Dense or Sparse : Elastic SPMM Implementation for Optimal Big-Data Processing

Abstract

Many real-world graph datasets can be represented using a sparse matrix format, and they are widely used for various big-data applications. The multiplication of two sparse matrices (SPMM) is a major kernel for various machine learning algorithms when using a sparsely expressed dataset. Apache Spark, a general-purpose big-data processing engine, includes the SPMM operation in its linear algebra package. The default Spark SPMM implementation, however, always converts a right sparse matrix to a dense format before performing multiplication, which can result in significant performance overhead for diverse SPMM scenarios. To address a limitation of the current Spark implementation, we describe an SPMM implementation that keeps the right matrix in a Compressed Sparse Column (CSC) format and propose an SPMM task latency prediction model based on a Deep Neural Network (DNN) architecture. Using the SPMM latency prediction model, we implement an elastic SPMM implementation recommendation service, which we name DoS ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> ense <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</b> r <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</b> parse). The proposed DoS recommends an optimal SPMM implementation method of either transforming a right matrix to a dense format or keeping it as a sparse format during the multiplication. Through evaluation of the proposed system using a real-world graph reveals that the proposed service can improve the SPMM latency of default Spark implementation by 2.2 times while shortening the overall execution time.