Communications of the ACM
Scalable Linear Algebra on a Relational Database System
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As data analytics has become an important application for modern data management systems, a new category of data management system has appeared recently: the scalable linear algebra system. We argue that a parallel or distributed database system is actually an excellent platform upon which to build such functionality. Most relational systems already have support for cost-based optimization—which is vital to scaling linear algebra computations—and it is well known how to make relational systems scalable.
We show that by making just a few changes to a parallel/distributed relational database system, such a system can become a competitive platform for scalable linear algebra. Taken together, our results should at least raise the possibility that brand new systems designed from the ground up to support scalable linear algebra are not absolutely necessary, and that such systems could instead be built on top of existing relational technology.
1. Introduction
Data analytics, such as machine learning and large-scale statistical processing, is an important application domain, and such computations often require linear algebra. As such, a lot of recent efforts have been targeted at building distributed linear algebra systems, with the goal of supporting large-scale data analytics. Unlike classical efforts in high-performance computing such as ScaLAPACK6, such systems may include support for storage/retrieval of data to/from disk, buffering/caching of data, and automatic logical/physical optimizations of computations (automatic rewriting of queries, pipelining, etc.). Such systems also typically offer some form of recovery, as well as a domain-specific language.
One example of such a system is SystemML, developed at IBM.12 Given deep learning's reliance on arrays and array-based operations such as matrix multiply, systems facilitating distributed deep learning, such as TensorFlow,3 can also be included among such efforts. In the database area, there has long been of interest in building array database systems.17,5 A motivating use case for these systems is distributed linear algebra. Moreover, there have also been significant efforts targeted at using dataflow systems such as Apache Spark20 to build distributed linear algebra dataflow APIs (such as Spark's mllib.linalg1).
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