1,132 research outputs found
The Dual JL Transforms and Superfast Matrix Algorithms
We call a matrix algorithm superfast (aka running at sublinear cost) if it
involves much fewer flops and memory cells than the matrix has entries. Using
such algorithms is highly desired or even imperative in computations for Big
Data, which involve immense matrices and are quite typically reduced to solving
linear least squares problem and/or computation of low rank approximation of an
input matrix. The known algorithms for these problems are not superfast, but we
prove that their certain superfast modifications output reasonable or even
nearly optimal solutions for large input classes. We also propose, analyze, and
test a novel superfast algorithm for iterative refinement of any crude but
sufficiently close low rank approximation of a matrix. The results of our
numerical tests are in good accordance with our formal study.Comment: 36.1 pages, 5 figures, and 1 table. arXiv admin note: text overlap
with arXiv:1710.07946, arXiv:1906.0411
Superfast Refinement of Low Rank Approximation of a Matrix
Low rank approximation (LRA) of a matrix is a hot subject of modern
computations. In application to Big Data mining and analysis the input matrices
are usually so immense that one must apply superfast algorithms, which only
access a tiny fraction of the input entries and involve much fewer memory cells
and flops than an input matrix has entries. Recently we devised and analyzed
some superfast LRA algorithms; in this paper we extend a classical algorithm of
iterative refinement of the solution of linear systems of equations to
superfast refinement of a crude but reasonably close LRA; we also list some
heuristic recipes for superfast a posteriori estimation of the errors of LRA
and support our superfast refinement algorithm with some superfast heuristic
recipes for a posteriori error estimation of LRA and with superfast back and
forth transition between any LRA of a matrix and its SVD. Our algorithm of
iterative refinement of LRA is the first attempt of this kind and should
motivate further effort in that direction, but already our initial tests are in
good accordance with our formal study.Comment: 12.5 pages,, 1 table and 1 figur
5-3 FUTURE DIRECTION OF WELDING STRUCTURE PRODUCTION(Session 5 : Utilization of Computers,SIMAP'88 Proceedings of International Symposium on Strategy of Innovation in Materials Processing-New Challenge for the 21st Century-)
THE STUDY ON INFLUENCES OF ONLINE REVIEW HELPFULNESS
With the surge in the number of the online review, how to get valuable information from a large number of useless information become a new problem that people face with when they shopping online. So far, many scholars have carried on some researches on this problem, but most of the studies were based on tangible goods\u27 online reviews, and studies about services\u27 online reviews are still very few. This research-in-progress aims to apply the ELM (Elaboration Likelihood Model) analysis framework to develop the model of customer review helpfulness from the perspective of cognitive theory. We plan to carry on empirical research on the review data of service from Dianping.com, and test the model presented in this paper according to the theoretical analysis
CUR Low Rank Approximation of a Matrix at Sublinear Cost
Low rank approximation of a matrix (hereafter LRA) is a highly important area
of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One
can operate with LRA at sublinear cost, that is, by using much fewer memory
cells and flops than an input matrix has entries, but no sublinear cost
algorithm can compute accurate LRA of the worst case input matrices or even of
the matrices of small families in our Appendix. Nevertheless we prove that
Cross-Approximation celebrated algorithms and even more primitive sublinear
cost algorithms output quite accurate LRA for a large subclass of the class of
all matrices that admit LRA and in a sense for most of such matrices. Moreover,
we accentuate the power of sublinear cost LRA by means of multiplicative
pre-processing of an input matrix, and this also reveals a link between C-A
algorithms and Randomized and Sketching LRA algorithms. Our tests are in good
accordance with our formal study.Comment: 29 pages, 5 figures, 5 tables. arXiv admin note: text overlap with
arXiv:1906.0492
Curvilinear object segmentation in medical images based on ODoS filter and deep learning network
Automatic segmentation of curvilinear objects in medical images plays an
important role in the diagnosis and evaluation of human diseases, yet it is a
challenging uncertainty in the complex segmentation tasks due to different
issues such as various image appearances, low contrast between curvilinear
objects and their surrounding backgrounds, thin and uneven curvilinear
structures, and improper background illumination conditions. To overcome these
challenges, we present a unique curvilinear structure segmentation framework
based on an oriented derivative of stick (ODoS) filter and a deep learning
network for curvilinear object segmentation in medical images. Currently, a
large number of deep learning models emphasize developing deep architectures
and ignore capturing the structural features of curvilinear objects, which may
lead to unsatisfactory results. Consequently, a new approach that incorporates
an ODoS filter as part of a deep learning network is presented to improve the
spatial attention of curvilinear objects. Specifically, the input image is
transfered into four-channel image constructed by the ODoS filter. In which,
the original image is considered the principal part to describe various image
appearance and complex background illumination conditions, a multi-step
strategy is used to enhance the contrast between curvilinear objects and their
surrounding backgrounds, and a vector field is applied to discriminate thin and
uneven curvilinear structures. Subsequently, a deep learning framework is
employed to extract various structural features for curvilinear object
segmentation in medical images. The performance of the computational model is
validated in experiments conducted on the publicly available DRIVE, STARE and
CHASEDB1 datasets. The experimental results indicate that the presented model
yields surprising results compared with those of some state-of-the-art methods.Comment: 20 pages, 8 figure
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