Ryan Sigurdson, Carmeliza Navasca · 2012
We present a method for the image classification problem. First, the set of images is organized in a tensor format. Then, we define several classes in terms of subtensors of the same type of images. The method relies on the tensor dimensionality reduction algorithm to create the basis of the subtensor. Our algorithm was tested on the AT&T database of faces. From our experiments, the algorithm successfully classifies unknown images from the measured residual.
Cited by 2
Darya V. Verveyko, Andrey Yu. Verisokin, Dmitry E. Postnov · 2020 11th Conference of the European Study Group on Cardiovascular Oscillations (ESGCO) · 2020
The following topics are dealt with: medical signal processing; electrocardiography; cardiovascular system; diseases; neurophysiology; cardiology; blood vessels; time series; pneumodynamics and haemodynamics.
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Kianna Wan, Mario Berta, Earl T. Campbell · Physical Review Letters · 2022
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyze a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent of the number of terms L in the Hamiltonian. Second, unlike previous L-independent approaches, such as those based on qDRIFT, all algorithmic errors in our method can be suppressed by collecting more data samples, without increasing the circuit depth.
Cited by 81Open access
Nader H. Bshouty, Nuha Diab, Shada R. Kawar et al. · arXiv (Cornell University) · 2017
We study the problem of group testing with a non-adaptive randomized algorithm in the random incidence design (RID) model where each entry in the test is chosen randomly independently from $\{0,1\}$ with a fixed probability $p$. The property that is sufficient and necessary for a unique decoding is the separability of the tests, but unfortunately no linear time algorithm is known for such tests. In order to achieve linear-time decodable tests, the algorithms in the literature use the disjunction property that gives almost optimal number of tests. We define a new property for the tests which we call semi-disjunction property. We show that there is a linear time decoding for such test and for $d\to \infty$ the number of tests converges to the number of tests with the separability property and is therefore optimal (in the RID model). Our analysis shows that, in the RID model, the number of tests in our algorithm is better than the one with the disjunction property even for small $d$.
Cited by 0Open access
Takayuki Wada, Yasumasa Fujisaki · Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications · 2017
Robust bilinear matrix inequality (BMI) optimization, which is to minimize an objective function subject to a parameter dependent BMI constraint, is considered. A recursive algorithm employing a branch-and-bound technique and randomization of a parameter is provided for solving the problem. When the algorithm finds a solution, this solution satisfies the parameter dependent constraint with a prescribed accuracy in a probabilistic sense. Furthermore, the objective function value at that solution ensures that the feasible set whose objective function value is less than this value is too small to be found.
Cited by 0Open access
Qiaochu Yuan, Ming Gu, Bo Li · 2018
The low rank approximation of a matrix is a crucial component in many data mining applications today. A competitive algorithm for this class of problems is the randomized block Lanczos algorithm - an amalgamation of the traditional block Lanczos algorithm with a randomized starting matrix. While empirically this algorithm performs well, there has been scant new theoretical insights on its convergence behavior and approximation accuracy, and those known results have been restricted to impractical settings in the all-important block-size parameter. In this paper, we present a unified singular value convergence analysis for this algorithm, for all valid choices of the block size. We present novel singular value lower bounds and demonstrate superlinear convergence in leading singular values for matrices with decaying singular values. Additionally, we provide results from numerical experiments that validate our analysis.
Cited by 13
Clark F. Olson · 1997
. Pose clustering is a method to perform object recognition by determining hypothetical object poses and finding clusters of the poses in the space of legal object positions. An object that appears in an image will yield a large cluster of such poses close to the correct position of the object. If there are m model features and n image features, then there are O(m 3 n 3 ) hypothetical poses that can be determined from minimal information for the case of recognition of three-dimensional objects from feature points in two-dimensional images. Rather than clustering all of these poses, we show that pose clustering can have equivalent performance for this case when examining only O(mn) poses, due to correlation between the poses, if we are given two correct matches between model features and image features. Since we do not usually know two correct matches in advance, this property is used with randomization to decompose the pose clustering problem into O(n 2 ) problems, each of which...
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Vinay Kumar Singhal, Akanksha Rastogi · 2012
Given a set of points P, a conflict-free coloring of P is an assignment of colors to points of P, such that there exist a point p in any subset of P whose color is distinct from all other points in that subset of P. This notion is motivated by frequency assignment in wireless cellular networks: one would like to minimize the number of frequencies (colors) assigned to base stations (points), such that within any range, there is no interference. We provide a framework for randomized conflict-free coloring (CF-coloring) any k-degenerate hypergraph. Our algorithm uses O(log n) colors with high probability.
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N.D. Botkin · 2007
An algorithm for solving linearly constrained general convex quadratic problems is proposed *. The expected running time of the algorithm is O(dd!m) where m is the number of inequality constraints and d is the number of variables. This algorithm is based on the ideas of Seidel's linear programming algorithm (Seidel,1991). It is closely related to algorithms of (Welzl,1991,Yoshiba,1992) and has some features of the one proposed in (Stoer,1992). Keywords Linearly constrained general convex quadratic problems, randomized algorithms. 1 INTRODUCTION This paper extends the class of problems which can be solved by means of randomized algorithms like the ones developed in (Seidel,1991,Welzl,1991,Yoshiba,1992). The linearly constrained general convex quadratic problem is included into the conception of randomized algorithms. The algorithm proposed has the structure which is typical for randomized procedures described in (Seidel,1991,Welzl,1991,Yoshiba,1992) and has the same estimate of the ...
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NTUR (臺灣機構典藏) · 2007
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Burak Yılmaz, Korkut Bekiroglu, Constantino Lagoa et al. · IEEE Transactions on Automatic Control · 2017
Identifying parsimonious models is generically a “hard” nonconvex problem. Available approaches typically rely on relaxations such as Group Lasso or nuclear norm minimization. Moreover, incorporating stability and model order constraints into the formalism in such methods entails a substantial increase in computational complexity. Motivated by these challenges, in this paper we present algorithms for parsimonious linear time invariant system identification aimed at identifying low-complexity models which i) incorporate a priori knowledge on the system (e.g., stability), ii) allow for data with missing/nonuniform measurements, and iii) are able to use data obtained from several runs of the system with different unknown initial conditions. The randomized algorithms proposed are based on the concept of atomic norm and provide a numerically efficient way to identify sparse models from large amounts of noisy data.
Cited by 24
E. Amaldi, Pietro Belotti, Raphael Hauser · Oxford University Research Archive (ORA) (University of Oxford) · 2005
We consider the NP-hard combinatorial optimization problem of finding a feasible subsystem of maximum cardinality among a given set of linear inequalities. In some new and challenging applications in digital broadcasting and in the modelling of protein folding potentials one faces very large MaxFS instances with up to millions of inequalities in thousands of variables. We introduce and analyze a randomized algorithm that is surprisingly successful at solving MaxFS instances that arise in these contexts and exhibit some numerical results. Raphael Hauser was supported through grant NAL/00720/G from the Nuffield Foundation and through grant GR/M30975 from the Engineering and Physical Sciences Research Council of the UK
Cited by 1Open access
Qiaochu Yuan, Ming Gu, Bo Li · arXiv (Cornell University) · 2018
The low rank approximation of matrices is a crucial component in many data mining applications today. A competitive algorithm for this class of problems is the randomized block Lanczos algorithm - an amalgamation of the traditional block Lanczos algorithm with a randomized starting matrix. While empirically this algorithm performs quite well, there has been scant new theoretical results on its convergence behavior and approximation accuracy, and past results have been restricted to certain parameter settings. In this paper, we present a unified singular value convergence analysis for this algorithm, for all valid choices of the block size parameter. We present novel results on the rate of singular value convergence and show that under certain spectrum regimes, the convergence is superlinear. Additionally, we provide results from numerical experiments that validate our analysis.
Cited by 2Open access
Konstantin Аmelin, Natalia Amelina, Oleg Granichin et al. · IFAC Proceedings Volumes · 2013
Cited by 21
Xingbo Wang · Journal of Advances in Mathematics and Computer Science · 2023
This paper investigates the densification of witnesses for randomized algorithm design and its application in factoring integers. By defining a set operation named with Cartesian subtraction on two countable sets and proving several properties of the operation, it is shown that the Cartesian subtraction can densify certain elements in a countable set so as to promote the abundance of witnesses for the randomized algorithm design. It is also proven that the Cartesian subtraction of two sets containing consecutive integers can form a triangular lattice zone that has a higher density of witnesses. Through designing an algorithm of a two-dimensional simple random walk on the triangular lattice zone, it is demonstrated that composite integers can be factored by means of the random walk. The study of the paper explores a pathway feasible and workable to densify the small witnesses in a countable set for randomized algorithm designs.
Cited by 1Open access
Thomas Strohmer, Roman Vershynin · Journal of Fourier Analysis and Applications · 2008
Cited by 892
Log Polynomial, Hing F. Ting, Andrew C. Yao · 1993
A well-known result by Rabin [1] implies that n 0 1 polynomial tests are necessary and sufficient in the worst case to find the maximum of n distinct real numbers. In this note we show that, for any fixed constant c ? 0, there is a randomized algorithm with error probability O(n 0c ) for finding the maximum of n distinct real numbers using only O((log n) 2 ) polynomial tests. keywords: algorithms, decision trees, maximum, parity tests, randomized algorithms. 1 Department of Computer Science, Chinese University of Hong Kong, Shatin, Hong Kong. 2 Department of Computer Science, Princeton University, Princeton, New Jersey 08544, USA. A polynomial decision tree is a decision tree using tertiary tests of the form p(x 1 ; x 2 ; 1 1 1 ; x n ) : 0 where p are polynomials over the reals. Clearly, there is a polynomial decision tree of height n 0 1 for finding the maximum of n distinct input numbers x 1 ; x 2 ; 1 1 1 ; x n . A well-known result by Rabin [1, Theorem 4] implies that th...
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Virendra K. Janakiram, Edward F. Gehringer, Dharma P. Agrawal et al. · International Journal of Parallel Programming · 1988
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Hongming Liu, Yujie Zhou, Nianhao Zhu · WIT transactions on information and communication technologies · 2014
Welcome to the WIT Press eLibrary - the home of the Transactions of the Wessex Institute collection, providing on-line access to papers presented at the Institute's prestigious international conferences and from its State-of-the-Art in Science & Engineering publications.
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2008
Abstract. Shop scheduling problems are known to be notoriously intractable, both in theory and practice. In this paper we give a randomized approximation algorithm for flow shop scheduling where the number of machines is part of the input problem. Our algorithm has a multiplicative factor of 2(1 + ffi) and an additive term of O(m ln(m + n)pmax)/ffi2). 1 Introduction Shop scheduling has been studied extensively in many varieties. The basic shopscheduling model consists of machines and jobs each of which consists of a set of operations. Each operation has an associated machine on which it has to beprocessed for a given length of time. The processing times of operations of a job cannot overlap. Each machine can process at most one operation at a giventime. We assume that there are m machines and n jobs. The processing time(ofan operation) of job j on machine i is denoted by pij and pmax = max pij. Wewill use the terms job(operation) size and processing time interchangeably.
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