Related papers: Construction of k-angle tight frames
The collection of $d \times N$ complex matrices with prescribed column norms and prescribed (nonzero) singular values forms a compact algebraic variety, which we refer to as a frame space. Elements of frame spaces -- i.e., frames -- are…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…
Recent feature matching methods have achieved remarkable performance but lack efficiency consideration. In this paper, we revisit the mainstream detector-free matching pipeline and improve all its stages considering both accuracy and…
Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…
Frames for $\R^n$ can be thought of as redundant or linearly dependent coordinate systems, and have important applications in such areas as signal processing, data compression, and sampling theory. The word "frame" has a different meaning…
We demonstrate an object tracking method for 3D images with fixed computational cost and state-of-the-art performance. Previous methods predicted transformation parameters from convolutional layers. We instead propose an architecture that…
Estimating fundamental matrices is a classic problem in computer vision. Traditional methods rely heavily on the correctness of estimated key-point correspondences, which can be noisy and unreliable. As a result, it is difficult for these…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
Non-integer dimensions are commonplace in quantum field theories (QFTs) through dimensional regularization. In particular this affects angular calculations involving dot products. The structure of these rises from the generally accepted…
Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…
Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
Many link prediction algorithms require the computation of a similarity metric on each vertex pair, which is quadratic in the number of vertices and infeasible for large networks. We develop a class of link prediction algorithms based on a…
Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix…
Efficient algorithms are presented for constructing spanners in geometric intersection graphs. For a unit ball graph in R^k, a (1+\epsilon)-spanner is obtained using efficient partitioning of the space into hypercubes and solving…
Time-dependent density functional theory (TDDFT) is a standard approach for calculating optical excitations of molecules and solids, while ensemble DFT (EDFT) is a promising alternative under development. We introduce ensemble TDDFT…
We introduce two federated learning frameworks for the classical SPDnet model operating on symmetric positive definite (SPD) matrices with Stiefel-constrained parameters. Unlike standard Euclidean averaging, which violates orthogonality,…
A framework is a graph and a map from its vertices to R^d. A framework is called universally rigid if there is no other framework with the same graph and edge lengths in R^d' for any d'. A framework attachment is a framework constructed by…
We show that real tight frames that generate lattices must be rational, and use this observation to describe a construction of lattices from vertex transitive graphs. In the case of irreducible group frames, we show that the corresponding…