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We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…
We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…
We address the parallelization of the LU factorization of hierarchical matrices ($\mathcal{H}$-matrices) arising from boundary element methods. Our approach exploits task-parallelism via the OmpSs programming model and runtime, which…
In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz generalized symmetric matrix factorization model that unifies a broad class of matrix factorization formulations arising in machine learning, image science, engineering, and…
Algorithms and implementations for computing the sign function of a triangular matrix are fundamental building blocks in algorithms for computing the sign of arbitrary square real or complex matrices. We present novel recursive and cache…
In this paper we introduce Farthest Sampling Segmentation (FSS), a new method for segmentation of triangulated surfaces, which consists of two fundamental steps: the computation of a submatrix $W^k$ of the affinity matrix $W$ and the…
Lattice structures have been widely used in applications due to their superior mechanical properties. To fabricate such structures, a geometric processing step called triangulation is often employed to transform them into the STL format…
Incomplete factorization is a powerful preconditioner for Krylov subspace methods for solving large-scale sparse linear systems. Existing incomplete factorization techniques, including incomplete Cholesky and incomplete LU factorizations,…
Bias-scalable analog computing is attractive for implementing machine learning (ML) processors with distinct power-performance specifications. For instance, ML implementations for server workloads are focused on higher computational…
In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplication of a matrix with…
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an approximate generalized LU/LDL…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
There are two intertwined factors that affect performance of concurrent data structures: the ability of processes to access the data in parallel and the cost of synchronization. It has been observed that for a large class of…
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…
Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…
Recent research has focused on mitigating algorithmic bias in clustering by incorporating fairness constraints into algorithmic design. Notions such as disparate impact, community cohesion, and cost per population have been implemented to…
We present an efficient distributed memory parallel algorithm for computing connected components in undirected graphs based on Shiloach-Vishkin's PRAM approach. We discuss multiple optimization techniques that reduce communication volume as…
Linear algebra operations, which are ubiquitous in machine learning, form major performance bottlenecks. The High-Performance Computing community invests significant effort in the development of architecture-specific optimized kernels, such…