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Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been…
We investigate a parallelization strategy for dense matrix factorization (DMF) algorithms, using OpenMP, that departs from the legacy (or conventional) solution, which simply extracts concurrency from a multithreaded version of BLAS. This…
Multiresponse data with complex group structures in both responses and predictors arises in many fields, yet, due to the difficulty in identifying complex group structures, only a few methods have been studied on this problem. We propose a…
We present a generic compact computational framework relying on structured random matrices that can be applied to speed up several machine learning algorithms with almost no loss of accuracy. The applications include new fast LSH-based…
Sparse matrix-vector products (SpMVs) are a bottleneck in many scientific codes. Due to the heavy strain on the main memory interface from loading the sparse matrix and the possibly irregular memory access pattern, SpMV typically exhibits…
HipMCL is a high-performance distributed memory implementation of the popular Markov Cluster Algorithm (MCL) and can cluster large-scale networks within hours using a few thousand CPU-equipped nodes. It relies on sparse matrix computations…
Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental computation in graph analytics, scientific simulation, and sparse deep learning workloads. However, the extreme irregularity of real-world sparse matrices prevents existing…
Deep learning demonstrates effectiveness across a wide range of tasks. However, the dense and over-parameterized nature of these models results in significant resource consumption during deployment. In response to this issue, weight…
Sparse matrix-vector and matrix-matrix multiplication (SpMV and SpMM) are fundamental in both conventional (graph analytics, scientific computing) and emerging (sparse DNN, GNN) domains. Workload-balancing and parallel-reduction are…
An improved version of the sparse multiway kernel spectral clustering (KSC) is presented in this brief. The original algorithm is derived from weighted kernel principal component (KPCA) analysis formulated within the primal-dual…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
Sparse linear algebra kernels play a critical role in numerous applications, covering from exascale scientific simulation to large-scale data analytics. Offloading linear algebra kernels on one GPU will no longer be viable in these…
As enjoying the closed form solution, least squares support vector machine (LSSVM) has been widely used for classification and regression problems having the comparable performance with other types of SVMs. However, LSSVM has two drawbacks:…
Numerical investigation of compressible flows faces two main challenges. In order to accurately describe the flow characteristics, high-resolution nonlinear numerical schemes are needed to capture discontinuities and resolve wide…
In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data…
Dense embedding models are commonly deployed in commercial search engines, wherein all the document vectors are pre-computed, and near-neighbor search (NNS) is performed with the query vector to find relevant documents. However, the…
Scientists increasingly rely on Python tools to perform scalable distributed memory array operations using rich, NumPy-like expressions. However, many of these tools rely on dynamic schedulers optimized for abstract task graphs, which often…
This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…