the observation manifold; however, GTM could not learn the double skinned nature of the observation manifold. To learn this double skinned manifold necessitated the use of a sensor model which imposes strong constraints on the mapping. The results using GTM with a fixed noise level suggested the noise level may vary as a function of wind speed. This was confirmed by experiments using a sensor model with input-dependent noise, where the variation in noise is most sensitive to the wind speed input. Both models successfully identified gross outliers with the largest differences between models occurring at low wind speeds. © 2003 Elsevier Science Ltd. All rights reserved.

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%.

Probabilistic methods for drug discovery

This thesis introduces a flexible visual data exploration framework which combines advanced projection algorithms from the machine learning domain with visual representation techniques developed in the information visualisation domain to help a user to explore and understand effectively large multi-dimensional datasets. The advantage of such a framework to other techniques currently available to the domain experts is that the user is directly involved in the data mining process and advanced machine learning algorithms are employed for better projection. A hierarchical visualisation model guided by a domain expert allows them to obtain an informed segmentation of the input space. Two other components of this thesis exploit properties of these principled probabilistic projection algorithms to develop a guided mixture of local experts algorithm which provides robust prediction and a model to estimate feature saliency simultaneously with the training of a projection algorithm.Local models are useful since a single global model cannot capture the full variability of a heterogeneous data space such as the chemical space. Probabilistic hierarchical visualisation techniques provide an effective soft segmentation of an input space by a visualisation hierarchy whose leaf nodes represent different regions of the input space. We use this soft segmentation to develop a guided mixture of local experts (GME) algorithm which is appropriate for the heterogeneous datasets found in chemoinformatics problems. Moreover, in this approach the domain experts are more involved in the model development process which is suitable for an intuition and domain knowledge driven task such as drug discovery. We also derive a generative topographic mapping (GTM) based data visualisation approach which estimates feature saliency simultaneously with the training of a visualisation model.