Related papers: An algorithm for identifying eigenvectors exhibiti…
In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…
We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its…
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…
The detection of the top eigenvalue and its corresponding eigenvector in ensembles of random matrices has significant applications across various fields. An existing method, based on the linear stability of a complementary set of cavity…
We describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large. We define the family of functions $f_{\alpha}: \left\{1.2. \dots,…
Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors…
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
Space and time are two critical components of many real world systems. For this reason, analysis of anomalies in spatiotemporal data has been a great of interest. In this work, application of tensor decomposition and eigenspace techniques…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
Mapper algorithm can be used to build graph-based representations of high-dimensional data capturing structurally interesting features such as loops, flares or clusters. The graph can be further annotated with additional colouring of…
Using our previously published algorithm, we analyze the eigenvectors of the generalized Laplacian for two metric graphs occurring in practical applications. As expected, localization of an eigenvector is rare and the network should be…
In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that…
Place classification is a fundamental ability that a robot should possess to carry out effective human-robot interactions. It is a nontrivial classification problem which has attracted many research. In recent years, there is a high…
We propose a new random process to construct the eigenvectors of some random operators which make a short and clean connection with the resolvent. In this process the center of localization has to be chosen randomly.
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…
Novel contour descriptors, called eigencontours, based on low-rank approximation are proposed in this paper. First, we construct a contour matrix containing all object boundaries in a training set. Second, we decompose the contour matrix…
Accurate localization in diverse environments is a fundamental challenge in computer vision and robotics. The task involves determining a sensor's precise position and orientation, typically a camera, within a given space. Traditional…
Reliable localization is crucial for autonomous robots to navigate efficiently and safely. Some navigation methods can plan paths with high localizability (which describes the capability of acquiring reliable localization). By following…
The ability of robots to estimate their location is crucial for a wide variety of autonomous operations. In settings where GPS is unavailable, measurements of transmissions from fixed beacons provide an effective means of estimating a…
Localization is the challenge of determining the robot's pose in a mapped environment. This is done by implementing a probabilistic algorithm to filter noisy sensor measurements and track the robot's position and orientation. This paper…