An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factorization leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK -- STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices

The Extended Edit Distance Metric

Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high dimensional data objects. We propose a new distance metric that is applied to symbolic data objects and we test it on time series data bases in a classification task. We compare it to other distances that are well known in the literature for symbolic data objects. We also prove, mathematically, that our distance is metric.Comment: Technical repor

The Algorithmic Information Content for randomly perturbed systems

In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai entropy relative to a partition for randomly perturbed dynamical systems. Our estimates use the entropy for the unperturbed system and are obtained using the notion of Algorithmic Information Content. The main result is an extension of known results to study time series obtained by the observation of real systems.Comment: 17 pages, 1 figur

The Variable Markov Oracle: Algorithms for Human Gesture Applications

This article introduces the Variable Markov Oracle (VMO) data structure for multivariate time series indexing. VMO can identify repetitive fragments and find sequential similarities between observations. VMO can also be viewed as a combination of online clustering algorithms with variable-order Markov constraints. The authors use VMO for gesture query-by-content and gesture following. A probabilistic interpretation of the VMO query-matching algorithm is proposed to find an analogy to the inference problem in a hidden Markov model (HMM). This probabilistic interpretation extends VMO to be not only a data structure but also a model for time series. Query-by-content experiments were conducted on a gesture database that was recorded using a Kinect 3D camera, showing state-of-the-art performance. The query-by-content experiments' results are compared to previous works using HMM and dynamic time warping. Gesture following is described in the context of an interactive dance environment that aims to integrate human movements with computer-generated graphics to create an augmented reality performance

Distributed graph-based state space generation

LTSMIN provides a framework in which state space generation can be distributed easily over many cores on a single compute node, as well as over multiple compute nodes. The tool works on the basis of a vector representation of the states; the individual cores are assigned the task of computing all successors of states that are sent to them. In this paper we show how this framework can be applied in the case where states are essentially graphs interpreted up to isomorphism, such as the ones we have been studying for GROOVE. This involves developing a suitable vector representation for a canonical form of those graphs. The canonical forms are computed using a third tool called BLISS. We combined the three tools to form a system for distributed state space generation based on graph grammars. We show that the time performance of the resulting system scales well (i.e., close to linear) with the number of cores. We also report surprising statistics on the memory\ud consumption, which imply that the vector representation used to store graphs in LTSMIN is more compact than the representation used in GROOVE