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Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…

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 analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming…

This paper analyzes the factorizability and geometry of transition matrices of multivariate Markov chains. Specifically, we demonstrate that the induced chains on factors of a product space can be regarded as information projections with…

This paper explores the performance optimization of out-of-core (OOC) Cholesky factorization on shared-memory systems equipped with multiple GPUs. We employ fine-grained computational tasks to expose concurrency while creating opportunities…

This paper presents a comparative analysis of distributed training strategies for large-scale neural networks, focusing on data parallelism, model parallelism, and hybrid approaches. We evaluate these strategies on image classification…

We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…

We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is $(A + iB)^{-1} = (A + BA^{-1}B)^{-1} - i A^{-1}B(A+BA^{-1} B)^{-1}$ when $A$ is invertible, which may be traced back to…

Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered…

In this paper, we consider two fundamental symmetric kernels in linear algebra: the Cholesky factorization and the symmetric rank-$k$ update (SYRK), with the classical three nested loops algorithms for these kernels. In addition, we…

Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…

Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…

A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…

Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…

In recent years, various means of efficiently detecting changepoints in the univariate setting have been proposed, with one popular approach involving minimising a penalised cost function using dynamic programming. In some situations, these…

In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

The binary-forking model is a parallel computation model, formally defined by Blelloch et al. very recently, in which a thread can fork a concurrent child thread, recursively and asynchronously. The model incurs a cost of $\Theta(\log n)$…

Matrix factorization (MF) discovers latent features from observations, which has shown great promises in the fields of collaborative filtering, data compression, feature extraction, word embedding, etc. While many problem-specific…