18,237 research outputs found
Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework
While many existing formal concept analysis algorithms are efficient, they
are typically unsuitable for distributed implementation. Taking the MapReduce
(MR) framework as our inspiration we introduce a distributed approach for
performing formal concept mining. Our method has its novelty in that we use a
light-weight MapReduce runtime called Twister which is better suited to
iterative algorithms than recent distributed approaches. First, we describe the
theoretical foundations underpinning our distributed formal concept analysis
approach. Second, we provide a representative exemplar of how a classic
centralized algorithm can be implemented in a distributed fashion using our
methodology: we modify Ganter's classic algorithm by introducing a family of
MR* algorithms, namely MRGanter and MRGanter+ where the prefix denotes the
algorithm's lineage. To evaluate the factors that impact distributed algorithm
performance, we compare our MR* algorithms with the state-of-the-art.
Experiments conducted on real datasets demonstrate that MRGanter+ is efficient,
scalable and an appealing algorithm for distributed problems.Comment: 17 pages, ICFCA 201, Formal Concept Analysis 201
Methodology for automatic recovering of 3D partitions from unstitched faces of non-manifold CAD models
Data exchanges between different software are currently used in industry to speed up the preparation of digital prototypes for Finite Element Analysis (FEA). Unfortunately, due to data loss, the yield of the transfer of manifold models rarely reaches 1. In the case of non-manifold models, the transfer results are even less satisfactory. This is particularly true for partitioned 3D models: during the data transfer based on the well-known exchange formats, all 3D partitions are generally lost. Partitions are mainly used for preparing mesh models required for advanced FEA: mapped meshing, material separation, definition of specific boundary conditions, etc. This paper sets up a methodology to automatically recover 3D partitions from exported non-manifold CAD models in order to increase the yield of the data exchange. Our fully automatic approach is based on three steps. First, starting from a set of potentially disconnected faces, the CAD model is stitched. Then, the shells used to create the 3D partitions are recovered using an iterative propagation strategy which starts from the so-called manifold vertices. Finally, using the identified closed shells, the 3D partitions can be reconstructed. The proposed methodology has been validated on academic as well as industrial examples.This work has been carried out under a research contract between the Research and Development Direction of the EDF Group and the Arts et Métiers ParisTech Aix-en-Provence
Iterative Residual Fitting for Spherical Harmonic Transform of Band-Limited Signals on the Sphere: Generalization and Analysis
We present the generalized iterative residual fitting (IRF) for the
computation of the spherical harmonic transform (SHT) of band-limited signals
on the sphere. The proposed method is based on the partitioning of the subspace
of band-limited signals into orthogonal subspaces. There exist sampling schemes
on the sphere which support accurate computation of SHT. However, there are
applications where samples~(or measurements) are not taken over the predefined
grid due to nature of the signal and/or acquisition set-up. To support such
applications, the proposed IRF method enables accurate computation of SHTs of
signals with randomly distributed sufficient number of samples. In order to
improve the accuracy of the computation of the SHT, we also present the
so-called multi-pass IRF which adds multiple iterative passes to the IRF. We
analyse the multi-pass IRF for different sampling schemes and for different
size partitions. Furthermore, we conduct numerical experiments to illustrate
that the multi-pass IRF allows sufficiently accurate computation of SHTs.Comment: 5 Pages, 7 Figure
Information-Preserving Markov Aggregation
We present a sufficient condition for a non-injective function of a Markov
chain to be a second-order Markov chain with the same entropy rate as the
original chain. This permits an information-preserving state space reduction by
merging states or, equivalently, lossless compression of a Markov source on a
sample-by-sample basis. The cardinality of the reduced state space is bounded
from below by the node degrees of the transition graph associated with the
original Markov chain.
We also present an algorithm listing all possible information-preserving
state space reductions, for a given transition graph. We illustrate our results
by applying the algorithm to a bi-gram letter model of an English text.Comment: 7 pages, 3 figures, 2 table
Computing Exact Clustering Posteriors with Subset Convolution
An exponential-time exact algorithm is provided for the task of clustering n
items of data into k clusters. Instead of seeking one partition, posterior
probabilities are computed for summary statistics: the number of clusters, and
pairwise co-occurrence. The method is based on subset convolution, and yields
the posterior distribution for the number of clusters in O(n * 3^n) operations,
or O(n^3 * 2^n) using fast subset convolution. Pairwise co-occurrence
probabilities are then obtained in O(n^3 * 2^n) operations. This is
considerably faster than exhaustive enumeration of all partitions.Comment: 6 figure
Hierarchical bases for non-hierarchic 3Dtriangular meshes
We describe a novel basis of hierarchical, multiscale functions that are linear combinations of standard Rao-Wilton- Glisson (RWG) functions. When the basis is used for discretizing the electric field integral equation (EFIE) for PEC objects it gives rise to a linear system immune from low-frequency breakdown, and well conditioned for dense meshes. The proposed scheme can be applied to any mesh with triangular facets, and therefore it can be used as if it were an algebraic preconditioner. The properties of the new system are confirmed by numerical results that show fast convergence rates of iterative solvers, significantly better than those for the loop-tree basis. As a byproduct of the basis generation, a generalization of the RWG functions to nonsimplex cells is introduced
Explicit Model Checking of Very Large MDP using Partitioning and Secondary Storage
The applicability of model checking is hindered by the state space explosion
problem in combination with limited amounts of main memory. To extend its
reach, the large available capacities of secondary storage such as hard disks
can be exploited. Due to the specific performance characteristics of secondary
storage technologies, specialised algorithms are required. In this paper, we
present a technique to use secondary storage for probabilistic model checking
of Markov decision processes. It combines state space exploration based on
partitioning with a block-iterative variant of value iteration over the same
partitions for the analysis of probabilistic reachability and expected-reward
properties. A sparse matrix-like representation is used to store partitions on
secondary storage in a compact format. All file accesses are sequential, and
compression can be used without affecting runtime. The technique has been
implemented within the Modest Toolset. We evaluate its performance on several
benchmark models of up to 3.5 billion states. In the analysis of time-bounded
properties on real-time models, our method neutralises the state space
explosion induced by the time bound in its entirety.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-24953-7_1
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