19,835 research outputs found
Divide and Conquer Partition for Fourier Reconstruction Sparse Inversion with its Applications
A partition method, with an efficient divide and conquer partition strategy, for the non-uniform sampling signal reconstruction based on Fourier reconstruction sparse inversion (FRSI) is developed. The novel partition FRSI(P-FRSI) is motivated by the observation that the partition processing of multi-dimensional signals can reduce the reconstruction difficulty and save the reconstruction time. Moreover, it is helpful to choose suitable reconstruction parameters. The P-FRSI employs divide and conquer strategy, and the signal is firstly partitioned into some blocks. Following that, traditional FRSI is applied to reconstruct signals in each block. We adopt linear or nonlinear superposition to determine the weight coefficients during integrating these blocks. Finally, P-FRSI is applied to two-dimensional seismic signal reconstruction. The superiority of the new method over conventional FRSI is demonstrated by numerical reconstruction experiments
Optimum Partition Parameter of Divide-and-Conquer Algorithm for Solving Closest-Pair Problem
Divide and Conquer is a well known algorithmic procedure for solving many
kinds of problem. In this procedure, the problem is partitioned into two parts
until the problem is trivially solvable. Finding the distance of the closest
pair is an interesting topic in computer science. With divide and conquer
algorithm we can solve closest pair problem. Here also the problem is
partitioned into two parts until the problem is trivially solvable. But it is
theoretically and practically observed that sometimes partitioning the problem
space into more than two parts can give better performances. In this paper, a
new proposal is given that dividing the problem space into (n) number of parts
can give better result while divide and conquer algorithm is used for solving
the closest pair of point's problem.Comment: arXiv admin note: substantial text overlap with arXiv:1010.590
A Divide-and-Conquer Solver for Kernel Support Vector Machines
The kernel support vector machine (SVM) is one of the most widely used
classification methods; however, the amount of computation required becomes the
bottleneck when facing millions of samples. In this paper, we propose and
analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the
division step, we partition the kernel SVM problem into smaller subproblems by
clustering the data, so that each subproblem can be solved independently and
efficiently. We show theoretically that the support vectors identified by the
subproblem solution are likely to be support vectors of the entire kernel SVM
problem, provided that the problem is partitioned appropriately by kernel
clustering. In the conquer step, the local solutions from the subproblems are
used to initialize a global coordinate descent solver, which converges quickly
as suggested by our analysis. By extending this idea, we develop a multilevel
Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction
strategy, which outperforms state-of-the-art methods in terms of training
speed, testing accuracy, and memory usage. As an example, on the covtype
dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in
obtaining the exact SVM solution (to within relative error) which
achieves 96.15% prediction accuracy. Moreover, with our proposed early
prediction strategy, DC-SVM achieves about 96% accuracy in only 12 minutes,
which is more than 100 times faster than LIBSVM
"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems
We extensively describe our recently established "divide-and-conquer"
semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett.
119, 010401 (2017)] and propose a new implementation of it to increase the
accuracy of results. The technique permits to perform spectroscopic
calculations of high dimensional systems by dividing the full-dimensional
problem into a set of smaller dimensional ones. The partition procedure,
originally based on a dynamical analysis of the Hessian matrix, is here more
rigorously achieved through a hierarchical subspace-separation criterion based
on Liouville's theorem. Comparisons of calculated vibrational frequencies to
exact quantum ones for a set of molecules including benzene show that the new
implementation performs better than the original one and that, on average, the
loss in accuracy with respect to full-dimensional semiclassical calculations is
reduced to only 10 wavenumbers. Furthermore, by investigating the challenging
Zundel cation, we also demonstrate that the "divide-and-conquer" approach
allows to deal with complex strongly anharmonic molecular systems. Overall the
method very much helps the assignment and physical interpretation of
experimental IR spectra by providing accurate vibrational fundamentals and
overtones decomposed into reduced dimensionality spectra
- …