A Probabilistic Transformation of Distance-Based Outliers

Abstract

The scores of distance-based outlier detection methods are difficult to interpret, and it is challenging to determine a suitable cut-off threshold between normal and outlier data points without additional context. We describe a generic transformation of distance-based outlier scores into interpretable, probabilistic estimates. The transformation is ranking-stable and increases the contrast between normal and outlier data points. Determining distance relationships between data points is necessary to identify the nearest-neighbor relationships in the data, yet most of the computed distances are typically discarded. We show that the distances to other data points can be used to model distance probability distributions and, subsequently, use the distributions to turn distance-based outlier scores into outlier probabilities. Over a variety of tabular and image benchmark datasets, we show that the probabilistic transformation does not impact outlier ranking (ROC AUC) or detection performance (AP, F1), and increases the contrast between normal and outlier score distributions (statistical distance). The experimental findings indicate that it is possible to transform distance-based outlier scores into interpretable probabilities with increased contrast between normal and outlier samples. Our work generalizes to a wide range of distance-based outlier detection methods, and, because existing distance computations are used, it adds no significant computational overhead.

A Hybrid Approach to Improve the Video Anomaly Detection Performance of Pixel- and Frame-Based Techniques Using Machine Learning Algorithms

“…By examining the techniques used in the literature, it can be observed that anomaly detection techniques such as sparse coding [6,19,20], weakly supervised learning [21,22], spatio-temporal [4,23], normality learning-based [24][25][26][27], Gaussian mixture [28][29][30], graphbased [31,32], autoencoder technique [33][34][35], unsupervised anomaly detection [36,37], self-supervised learning [38][39][40][41] and probabilistic [42,43] models have been used.…”

Nonlinear Filter-Based Adaptive Output-Feedback Control for Uncertain Fractional-Order Nonlinear Systems with Unknown External Disturbance

“…Consider FO nonlinear systems (8) subject to unknown external disturbances and unmeasurable states. If the Assumptions 1-3 are satisfied, and a constant q > 0 exists , which guarantees V(0) ≤ q, then, by constructing a fractional fuzzy state observer (11), control functions (24), FO nonlinear filter (20), parameter updating laws (21) and (26), and a disturbance observer (28), all the closed-loop signals are bounded, and the system output y can track the given reference signal y d well.…”

“…. , n, and construct the FO state observer (11), the virtual controller and the actual controller (24), the parameter adaptation law (26), the disturbance observer (28), and the FO nonlinear filter (20), respectively.…”

“…In addition, many physical systems, such as circuit systems, can be expressed as FO nonlinear systems and are susceptible to electromagnetic perturbations from external environments. Electromagnetic interference is caused by the conduction and electrical radiation generated by devices similar to electromagnetic circles in the process of using current and voltage in the network environment [19][20][21], which has a destructive effect on electronic components and leads to abnormalities in the internal pulse clock system of electronic components. Consequently, it is necessary to address the disturbance suppression control for FO nonlinear systems with disturbances and modeling errors.…”