相关论文: Eigenbackground Revisited: Can We Model the Backgr…

Eigenvector localization refers to the situation when most of the components of an eigenvector are zero or near-zero. This phenomenon has been observed on eigenvectors associated with extremal eigenvalues, and in many of those cases it can…

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…

Eigentrust is a simple and widely used algorithm, which quantifies trust based on the repeated application of an update matrix to a vector of initial trust values. In some cases, however, this procedure is rendered uninformative. Here, we…

One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…

We describe algorithms for computing eigenpairs (eigenvalue--eigenvector) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…

We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary…

Recent studies have shown that higher accuracy on ImageNet usually leads to better robustness against different corruptions. Therefore, in this paper, instead of following the traditional research paradigm that investigates new…

Reliably detecting anomalies in a given set of images is a task of high practical relevance for visual quality inspection, surveillance, or medical image analysis. Autoencoder neural networks learn to reconstruct normal images, and hence…

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…

The foreground segmentation algorithms suffer performance degradation in the presence of various challenges such as dynamic backgrounds, and various illumination conditions. To handle these challenges, we present a foreground segmentation…

With the rise of powerful foundation models, a pre-training-fine-tuning paradigm becomes increasingly popular these days: A foundation model is pre-trained using a huge amount of data from various sources, and then the downstream users only…

Background subtraction is a fundamental task in computer vision with numerous real-world applications, ranging from object tracking to video surveillance. Dynamic backgrounds poses a significant challenge here. Supervised deep…

Moran Eigenvector Spatial Filtering (ESF) approaches have shown promise in accounting for spatial effects in statistical models. Can this extend to machine learning? This paper examines the effectiveness of using Moran Eigenvectors as…

Despite unconditional feature inversion being the foundation of many image synthesis applications, training an inverter demands a high computational budget, large decoding capacity and imposing conditions such as autoregressive priors. To…

We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely…

Black-box adversarial attack has attracted a lot of research interests for its practical use in AI safety. Compared with the white-box attack, a black-box setting is more difficult for less available information related to the attacked…

Given a graph and one of its weighted Laplacian matrix, a Fiedler vector is an eigenvector with respect to the second smallest eigenvalue. The Fiedler vectors have been used widely for graph partitioning, graph drawing, spectral clustering,…

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…

Orthogonal weight matrices are used in many areas of deep learning. Much previous work attempt to alleviate the additional computational resources it requires to constrain weight matrices to be orthogonal. One popular approach utilizes…

Face Recognition is a common problem in Machine Learning. This technology has already been widely used in our lives. For example, Facebook can automatically tag people's faces in images, and also some mobile devices use face recognition to…