Hyperspectral unmixing algorithm via dependent component analysis

This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corresponding abundance fractions at each pixel. DECA assumes that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abudances are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. This method overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.

An approach to operational modal analysis using the expectation maximization algorithm

This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

Operational Modal Analysis using Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on Maximum Likelihood Estimation and the Expectation Maximization algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated applying the proposed identification method to a set of 100 simulated cases. The numerical results show that the proposed method estimates all the modal parameters reasonably well in the presence of 30% measurement noise even. Finally, advantages and disadvantages of the method have been discussed.

Understanding Interactions in Social Networks and Committees

While much of the literature on cross section dependence has focused mainly on estimation of the regression coefficients in the underlying model, estimation and inferences on the magnitude and strength of spill-overs and interactions has been largely ignored. At the same time, such inferences are important in many applications, not least because they have structural interpretations and provide useful interpretation and structural explanation for the strength of any interactions. In this paper we propose GMM methods designed to uncover underlying (hidden) interactions in social networks and committees. Special attention is paid to the interval censored regression model. Our methods are applied to a study of committee decision making within the Bank of England’s monetary policy committee.

Quantitative modelling of transcription factor binding sites

Abstract One of the most important issues in molecular biology is to understand regulatory mechanisms that control gene expression. Gene expression is often regulated by proteins, called transcription factors which bind to short (5 to 20 base pairs),degenerate segments of DNA. Experimental efforts towards understanding the sequence specificity of transcription factors is laborious and expensive, but can be substantially accelerated with the use of computational predictions. This thesis describes the use of algorithms and resources for transcriptionfactor binding site analysis in addressing quantitative modelling, where probabilitic models are built to represent binding properties of a transcription factor and can be used to find new functional binding sites in genomes. Initially, an open-access database(HTPSELEX) was created, holding high quality binding sequences for two eukaryotic families of transcription factors namely CTF/NF1 and LEFT/TCF. The binding sequences were elucidated using a recently described experimental procedure called HTP-SELEX, that allows generation of large number (> 1000) of binding sites using mass sequencing technology. For each HTP-SELEX experiments we also provide accurate primary experimental information about the protein material used, details of the wet lab protocol, an archive of sequencing trace files, and assembled clone sequences of binding sequences. The database also offers reasonably large SELEX libraries obtained with conventional low-throughput protocols.The database is available at http://wwwisrec.isb-sib.ch/htpselex/ and and ftp://ftp.isrec.isb-sib.ch/pub/databases/htpselex. The Expectation-Maximisation(EM) algorithm is one the frequently used methods to estimate probabilistic models to represent the sequence specificity of transcription factors. We present computer simulations in order to estimate the precision of EM estimated models as a function of data set parameters(like length of initial sequences, number of initial sequences, percentage of nonbinding sequences). We observed a remarkable robustness of the EM algorithm with regard to length of training sequences and the degree of contamination. The HTPSELEX database and the benchmarked results of the EM algorithm formed part of the foundation for the subsequent project, where a statistical framework called hidden Markov model has been developed to represent sequence specificity of the transcription factors CTF/NF1 and LEF1/TCF using the HTP-SELEX experiment data. The hidden Markov model framework is capable of both predicting and classifying CTF/NF1 and LEF1/TCF binding sites. A covariance analysis of the binding sites revealed non-independent base preferences at different nucleotide positions, providing insight into the binding mechanism. We next tested the LEF1/TCF model by computing binding scores for a set of LEF1/TCF binding sequences for which relative affinities were determined experimentally using non-linear regression. The predicted and experimentally determined binding affinities were in good correlation.

A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models

Nous y introduisons une nouvelle classe de distributions bivariées de type Marshall-Olkin, la distribution Erlang bivariée. La transformée de Laplace, les moments et les densités conditionnelles y sont obtenus. Les applications potentielles en assurance-vie et en finance sont prises en considération. Les estimateurs du maximum de vraisemblance des paramètres sont calculés par l'algorithme Espérance-Maximisation. Ensuite, notre projet de recherche est consacré à l'étude des processus de risque multivariés, qui peuvent être utiles dans l'étude des problèmes de la ruine des compagnies d'assurance avec des classes dépendantes. Nous appliquons les résultats de la théorie des processus de Markov déterministes par morceaux afin d'obtenir les martingales exponentielles, nécessaires pour établir des bornes supérieures calculables pour la probabilité de ruine, dont les expressions sont intraitables.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

Using the EM algorithm to estimate the state space model for OMAX

This paper presents a time-domain stochastic system identification method based on Maximum Likelihood Estimation and the Expectation Maximization algorithm that is applied to the estimation of modal parameters from system input and output data. The effectiveness of this structural identification method is evaluated through numerical simulation. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the simulated structure are estimated applying the proposed identification method to a set of 100 simulated cases. The numerical results show that the proposed method estimates the modal parameters with precision in the presence of 20% measurement noise even. Finally, advantages and disadvantages of the method have been discussed.

A maximum likelihood algorithm for genome mapping of cytogenetic loci from meiotic configuration data.

Frequencies of meiotic configurations in cytogenetic stocks are dependent on chiasma frequencies in segments defined by centromeres, breakpoints, and telomeres. The expectation maximization algorithm is proposed as a general method to perform maximum likelihood estimations of the chiasma frequencies in the intervals between such locations. The estimates can be translated via mapping functions into genetic maps of cytogenetic landmarks. One set of observational data was analyzed to exemplify application of these methods, results of which were largely concordant with other comparable data. The method was also tested by Monte Carlo simulation of frequencies of meiotic configurations from a monotelodisomic translocation heterozygote, assuming six different sample sizes. The estimate averages were always close to the values given initially to the parameters. The maximum likelihood estimation procedures can be extended readily to other kinds of cytogenetic stocks and allow the pooling of diverse cytogenetic data to collectively estimate lengths of segments, arms, and chromosomes.

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.

Disruption prediction at JET [Joint European Torus]

The sudden loss of the plasma magnetic confinement, known as disruption, is one of the major issue in a nuclear fusion machine as JET (Joint European Torus), Disruptions pose very serious problems to the safety of the machine. The energy stored in the plasma is released to the machine structure in few milliseconds resulting in forces that at JET reach several Mega Newtons. The problem is even more severe in the nuclear fusion power station where the forces are in the order of one hundred Mega Newtons. The events that occur during a disruption are still not well understood even if some mechanisms that can lead to a disruption have been identified and can be used to predict them. Unfortunately it is always a combination of these events that generates a disruption and therefore it is not possible to use simple algorithms to predict it. This thesis analyses the possibility of using neural network algorithms to predict plasma disruptions in real time. This involves the determination of plasma parameters every few milliseconds. A plasma boundary reconstruction algorithm, XLOC, has been developed in collaboration with Dr. D. Ollrien and Dr. J. Ellis capable of determining the plasma wall/distance every 2 milliseconds. The XLOC output has been used to develop a multilayer perceptron network to determine plasma parameters as ?i and q? with which a machine operational space has been experimentally defined. If the limits of this operational space are breached the disruption probability increases considerably. Another approach for prediction disruptions is to use neural network classification methods to define the JET operational space. Two methods have been studied. The first method uses a multilayer perceptron network with softmax activation function for the output layer. This method can be used for classifying the input patterns in various classes. In this case the plasma input patterns have been divided between disrupting and safe patterns, giving the possibility of assigning a disruption probability to every plasma input pattern. The second method determines the novelty of an input pattern by calculating the probability density distribution of successful plasma patterns that have been run at JET. The density distribution is represented as a mixture distribution, and its parameters arc determined using the Expectation-Maximisation method. If the dataset, used to determine the distribution parameters, covers sufficiently well the machine operational space. Then, the patterns flagged as novel can be regarded as patterns belonging to a disrupting plasma. Together with these methods, a network has been designed to predict the vertical forces, that a disruption can cause, in order to avoid that too dangerous plasma configurations are run. This network can be run before the pulse using the pre-programmed plasma configuration or on line becoming a tool that allows to stop dangerous plasma configuration. All these methods have been implemented in real time on a dual Pentium Pro based machine. The Disruption Prediction and Prevention System has shown that internal plasma parameters can be determined on-line with a good accuracy. Also the disruption detection algorithms showed promising results considering the fact that JET is an experimental machine where always new plasma configurations are tested trying to improve its performances.

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.

Gaussian process quantile regression using expectation propagation

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the expected tilted loss function. The integration required in learning is not analytically tractable so to speed up the learning we employ the Expectation Propagation algorithm. We describe how this work relates to other quantile regression methods and apply the method on both synthetic and real data sets. The method is shown to be competitive with state of the art methods whilst allowing for the leverage of the full Gaussian process probabilistic framework.

Visualisation of heterogeneous data with simultaneous feature saliency using Generalised Generative Topographic Mapping

Most machine-learning algorithms are designed for datasets with features of a single type whereas very little attention has been given to datasets with mixed-type features. We recently proposed a model to handle mixed types with a probabilistic latent variable formalism. This proposed model describes the data by type-specific distributions that are conditionally independent given the latent space and is called generalised generative topographic mapping (GGTM). It has often been observed that visualisations of high-dimensional datasets can be poor in the presence of noisy features. In this paper we therefore propose to extend the GGTM to estimate feature saliency values (GGTMFS) as an integrated part of the parameter learning process with an expectation-maximisation (EM) algorithm. The efficacy of the proposed GGTMFS model is demonstrated both for synthetic and real datasets.