Extending the Generalised Pareto Distribution for Novelty Detection in High-Dimensional Spaces

Clifton, David A.; Clifton, Lei; Hugueny, Samuel; Tarassenko, Lionel

doi:10.1007/s11265-013-0835-2

Cited by 19 publications

(14 citation statements)

References 25 publications

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“…This type of movements can also be found in other situations, like birdflights, and these models are also known as visual foraging or Levy-flight models (for more information see [1][2][3][4]). It is also related to the general problem of novelty detection (see [5]). As mentioned in the previous section we are here only interested in the statistical properties of the time-series of these eye-movements.…”

Section: Extreme Value Statistics and Information Geometrymentioning

confidence: 99%

Eye movements and information geometry

Lenz

2016

J. Opt. Soc. Am. A

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The human visual system uses scanning processes to gather visual information. These scanning processes can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks and recent models based on heavy tail distributions, also known as Levý flights, have been used in these investigations. In contrast to these approaches we do not model the stochastic processes, but we will show that the step length of the movements between fixation points follow generalized Pareto distributions (GPD). We will use general arguments from the theory of extreme value statistics to motivate the usage of the GPD and show empirically that the GPDs provide good fits for measured eye tracking data. In the framework of information geometry the GPDs with a common threshold form a two-dimensional Riemann manifold with the Fisher information matrix as a metric. We compute the Fisher information matrix for the GPDs and introduce a feature vector describing a GPD by its parameters and different geometrical properties of its Fisher information matrix. In our statistical analysis we use eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. We use standard software from toolboxes in Matlab ® with their standard parameter settings and show that a naive Bayes classifier using the eigenvalues of the Fisher information matrix provides a high classification rate identifying the 15 observers in the database.

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Section: Extreme Value Statistics and Information Geometrymentioning

confidence: 99%

Eye movements and information geometry

Lenz

2016

J. Opt. Soc. Am. A

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“…It would therefore be interesting to generalize this model such that the full magnitude vector can be utilized. This can be done by using GPD's in higher dimensional data spaces as described in [18].…”

Section: Extreme Value and Pareto Distributionsmentioning

confidence: 99%

Generalized Pareto Distributions—Application to Autofocus in Automated Microscopy

Lenz

2016

IEEE J. Sel. Top. Signal Process.

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Abstract-Dihedral filters correspond to the Fourier transform of functions defined on square grids. For gray value images there are six pairs of dihedral edge-detector pairs on 5x5 windows. In low-level image statistics the Weibull-or the generalized extreme value distributions are often used as statistical distributions modeling such filter results. Since only points with high filter magnitudes are of interest we argue that the generalized Pareto distribution is a better choice. Practically this also leads to more efficient algorithms since only a fraction of the raw filter results have to analyzed. The generalized Pareto distributions with a fixed threshold form a Riemann manifold with the Fisher information matrix as a metric tensor. For the generalized Pareto distributions we compute the determinant of the inverse Fisher information matrix as a function of the shape and scale parameters and show that it is the product of a polynomial in the shape parameter and the squared scale parameter. We then show that this determinant defines a sharpness function that can be used in autofocus algorithms. We evaluate the properties of this sharpness function with the help of a benchmark database of microscopy images with known ground truth focus positions. We show that the method based on this sharpness function results in a focus estimation that is within the given ground truth interval for a vast majority of focal sequences. Cases where it fails are mainly sequences with very poor image quality and sequences with sharp structures in different layers. The analytical structure given by the Riemann geometry of the space of probability density functions can be used to construct more efficient autofocus methods than other methods based on empirical moments.

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“…Vital-sign data from wearable sensors were fused with the manual observations made by the clinical staff for acutely ill, ambulatory patients in Clifton et al [23][24][25], using GPs and one-class support vector machines. Such methods have been extended by the use of health informatics based on extreme value theory, a branch of statistics used to model extremal data, and which have been demonstrated in a patient monitoring study in a US hospital [26,27]. The evidence base for the use of health informatics systems based on machine learning was questioned in [28], where methods for evaluating the efficacy of a system used for identifying the deteriorating patient in a large Emergency Department setting were described.…”

Section: Clinical Management Outside the Icu: Wearable Sensorsmentioning

confidence: 99%