Related papers: Supercomputer Environment for Recursive Matrix Alg…
The inversion of structured sparse matrices is a key but computationally and memory-intensive operation in many scientific applications. There are cases, however, where only particular entries of the full inverse are required. This has…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…
We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank matrices at an exponential rate in the block…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
In inverting large sparse matrices, the key difficulty lies in effectively exploiting sparsity during the inversion process. One well-established strategy is the nested dissection, which seeks the so-called sparse Cholesky factorization. We…
We consider the problem of designing a coding scheme that allows both sparsity and privacy for distributed matrix-vector multiplication. Perfect information-theoretic privacy requires encoding the input sparse matrices into matrices…
This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…
Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
Large-scale machine learning (ML) models are increasingly being used in critical domains like education, lending, recruitment, healthcare, criminal justice, etc. However, the training, deployment, and utilization of these models demand…
The material in this note is used as an introduction to distributed algorithms in a four year course on software and automatic control system in the computer technology department of the Komsomolsk-on-Amur state technical university. All…
Associative memories are data structures addressed using part of the content rather than an index. They offer good fault reliability and biological plausibility. Among different families of associative memories, sparse ones are known to…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an…