Robust automatic mapping algorithms in a network monitoring scenario

Automatically generating maps of a measured variable of interest can be problematic. In this work we focus on the monitoring network context where observations are collected and reported by a network of sensors, and are then transformed into interpolated maps for use in decision making. Using traditional geostatistical methods, estimating the covariance structure of data collected in an emergency situation can be difficult. Variogram determination, whether by method-of-moment estimators or by maximum likelihood, is very sensitive to extreme values. Even when a monitoring network is in a routine mode of operation, sensors can sporadically malfunction and report extreme values. If this extreme data destabilises the model, causing the covariance structure of the observed data to be incorrectly estimated, the generated maps will be of little value, and the uncertainty estimates in particular will be misleading. Marchant and Lark [2007] propose a REML estimator for the covariance, which is shown to work on small data sets with a manual selection of the damping parameter in the robust likelihood. We show how this can be extended to allow treatment of large data sets together with an automated approach to all parameter estimation. The projected process kriging framework of Ingram et al. [2007] is extended to allow the use of robust likelihood functions, including the two component Gaussian and the Huber function. We show how our algorithm is further refined to reduce the computational complexity while at the same time minimising any loss of information. To show the benefits of this method, we use data collected from radiation monitoring networks across Europe. We compare our results to those obtained from traditional kriging methodologies and include comparisons with Box-Cox transformations of the data. We discuss the issue of whether to treat or ignore extreme values, making the distinction between the robust methods which ignore outliers and transformation methods which treat them as part of the (transformed) process. Using a case study, based on an extreme radiological events over a large area, we show how radiation data collected from monitoring networks can be analysed automatically and then used to generate reliable maps to inform decision making. We show the limitations of the methods and discuss potential extensions to remedy these.

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.

Self-calibrated, multi-spectral photometric stereo for 3D face capture

This paper addresses the problem of obtaining 3d detailed reconstructions of human faces in real-time and with inexpensive hardware. We present an algorithm based on a monocular multi-spectral photometric-stereo setup. This system is known to capture high-detailed deforming 3d surfaces at high frame rates and without having to use any expensive hardware or synchronized light stage. However, the main challenge of such a setup is the calibration stage, which depends on the lights setup and how they interact with the specific material being captured, in this case, human faces. For this purpose we develop a self-calibration technique where the person being captured is asked to perform a rigid motion in front of the camera, maintaining a neutral expression. Rigidity constrains are then used to compute the head's motion with a structure-from-motion algorithm. Once the motion is obtained, a multi-view stereo algorithm reconstructs a coarse 3d model of the face. This coarse model is then used to estimate the lighting parameters with a stratified approach: In the first step we use a RANSAC search to identify purely diffuse points on the face and to simultaneously estimate this diffuse reflectance model. In the second step we apply non-linear optimization to fit a non-Lambertian reflectance model to the outliers of the previous step. The calibration procedure is validated with synthetic and real data.

Managing performance of organisational units with PIMsoft:a new DEA software

DEA literature continues apace but software has lagged behind. This session uses suitably selected data to present newly developed software which includes many of the most recent DEA models. The software enables the user to address a variety of issues not frequently found in existing DEA software such as: -Assessments under a variety of possible assumptions of returns to scale including NIRS and NDRS; -Scale elasticity computations; -Numerous Input/Output variables and truly unlimited number of assessment units (DMUs) -Panel data analysis -Analysis of categorical data (multiple categories) -Malmquist Index and its decompositions -Computations of Supper efficiency -Automated removal of super-efficient outliers under user-specified criteria; -Graphical presentation of results -Integrated statistical tests

Outlier-resisting graph embedding

Graph embedding is a general framework for subspace learning. However, because of the well-known outlier-sensitiveness disadvantage of the L2-norm, conventional graph embedding is not robust to outliers which occur in many practical applications. In this paper, an improved graph embedding algorithm (termed LPP-L1) is proposed by replacing L2-norm with L1-norm. In addition to its robustness property, LPP-L1 avoids small sample size problem. Experimental results on both synthetic and real-world data demonstrate these advantages. © 2009 Elsevier B.V. All rights reserved.

A laser induced breakdown spectroscopy quantitative analysis method based on the robust least squares support vector machine regression model

Data fluctuation in multiple measurements of Laser Induced Breakdown Spectroscopy (LIBS) greatly affects the accuracy of quantitative analysis. A new LIBS quantitative analysis method based on the Robust Least Squares Support Vector Machine (RLS-SVM) regression model is proposed. The usual way to enhance the analysis accuracy is to improve the quality and consistency of the emission signal, such as by averaging the spectral signals or spectrum standardization over a number of laser shots. The proposed method focuses more on how to enhance the robustness of the quantitative analysis regression model. The proposed RLS-SVM regression model originates from the Weighted Least Squares Support Vector Machine (WLS-SVM) but has an improved segmented weighting function and residual error calculation according to the statistical distribution of measured spectral data. Through the improved segmented weighting function, the information on the spectral data in the normal distribution will be retained in the regression model while the information on the outliers will be restrained or removed. Copper elemental concentration analysis experiments of 16 certified standard brass samples were carried out. The average value of relative standard deviation obtained from the RLS-SVM model was 3.06% and the root mean square error was 1.537%. The experimental results showed that the proposed method achieved better prediction accuracy and better modeling robustness compared with the quantitative analysis methods based on Partial Least Squares (PLS) regression, standard Support Vector Machine (SVM) and WLS-SVM. It was also demonstrated that the improved weighting function had better comprehensive performance in model robustness and convergence speed, compared with the four known weighting functions.

Trimmed Likelihood Estimation of the Parameters of the Generalized Extreme Value Distributions: a Monte-Carlo Study

2000 Mathematics Subject Classification: Primary 62F35; Secondary 62P99

Analysis and Data Mining of Lead-Zinc Ore Data

This paper presents the results of our data mining study of Pb-Zn (lead-zinc) ore assay records from a mine enterprise in Bulgaria. We examined the dataset, cleaned outliers, visualized the data, and created dataset statistics. A Pb-Zn cluster data mining model was created for segmentation and prediction of Pb-Zn ore assay data. The Pb-Zn cluster data model consists of five clusters and DMX queries. We analyzed the Pb-Zn cluster content, size, structure, and characteristics. The set of the DMX queries allows for browsing and managing the clusters, as well as predicting ore assay records. A testing and validation of the Pb-Zn cluster data mining model was developed in order to show its reasonable accuracy before beingused in a production environment. The Pb-Zn cluster data mining model can be used for changes of the mine grinding and floatation processing parameters in almost real-time, which is important for the efficiency of the Pb-Zn ore beneficiation process. ACM Computing Classification System (1998): H.2.8, H.3.3.

On the Lp-Norm Regression Models for Estimating Value-at-Risk

Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Generalized KPCA by adaptive rules in feature space

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. © 2010 Taylor & Francis.

L1-norm-based 2DPCA

In this paper, we first present a simple but effective L1-norm-based two-dimensional principal component analysis (2DPCA). Traditional L2-norm-based least squares criterion is sensitive to outliers, while the newly proposed L1-norm 2DPCA is robust. Experimental results demonstrate its advantages. © 2006 IEEE.

Robust tensor analysis with L1-norm

Tensor analysis plays an important role in modern image and vision computing problems. Most of the existing tensor analysis approaches are based on the Frobenius norm, which makes them sensitive to outliers. In this paper, we propose L1-norm-based tensor analysis (TPCA-L1), which is robust to outliers. Experimental results upon face and other datasets demonstrate the advantages of the proposed approach. © 2006 IEEE.

Application of support vector machines on the basis of the first Hungarian bankruptcy model

In our study we rely on a data mining procedure known as support vector machine (SVM) on the database of the first Hungarian bankruptcy model. The models constructed are then contrasted with the results of earlier bankruptcy models with the use of classification accuracy and the area under the ROC curve. In using the SVM technique, in addition to conventional kernel functions, we also examine the possibilities of applying the ANOVA kernel function and take a detailed look at data preparation tasks recommended in using the SVM method (handling of outliers). The results of the models assembled suggest that a significant improvement of classification accuracy can be achieved on the database of the first Hungarian bankruptcy model when using the SVM method as opposed to neural networks.