Since data sizes of analytical applications are continuously growing, many data scientists are switching from customized micro-solutions to scalable alternatives, such as statistical and scientific databases. However, many algorithms in data mining and science are expressed in terms of linear algebra, which is barely supported by major database vendors and big data solutions. On the other side, conventional linear algebra algorithms and legacy matrix representations are often not suitable for very large matrices. We propose a strategy for large matrix processing on modern multicore systems that is based on a novel, adaptive tile matrix representation (AT MATRIX). Our solution utilizes multiple techniques inspired from database technology, such as multidimensional data partitioning, cardinality estimation, indexing, dynamic rewrites, and many more in order to optimize the execution time. Based thereon we present a matrix multiplication operator ATMULT, which outperforms alternative approaches. The aim of our solution is to overcome the burden for data scientists of selecting appropriate algorithms and matrix storage representations. We evaluated AT MATRIX together with ATMULT on several real-world and synthetic random matrices.

In the age of statistical and scientific databases, there is an emerging trend of integrating analytical algorithms into database systems. Many of these algorithms are based on linear algebra with large, sparse matrices. However, linear algebra expressions often contain multiplications of more then two matrices. The execution of sparse matrix chains is nontrivial, since the runtime depends on the parenthesization and on physical properties of intermediate results. Our approach targets to overcome the burden for data scientists of selecting appropriate algorithms, matrix storage representations, and execution paths. In this paper, we present a sparse matrix chain optimizer (SpMachO) that creates an execution plan, which is composed of multiplication operators and transformations between sparse and dense matrix storage representations. We introduce a comprehensive cost model for sparse-, dense- and hybrid multiplication kernels. Moreover, we propose a sparse matrix product density estimator (SpProdest) for intermediate result matrices. We evaluated SpMachO and SpProdest using real-world matrices and random matrix chains.

Scientific computations and analytical business applications are often based on linear algebra operations on large, sparse matrices. With the hardware shift of the primary storage from disc into memory it is now feasible to execute linear algebra queries directly in the database engine. This paper presents and compares different approaches of storing sparse matrices in an in-memory column-oriented database system. We show that a system layout derived from the compressed sparse row representation integrates well with a columnar database design and that the resulting architecture is moreover amenable to a wide range of non-numerical use cases when dictionary encoding is used. Dynamic matrix manipulation operations, like online insertion or deletion of elements, are not covered by most linear algebra frameworks. Therefore, we present a hybrid architecture that consists of a read-optimized main and a write-optimized delta structure and evaluate the performance for dynamic sparse matrix workloads by applying workflows of nuclear science and network graphs.

Ambient Assisted Living (AAL) is a field of research activities focusing on IT support for healthcare, comfort and control applications for private home environments and seniors that has gained importance over the last years. AAL facilities often require positioning services, and generally need to offer easy installation and low energy consumption. We present an approach based on an ultrasound and RF system for three-dimensional indoor positioning and tracking using wall-mounted anchor nodes and a mobile positioning target. The target is a multifunctional customized handheld display and input device connected to the AAL environment. Positioning is achieved using TDoA distance measurement and a multilateration algorithm. To fulfill the low energy requirement, wall nodes are woken up only for positioning cycles by an ultrasonic pulse decoded by a custom electronic circuit and RF traffic is modelled with a small protocol footprint.