相关论文: Matrix Construction Using Cyclic Shifts of a Colum…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
Let $X$ be a $2$-dimensional subshift of finite type generated by a finite set of forbidden blocks (of finite size). We give an algorithm for generating the elements of the shift space using sequence of finite matrices (of increasing size).…
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of…
Symmetric positive semidefinite (SPSD) matrix approximation is an important problem with applications in kernel methods. However, existing SPSD matrix approximation methods such as the Nystr\"om method only have weak error bounds. In this…
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss…
We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs…
Finding an efficient optimal partial tiling algorithm is still an open problem. We have worked on a special case, the tiling of Manhattan polyominoes with dominoes, for which we give an algorithm linear in the number of columns. Some…
We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive…
A transfer-matrix algorithm is presented herein as a beginning to study the transmission characteristics of coherent light through three-dimensional periodic microstructures, in which the structures are treated as two-dimensional-layer…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
How can we leverage existing column relationships within silos, to predict similar ones across silos? Can we do this efficiently and effectively? Existing matching approaches do not exploit prior knowledge, relying on prohibitively…
Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to $O(n \sqrt{n})$. We also…