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

Vibration-based adaptive novelty detection method for monitoring faults in a kinematic chain

Postprint (published version

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Automated novelty detection in the WISE survey with one-class support vector machines

Wide-angle photometric surveys of previously uncharted sky areas or wavelength regimes will always bring in unexpected sources whose existence and properties cannot be easily predicted from earlier observations: novelties or even anomalies. Such objects can be efficiently sought for with novelty detection algorithms. Here we present an application of such a method, called one-class support vector machines (OCSVM), to search for anomalous patterns among sources preselected from the mid-infrared AllWISE catalogue covering the whole sky. To create a model of expected data we train the algorithm on a set of objects with spectroscopic identifications from the SDSS DR13 database, present also in AllWISE. OCSVM detects as anomalous those sources whose patterns - WISE photometric measurements in this case - are inconsistent with the model. Among the detected anomalies we find artefacts, such as objects with spurious photometry due to blending, but most importantly also real sources of genuine astrophysical interest. Among the latter, OCSVM has identified a sample of heavily reddened AGN/quasar candidates distributed uniformly over the sky and in a large part absent from other WISE-based AGN catalogues. It also allowed us to find a specific group of sources of mixed types, mostly stars and compact galaxies. By combining the semi-supervised OCSVM algorithm with standard classification methods it will be possible to improve the latter by accounting for sources which are not present in the training sample but are otherwise well-represented in the target set. Anomaly detection adds flexibility to automated source separation procedures and helps verify the reliability and representativeness of the training samples. It should be thus considered as an essential step in supervised classification schemes to ensure completeness and purity of produced catalogues.Comment: 14 pages, 15 figure