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The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

Anomaly detection or outlier detection is a common task in various domains, which has attracted significant research efforts in recent years. Existing works mainly focus on structured data such as numerical or categorical data; however,…

For open world applications, deep neural networks (DNNs) need to be aware of previously unseen data and adaptable to evolving environments. Furthermore, it is desirable to detect and learn novel classes which are not included in the DNNs…

In the real world, out-of-distribution samples, noise and distortions exist in test data. Existing deep networks developed for point cloud data analysis are prone to overfitting and a partial change in test data leads to unpredictable…

Semi-supervised video anomaly detection (VAD) methods formulate the task of anomaly detection as detection of deviations from the learned normal patterns. Previous works in the field (reconstruction or prediction-based methods) suffer from…

Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network…

This thesis makes considerable contributions to the realm of machine learning, specifically in the context of open-world scenarios where systems face previously unseen data and contexts. Traditional machine learning models are usually…

Unsupervised anomaly detection encompasses diverse applications in industrial settings where a high-throughput and precision is imperative. Early works were centered around one-class-one-model paradigm, which poses significant challenges in…

Recent advancements in weakly-supervised video anomaly detection have achieved remarkable performance by applying the multiple instance learning paradigm based on multimodal foundation models such as CLIP to highlight anomalous instances…

In anomaly detection, a prominent task is to induce a model to identify anomalies learned solely based on normal data. Generally, one is interested in finding an anomaly detector that correctly identifies anomalies, i.e., data points that…

Hacking and false data injection from adversaries can threaten power grids' everyday operations and cause significant economic loss. Anomaly detection in power grids aims to detect and discriminate anomalies caused by cyber attacks against…

One-class support vector machine (OC-SVM) for a long time has been one of the most effective anomaly detection methods and extensively adopted in both research as well as industrial applications. The biggest issue for OC-SVM is yet the…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…

Object detection is a pivotal task in computer vision that has received significant attention in previous years. Nonetheless, the capability of a detector to localise objects out of the training distribution remains unexplored. Whilst…

In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an…

Distance-based methods involve the computation of distance values between features and are a well-established paradigm in machine learning. In anomaly detection, anomalies are identified by their large distance from normal data points.…

Unsupervised deep learning techniques are widely used to identify anomalous behaviour. The performance of such methods is a product of the amount of training data and the model size. However, the size is often a limiting factor for the…

The effective application of representation learning to real-world problems requires both techniques for learning useful representations, and also robust ways to evaluate properties of representations. Recent work in disentangled…