A taxonomy framework for unsupervised outlier detection techniques for multi-type data sets

The term "outlier" can generally be defined as an observation that is significantly different from the other values in a data set. The outliers may be instances of error or indicate events. The task of outlier detection aims at identifying such outliers in order to improve the analysis of data and further discover interesting and useful knowledge about unusual events within numerous applications domains. In this paper, we report on contemporary unsupervised outlier detection techniques for multiple types of data sets and provide a comprehensive taxonomy framework and two decision trees to select the most suitable technique based on data set. Furthermore, we highlight the advantages, disadvantages and performance issues of each class of outlier detection techniques under this taxonomy framework

A survey of outlier detection methodologies

Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review

Kernel Ellipsoidal Trimming

Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered information matrix. Although the method is very general and can be applied to many of the aforementioned problems, the main focus in this paper is the problem of novelty or outlier detection associated with fault detection. A simple iterative algorithm based on Titterington's minimum volume ellipsoid method is proposed for practical implementation. The KIMEE method demonstrates very good performance on a set of real-life and simulated datasets compared with support vector machine methods

Random Subspace Learning on Outlier Detection and Classification with Minimum Covariance Determinant Estimator

The questions brought by high dimensional data is interesting and challenging. Our study is targeting on the particular type of data in this situation that namely “large p, small n”. Since the dimensionality is massively larger than the number of observations in the data, any measurement of covariance and its inverse will be miserably affected. The definition of high dimension in statistics has been changed throughout decades. Modern datasets with over thousands of dimensions are demanding the ability to gain deeper understanding but hindered by the curse of dimensionality. We decide to review and explore further to negotiate with the curse and extend previous studies to pave a new way for estimating robustness then apply it to outlier detection and classification. We explored the random subspace learning and expand other classification and outlier detection algorithms to adapt its framework. Our proposed methods can handle both high-dimension low-sample size and traditional low-dimensional high-sample size datasets. Essentially, we avoid the computational bottleneck of techniques like Minimum Covariance Determinant (MCD) by computing the needed determinants and associated measures in much lower dimensional subspaces. Both theoretical and computational development of our approach reveal that it is computationally more efficient than the regularized methods in high-dimensional low-sample size, and often competes favorably with existing methods as far as the percentage of correct outlier detection are concerned

On the relevance of preprocessing in predictive maintenance for dynamic systems

The complexity involved in the process of real-time data-driven monitoring dynamic systems for predicted maintenance is usually huge. With more or less in-depth any data-driven approach is sensitive to data preprocessing, understood as any data treatment prior to the application of the monitoring model, being sometimes crucial for the final development of the employed monitoring technique. The aim of this work is to quantify the sensitiveness of data-driven predictive maintenance models in dynamic systems in an exhaustive way. We consider a couple of predictive maintenance scenarios, each of them defined by some public available data. For each scenario, we consider its properties and apply several techniques for each of the successive preprocessing steps, e.g. data cleaning, missing values treatment, outlier detection, feature selection, or imbalance compensation. The pretreatment configurations, i.e. sequential combinations of techniques from different preprocessing steps, are considered together with different monitoring approaches, in order to determine the relevance of data preprocessing for predictive maintenance in dynamical systems

Hyperspectral Imagery Target Detection Using Improved Anomaly Detection and Signature Matching Methods

This research extends the field of hyperspectral target detection by developing autonomous anomaly detection and signature matching methodologies that reduce false alarms relative to existing benchmark detectors, and are practical for use in an operational environment. The proposed anomaly detection methodology adapts multivariate outlier detection algorithms for use with hyperspectral datasets containing tens of thousands of non-homogeneous, high-dimensional spectral signatures. In so doing, the limitations of existing, non-robust, anomaly detectors are identified, an autonomous clustering methodology is developed to divide an image into homogeneous background materials, and competing multivariate outlier detection methods are evaluated for their ability to uncover hyperspectral anomalies. To arrive at a final detection algorithm, robust parameter design methods are employed to determine parameter settings that achieve good detection performance over a range of hyperspectral images and targets, thereby removing the burden of these decisions from the user. The final anomaly detection algorithm is tested against existing local and global anomaly detectors, and is shown to achieve superior detection accuracy when applied to a diverse set of hyperspectral images. The proposed signature matching methodology employs image-based atmospheric correction techniques in an automated process to transform a target reflectance signature library into a set of image signatures. This set of signatures is combined with an existing linear filter to form a target detector that is shown to perform as well or better relative to detectors that rely on complicated, information-intensive, atmospheric correction schemes. The performance of the proposed methodology is assessed using a range of target materials in both woodland and desert hyperspectral scenes

Méthodes statistiques de détection d’observations atypiques pour des données en grande dimension

La détection d’observations atypiques de manière non-supervisée est un enjeu crucial dans la pratique de la statistique. Dans le domaine de la détection de défauts industriels, cette tâche est d’une importance capitale pour assurer une production de haute qualité. Avec l’accroissement exponentiel du nombre de mesures effectuées sur les composants électroniques, la problématique de la grande dimension se pose lors de la recherche d’anomalies. Pour relever ce challenge, l’entreprise ippon innovation, spécialiste en statistique industrielle et détection d’anomalies, s’est associée au laboratoire de recherche TSE-R en finançant ce travail de thèse. Le premier chapitre commence par présenter le contexte du contrôle de qualité et les différentes procédures déjà mises en place, principalement dans les entreprises de semi-conducteurs pour l’automobile. Comme ces pratiques ne répondent pas aux nouvelles attentes requises par le traitement de données en grande dimension, d’autres solutions doivent être envisagées. La suite du chapitre résume l’ensemble des méthodes multivariées et non supervisées de détection d’observations atypiques existantes, en insistant tout particulièrement sur celles qui gèrent des données en grande dimension. Le Chapitre 2 montre théoriquement que la très connue distance de Mahalanobis n’est pas adaptée à la détection d’anomalies si celles-ci sont contenues dans un sous-espace de petite dimension alors que le nombre de variables est grand.Dans ce contexte, la méthode Invariant Coordinate Selection (ICS) est alors introduite comme une alternative intéressante à la mise en évidence de la structure des données atypiques. Une méthodologie pour sélectionner seulement les composantes d’intérêt est proposée et ses performances sont comparées aux standards habituels sur des simulations ainsi que sur des exemples réels industriels. Cette nouvelle procédure a été mise en oeuvre dans un package R, ICSOutlier, présenté dans le Chapitre 3 ainsi que dans une application R shiny (package ICSShiny) qui rend son utilisation plus simple et plus attractive.Une des conséquences directes de l’augmentation du nombre de dimensions est la singularité des estimateurs de dispersion multivariés, dès que certaines variables sont colinéaires ou que leur nombre excède le nombre d’individus. Or, la définition d’ICS par Tyler et al. (2009) se base sur des estimateurs de dispersion définis positifs. Le Chapitre 4 envisage différentes pistes pour adapter le critère d’ICS et investigue de manière théorique les propriétés de chacune des propositions présentées. La question de l’affine invariance de la méthode est en particulier étudiée. Enfin le dernier chapitre, se consacre à l’algorithme développé pour l’entreprise. Bien que cet algorithme soit confidentiel, le chapitre donne les idées générales et précise les challenges relevés, notamment numériques.The unsupervised outlier detection is a crucial issue in statistics. More specifically, in the industrial context of fault detection, this task is of great importance for ensuring a high quality production. With the exponential increase in the number of measurements on electronic components, the concern of high dimensional data arises in the identification of outlying observations. The ippon innovation company, an expert in industrial statistics and anomaly detection, wanted to deal with this new situation. So, it collaborated with the TSE-R research laboratory by financing this thesis work. The first chapter presents the quality control context and the different procedures mainly used in the automotive industry of semiconductors. However, these practices do not meet the new expectations required in dealing with high dimensional data, so other solutions need to be considered. The remainder of the chapter summarizes unsupervised multivariate methods for outlier detection, with a particular emphasis on those dealing with high dimensional data. Chapter 2 demonstrates that the well-known Mahalanobis distance presents some difficulties to detect the outlying observations that lie in a smaller subspace while the number of variables is large. In this context, the Invariant Coordinate Selection (ICS) method is introduced as an interesting alternative for highlighting the structure of outlierness. A methodology for selecting only the relevant components is proposed. A simulation study provides a comparison with benchmark methods. The performance of our proposal is also evaluated on real industrial data sets. This new procedure has been implemented in an R package, ICSOutlier, presented in Chapter 3, and in an R shiny application (package ICSShiny) that makes it more user-friendly. When the number of dimensions increases, the multivariate scatter matrices turn out to be singular as soon as some variables are collinear or if their number exceeds the number of individuals. However, in the presentation of ICS by Tyler et al. (2009), the scatter estimators are defined as positive definite matrices. Chapter 4 proposes three different ways for adapting the ICS method to singular scatter matrices and theoretically investigates their properties. The question of affine invariance is analyzed in particular. Finally, the last chapter is dedicated to the algorithm developed for the company. Although the algorithm is confidential, the chapter presents the main ideas and the challenges, mostly numerical, encountered during its development