Related papers: Leveraging Sparsity to Speed Up Polynomial Feature…
In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which…
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…
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has…
Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…
Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…
Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks…
The emergence of long-context text applications utilizing large language models (LLMs) has presented significant scalability challenges, particularly in memory footprint. The linear growth of the Key-Value (KV) cache responsible for storing…
A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion.…
High-dimensional data has become ubiquitous across the sciences but presents computational and statistical challenges. A common approach to addressing these challenges is through sparsity. In this paper, we introduce a new concept of…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
Fast matrix multiplication algorithms may be useful, provided that their running time is good in practice. Particularly, the leading coefficient of their arithmetic complexity needs to be small. Many sub-cubic algorithms have large leading…
K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as…