Novelty detection involves the construction of a "model of normality", and then classifies test d... more Novelty detection involves the construction of a "model of normality", and then classifies test data as being either "normal" or "abnormal" with respect to that model. For this reason, it is often termed one-class classification. The approach is suitable for cases in which examples of "normal" behaviour are commonly available, but in which cases of "abnormal" data are comparatively rare. When performing novelty detection, we are typically most interested in the tails of the normal model, because it is in these tails that a decision boundary between "normal" and "abnormal" areas of data space usually lies. Extreme value statistics provides an appropriate theoretical framework for modelling the tails of univariate (or low-dimensional) distributions, using the generalised Pareto distribution (GPD), which can be demonstrated to be the limiting distribution for data occurring within the tails of most practically-encountered probability distributions. This paper provides an extension of the GPD, allowing the modelling of probability distributions of arbitrarily high dimension, such as occurs when using complex, multimodel, multivariate distributions for performing novelty detection in most real-life cases. We demonstrate our extension to the GPD using examples from patient physiological monitoring, in which we have acquired data from hospital patients in large clinical studies of high-acuity wards, and in which we wish to determine "abnormal" patient data, such that early warning of patient physiological deterioration may be provided.
... Azevedo Pedro Encarnação Teodiano Freire Bastos Filho Hugo Gamboa Ana Rita Londral António ..... more ... Azevedo Pedro Encarnação Teodiano Freire Bastos Filho Hugo Gamboa Ana Rita Londral António ... Coelhas INSTICC, Portugal Vera Coelho INSTICC, Portugal Andreia Costa INSTICC, Portugal ... Papadopoulos, Greece Laura Papaleo, Italy José Luis Martínez Pérez, Spain Jose ...
... Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board Dav... more ... Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon ... 133 Gayathri Nadarajan and Arnaud Renouf Rectified Reconstruction from Stereo Pairs and Robot Mapping ...
We introduce an extreme function theory as a novel method by which probabilistic novelty detectio... more We introduce an extreme function theory as a novel method by which probabilistic novelty detection may be performed with functions, where the functions are represented by time-series of (potentially multivariate) discrete observations. We set the method within the framework of Gaussian processes (GP), which offers a convenient means of constructing a distribution over functions. Whereas conventional novelty detection methods aim to identify individually extreme data points, with respect to a model of normality constructed using examples of "normal" data points, the proposed method aims to identify extreme functions, with respect to a model of normality constructed using examples of "normal" functions, where those functions are represented by time-series of observations. The method is illustrated using synthetic data, physiological data acquired from a large clinical trial, and a benchmark time-series dataset.
Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-det... more Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-determined thresholds, but the false-alarm rate of such monitors in hospitals is so high that alarms are typically ignored. We propose a principled, probabilistic method for combining vital signs into a multivariate model of patient state, using extreme value theory (EVT) to generate robust alarms if a patient's vital signs are deemed to have become sufficiently "extreme". Our proposed formulation operates many orders of magnitude faster than existing methods, allowing on-line learning of models, leading ultimately to patient-specific monitoring.
Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-det... more Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-determined thresholds, but the false-alarm rate of such monitors in hospitals is so high that alarms are typically ignored. We propose a principled, probabilistic method for combining vital signs into a multivariate model of patient state, using extreme value theory (EVT) to generate robust alarms if a patient's vital signs are deemed to have become sufficiently "extreme". Our proposed formulation operates many orders of magnitude faster than existing methods, allowing on-line learning of models, leading ultimately to patientspecific monitoring.
Novelty detection, or one-class classification, aims to determine if data are "normal" with respe... more Novelty detection, or one-class classification, aims to determine if data are "normal" with respect to some model of normality constructed using examples of normal system behaviour. If that model is composed of generative probability distributions, the extent of "normality" in the data space can be described using Extreme Value Theory (EVT), a branch of statistics concerned with describing the tails of distributions. This paper demonstrates that existing approaches to the use of EVT for novelty detection are appropriate only for univariate, unimodal problems. We generalise the use of EVT for novelty detection to the analysis of data with multivariate, multimodal distributions, allowing a principled approach to the analysis of high-dimensional data to be taken. Examples are provided using vitalsign data obtained from a large clinical study of patients in a high-dependency hospital ward.
Novelty detection is often used for analysis where there are insufficient examples of “abnormal” ... more Novelty detection is often used for analysis where there are insufficient examples of “abnormal” data to take a multi-class approach to classification. Models of normality are constructed from commonly-available examples of “normal” behaviour, and we then reason about the presence of abnormalities with respect to this normal model. Extreme value theory (EVT) is a branch of statistics that is concerned with modelling extremal events, and is therefore appealing for use with novelty detection. However, conventional existing EVT approaches are limited to the analysis of univariate or low-dimension data. This paper considers the peaks-over-threshold method of EVT, in which exceedances over a (typically univariate) threshold can be shown to tend towards the generalised Pareto distribution (GPD). We extend this method for use with high-dimensional data, allowing us to reason about the “extreme” data lying in the tails of the distributions of complex, real-world datasets, which are typically multivariate and multimodal. Illustrations are provided from the analysis of large clinical studies of hospital patient vital-sign data.
Novelty detection, one-class classification, or outlier detection, is typically employed for anal... more Novelty detection, one-class classification, or outlier detection, is typically employed for analysing signals when few examples of ldquoabnormalrdquo data are available, such that a multiclass approach cannot be taken. Multivariate, multimodal density estimation can be used to construct a model of the distribution of normal data. However, setting a decision boundary such that test data can be classified ldquonormalrdquo or ldquoabnormalrdquo with respect to the model of normality is typically performed using heuristic methods, such as thresholding the unconditional data density, p(x). This paper describes two principled methods of setting a decision boundary based on extreme value statistics: (i) a numerical method that produces an ldquooptimalrdquo solution, and (ii) an analytical approximation in closed form. We compare the performance of both approaches using large datasets from biomedical patient monitoring and jet engine health monitoring, and conclude that the analytical approach performs novelty detection as successfully as the ldquooptimalrdquo numerical approach, both of which outperform the conventional method.
Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-det... more Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-determined thresholds, but the false-alarm rate of such monitors in hospitals is so high that alarms are typically ignored. We propose a principled, probabilistic method for combining vital signs into a multivariate model of patient state, using extreme value theory (EVT) to generate robust alarms if a patient's vital signs are deemed to have become sufficiently "extreme". Our proposed formulation operates many orders of magnitude faster than existing methods, allowing on-line learning of models, leading ultimately to patient-specific monitoring.
Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to ... more Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to some generative distribution, effectively modelling the tails of that distribution. In novelty detection, or one-class classification, we wish to determine if data are ldquonormalrdquo with respect to some model of normality. If that model consists of generative distributions, then EVT is appropriate for describing the behaviour of extremes generated from the model, and can be used to determine the location of decision boundaries that separate ldquonormalrdquo areas of data space from ldquoabnormalrdquo areas in a principled manner. This paper introduces existing work in the use of EVT for novelty detection, shows that existing work does not accurately describe the extrema of multivariate, multimodal generative distributions, and proposes a novel method for overcoming such problems. The method is numerical, and provides optimal solutions for generative multivariate, multimodal distributions of arbitrary complexity. In a companion paper, we present analytical closed-form solutions which are currently limited to unimodal, multivariate generative distributions.
Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to ... more Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to some generative distribution, effectively modelling the tails of that distribution. In novelty detection, we wish to determine if data are ldquonormalrdquo with respect to some model of normality. If that model consists of generative distributions, then EVT is appropriate for describing the behaviour of extrema generated from the model, and can be used to separate ldquonormalrdquo areas from ldquoabnormalrdquo areas of feature space in a principled manner. In a companion paper, we show that existing work in the use of EVT for novelty detection does not accurately describe the extrema of multimodal, multivariate distributions and propose a numerical method for overcoming such problems. In this paper, we introduce an analytical approach to obtain closed-form solutions for the extreme value distributions of multivariate Gaussian distributions and present an application to vital-sign monitoring.
We propose a framework for fast and automated initialization of segmentation algorithms in Comput... more We propose a framework for fast and automated initialization of segmentation algorithms in Computed Tomography images. Based on the idea that time-consuming voxel classification should be done only on spatially constrained areas, we build classifiers at body and slice levels which quickly define a constrained region of interest. Voxel classification is then performed by a divide-and-conquer strategy using a probabilistic-boosting tree. In addition, this framework can incorporate additional information on the volume, if available, such as the position of another organ to improve its accuracy and robustness. The framework is applied to seed extraction in kidneys and liver.
Novelty detection involves the construction of a "model of normality", and then classifies test d... more Novelty detection involves the construction of a "model of normality", and then classifies test data as being either "normal" or "abnormal" with respect to that model. For this reason, it is often termed one-class classification. The approach is suitable for cases in which examples of "normal" behaviour are commonly available, but in which cases of "abnormal" data are comparatively rare. When performing novelty detection, we are typically most interested in the tails of the normal model, because it is in these tails that a decision boundary between "normal" and "abnormal" areas of data space usually lies. Extreme value statistics provides an appropriate theoretical framework for modelling the tails of univariate (or low-dimensional) distributions, using the generalised Pareto distribution (GPD), which can be demonstrated to be the limiting distribution for data occurring within the tails of most practically-encountered probability distributions. This paper provides an extension of the GPD, allowing the modelling of probability distributions of arbitrarily high dimension, such as occurs when using complex, multimodel, multivariate distributions for performing novelty detection in most real-life cases. We demonstrate our extension to the GPD using examples from patient physiological monitoring, in which we have acquired data from hospital patients in large clinical studies of high-acuity wards, and in which we wish to determine "abnormal" patient data, such that early warning of patient physiological deterioration may be provided.
... Azevedo Pedro Encarnação Teodiano Freire Bastos Filho Hugo Gamboa Ana Rita Londral António ..... more ... Azevedo Pedro Encarnação Teodiano Freire Bastos Filho Hugo Gamboa Ana Rita Londral António ... Coelhas INSTICC, Portugal Vera Coelho INSTICC, Portugal Andreia Costa INSTICC, Portugal ... Papadopoulos, Greece Laura Papaleo, Italy José Luis Martínez Pérez, Spain Jose ...
... Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board Dav... more ... Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon ... 133 Gayathri Nadarajan and Arnaud Renouf Rectified Reconstruction from Stereo Pairs and Robot Mapping ...
We introduce an extreme function theory as a novel method by which probabilistic novelty detectio... more We introduce an extreme function theory as a novel method by which probabilistic novelty detection may be performed with functions, where the functions are represented by time-series of (potentially multivariate) discrete observations. We set the method within the framework of Gaussian processes (GP), which offers a convenient means of constructing a distribution over functions. Whereas conventional novelty detection methods aim to identify individually extreme data points, with respect to a model of normality constructed using examples of "normal" data points, the proposed method aims to identify extreme functions, with respect to a model of normality constructed using examples of "normal" functions, where those functions are represented by time-series of observations. The method is illustrated using synthetic data, physiological data acquired from a large clinical trial, and a benchmark time-series dataset.
Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-det... more Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-determined thresholds, but the false-alarm rate of such monitors in hospitals is so high that alarms are typically ignored. We propose a principled, probabilistic method for combining vital signs into a multivariate model of patient state, using extreme value theory (EVT) to generate robust alarms if a patient's vital signs are deemed to have become sufficiently "extreme". Our proposed formulation operates many orders of magnitude faster than existing methods, allowing on-line learning of models, leading ultimately to patient-specific monitoring.
Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-det... more Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-determined thresholds, but the false-alarm rate of such monitors in hospitals is so high that alarms are typically ignored. We propose a principled, probabilistic method for combining vital signs into a multivariate model of patient state, using extreme value theory (EVT) to generate robust alarms if a patient's vital signs are deemed to have become sufficiently "extreme". Our proposed formulation operates many orders of magnitude faster than existing methods, allowing on-line learning of models, leading ultimately to patientspecific monitoring.
Novelty detection, or one-class classification, aims to determine if data are "normal" with respe... more Novelty detection, or one-class classification, aims to determine if data are "normal" with respect to some model of normality constructed using examples of normal system behaviour. If that model is composed of generative probability distributions, the extent of "normality" in the data space can be described using Extreme Value Theory (EVT), a branch of statistics concerned with describing the tails of distributions. This paper demonstrates that existing approaches to the use of EVT for novelty detection are appropriate only for univariate, unimodal problems. We generalise the use of EVT for novelty detection to the analysis of data with multivariate, multimodal distributions, allowing a principled approach to the analysis of high-dimensional data to be taken. Examples are provided using vitalsign data obtained from a large clinical study of patients in a high-dependency hospital ward.
Novelty detection is often used for analysis where there are insufficient examples of “abnormal” ... more Novelty detection is often used for analysis where there are insufficient examples of “abnormal” data to take a multi-class approach to classification. Models of normality are constructed from commonly-available examples of “normal” behaviour, and we then reason about the presence of abnormalities with respect to this normal model. Extreme value theory (EVT) is a branch of statistics that is concerned with modelling extremal events, and is therefore appealing for use with novelty detection. However, conventional existing EVT approaches are limited to the analysis of univariate or low-dimension data. This paper considers the peaks-over-threshold method of EVT, in which exceedances over a (typically univariate) threshold can be shown to tend towards the generalised Pareto distribution (GPD). We extend this method for use with high-dimensional data, allowing us to reason about the “extreme” data lying in the tails of the distributions of complex, real-world datasets, which are typically multivariate and multimodal. Illustrations are provided from the analysis of large clinical studies of hospital patient vital-sign data.
Novelty detection, one-class classification, or outlier detection, is typically employed for anal... more Novelty detection, one-class classification, or outlier detection, is typically employed for analysing signals when few examples of ldquoabnormalrdquo data are available, such that a multiclass approach cannot be taken. Multivariate, multimodal density estimation can be used to construct a model of the distribution of normal data. However, setting a decision boundary such that test data can be classified ldquonormalrdquo or ldquoabnormalrdquo with respect to the model of normality is typically performed using heuristic methods, such as thresholding the unconditional data density, p(x). This paper describes two principled methods of setting a decision boundary based on extreme value statistics: (i) a numerical method that produces an ldquooptimalrdquo solution, and (ii) an analytical approximation in closed form. We compare the performance of both approaches using large datasets from biomedical patient monitoring and jet engine health monitoring, and conclude that the analytical approach performs novelty detection as successfully as the ldquooptimalrdquo numerical approach, both of which outperform the conventional method.
Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-det... more Conventional patient monitoring is performed by generating alarms when vital signs exceed pre-determined thresholds, but the false-alarm rate of such monitors in hospitals is so high that alarms are typically ignored. We propose a principled, probabilistic method for combining vital signs into a multivariate model of patient state, using extreme value theory (EVT) to generate robust alarms if a patient's vital signs are deemed to have become sufficiently "extreme". Our proposed formulation operates many orders of magnitude faster than existing methods, allowing on-line learning of models, leading ultimately to patient-specific monitoring.
Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to ... more Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to some generative distribution, effectively modelling the tails of that distribution. In novelty detection, or one-class classification, we wish to determine if data are ldquonormalrdquo with respect to some model of normality. If that model consists of generative distributions, then EVT is appropriate for describing the behaviour of extremes generated from the model, and can be used to determine the location of decision boundaries that separate ldquonormalrdquo areas of data space from ldquoabnormalrdquo areas in a principled manner. This paper introduces existing work in the use of EVT for novelty detection, shows that existing work does not accurately describe the extrema of multivariate, multimodal generative distributions, and proposes a novel method for overcoming such problems. The method is numerical, and provides optimal solutions for generative multivariate, multimodal distributions of arbitrary complexity. In a companion paper, we present analytical closed-form solutions which are currently limited to unimodal, multivariate generative distributions.
Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to ... more Extreme Value Theory (EVT) describes the distribution of data considered extreme with respect to some generative distribution, effectively modelling the tails of that distribution. In novelty detection, we wish to determine if data are ldquonormalrdquo with respect to some model of normality. If that model consists of generative distributions, then EVT is appropriate for describing the behaviour of extrema generated from the model, and can be used to separate ldquonormalrdquo areas from ldquoabnormalrdquo areas of feature space in a principled manner. In a companion paper, we show that existing work in the use of EVT for novelty detection does not accurately describe the extrema of multimodal, multivariate distributions and propose a numerical method for overcoming such problems. In this paper, we introduce an analytical approach to obtain closed-form solutions for the extreme value distributions of multivariate Gaussian distributions and present an application to vital-sign monitoring.
We propose a framework for fast and automated initialization of segmentation algorithms in Comput... more We propose a framework for fast and automated initialization of segmentation algorithms in Computed Tomography images. Based on the idea that time-consuming voxel classification should be done only on spatially constrained areas, we build classifiers at body and slice levels which quickly define a constrained region of interest. Voxel classification is then performed by a divide-and-conquer strategy using a probabilistic-boosting tree. In addition, this framework can incorporate additional information on the volume, if available, such as the position of another organ to improve its accuracy and robustness. The framework is applied to seed extraction in kidneys and liver.
Uploads
Papers by Samuel Hugueny