Related papers: SPIN: A Fast and Scalable Matrix Inversion Method …

Block projections have been used, in [Eberly et al. 2006], to obtain an efficient algorithm to find solutions for sparse systems of linear equations. A bound of softO(n^(2.5)) machine operations is obtained assuming that the input matrix…

Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…

With the explosive increase of big data in industry and academic fields, it is necessary to apply large-scale data processing systems to analysis Big Data. Arguably, Spark is state of the art in large-scale data computing systems nowadays,…

A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…

Apache Spark is a Big Data framework for working on large distributed datasets. Although widely used in the industry, it remains rather limited in the academic community or often restricted to software engineers. The goal of this paper is…

While Strassen's matrix multiplication algorithm reduces the complexity of naive matrix multiplication, general-purpose hardware is not suitable for achieving the algorithm's promised theoretical speedups. This leaves the question of if it…

We explore the trade-offs of performing linear algebra using Apache Spark, compared to traditional C and MPI implementations on HPC platforms. Spark is designed for data analytics on cluster computing platforms with access to local disks…

We construct a Neural Network that approximates the matrix multiplication operator for any activation function such that there exists a Neural Network which can approximate the scalar multiplication function. In particular, we use the…

The Apache Spark stack has enabled fast large-scale data processing. Despite a rich library of statistical models and inference algorithms, it does not give domain users the ability to develop their own models. The emergence of…

In the process of knowledge discovery and representation in large datasets using formal concept analysis, complexity plays a major role in identifying all the formal concepts and constructing the concept lattice(digraph of the concepts).…

How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…

In this paper we explore the performance limits of Apache Spark for machine learning applications. We begin by analyzing the characteristics of a state-of-the-art distributed machine learning algorithm implemented in Spark and compare it to…

Matrix multiplication $A^t A$ appears as intermediate operation during the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm for the $A^t A$ multiplication. Our algorithm, A$\scriptstyle…

The proliferation of mobile devices, such as smartphones and Internet of Things (IoT) gadgets, results in the recent mobile big data (MBD) era. Collecting MBD is unprofitable unless suitable analytics and learning methods are utilized for…

Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…

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…

Training deep networks is expensive and time-consuming with the training period increasing with data size and growth in model parameters. In this paper, we provide a framework for distributed training of deep networks over a cluster of CPUs…

Current trends in scientific imaging are challenged by the emerging need of integrating sophisticated machine learning with Big Data analytics platforms. This work proposes an in-memory distributed learning architecture for enabling…

In this paper, we evaluate Apache Spark for a data-intensive machine learning problem. Our use case focuses on policy diffusion detection across the state legislatures in the United States over time. Previous work on policy diffusion has…