Abstract

The performance of an anomaly detection task depends on the modeling of the input data. In the case of proportional data, Dirichlet and its general form distributions are a convenient choice to effectively capture the underlying characteristics of this kind of data.
In this thesis, we propose a normality score approach based on transformations that consist of learning a normality function. We suggest geometric transformations for image data and transformation-based neural networks for non-image data. Then, we propose an approximation of the softmax output vector of a classifier with generalized Dirichlet (GD), scaled Dirichlet (SD), shifted scaled Dirichlet (SSD), and Beta-Liouville (BL) distributions. We use a technique based on likelihood to determine its parameters.
Motivated by the salient characteristics of Liouville and Libby-Novick Beta distributions, we expand the Beta-Liouville distribution and build a new distribution called the Libby-Novick Beta-Liouville distribution. We demonstrate the efficiency of our proposed distribution through three challenging approaches. First, we develop generative models, namely finite mixture models of
Libby-Novick Beta-Liouville distributions. Then, we propose two discriminative techniques: normality scores based on selecting the given distribution to approximate the softmax output vector of
a deep classifier, and an improved version of the Support Vector Machine (SVM) by suggesting a feature mapping method. We test the efficiency of our suggested techniques for anomaly detection
tasks using several experimental settings and five data sets: three image data sets and two non-image data sets.