Matrix Factorization at Scale: a Comparison of Scientific Data Analytics in Spark and C+MPI Using Three Case Studies

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 and is optimized for data-parallel tasks. We examine three widely-used and important matrix factorizations: NMF (for physical plausability), PCA (for its ubiquity) and CX (for data interpretability). We apply these methods to TB-sized problems in particle physics, climate modeling and bioimaging. The data matrices are tall-and-skinny which enable the algorithms to map conveniently into Spark's data-parallel model. We perform scaling experiments on up to 1600 Cray XC40 nodes, describe the sources of slowdowns, and provide tuning guidance to obtain high performance

Online Tensor Methods for Learning Latent Variable Models

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2) topic modeling, in which we infer hidden topics of text articles. We consider decomposition of moment tensors using stochastic gradient descent. We conduct optimization of multilinear operations in SGD and avoid directly forming the tensors, to save computational and storage costs. We present optimized algorithm in two platforms. Our GPU-based implementation exploits the parallelism of SIMD architectures to allow for maximum speed-up by a careful optimization of storage and data transfer, whereas our CPU-based implementation uses efficient sparse matrix computations and is suitable for large sparse datasets. For the community detection problem, we demonstrate accuracy and computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic modeling problem, we also demonstrate good performance on the New York Times dataset. We compare our results to the state-of-the-art algorithms such as the variational method, and report a gain of accuracy and a gain of several orders of magnitude in the execution time.Comment: JMLR 201

Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.Comment: 24 pages, Elsevier Journal of Computational and Applied Mathematics, Dec 201

Accelerating Large-Scale Data Analysis by Offloading to High-Performance Computing Libraries using Alchemist

Apache Spark is a popular system aimed at the analysis of large data sets, but recent studies have shown that certain computations---in particular, many linear algebra computations that are the basis for solving common machine learning problems---are significantly slower in Spark than when done using libraries written in a high-performance computing framework such as the Message-Passing Interface (MPI). To remedy this, we introduce Alchemist, a system designed to call MPI-based libraries from Apache Spark. Using Alchemist with Spark helps accelerate linear algebra, machine learning, and related computations, while still retaining the benefits of working within the Spark environment. We discuss the motivation behind the development of Alchemist, and we provide a brief overview of its design and implementation. We also compare the performances of pure Spark implementations with those of Spark implementations that leverage MPI-based codes via Alchemist. To do so, we use data science case studies: a large-scale application of the conjugate gradient method to solve very large linear systems arising in a speech classification problem, where we see an improvement of an order of magnitude; and the truncated singular value decomposition (SVD) of a 400GB three-dimensional ocean temperature data set, where we see a speedup of up to 7.9x. We also illustrate that the truncated SVD computation is easily scalable to terabyte-sized data by applying it to data sets of sizes up to 17.6TB.Comment: Accepted for publication in Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, London, UK, 201