1,749 research outputs found
Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
Euclidean distance matrices (EDM) are matrices of squared distances between
points. The definition is deceivingly simple: thanks to their many useful
properties they have found applications in psychometrics, crystallography,
machine learning, wireless sensor networks, acoustics, and more. Despite the
usefulness of EDMs, they seem to be insufficiently known in the signal
processing community. Our goal is to rectify this mishap in a concise tutorial.
We review the fundamental properties of EDMs, such as rank or
(non)definiteness. We show how various EDM properties can be used to design
algorithms for completing and denoising distance data. Along the way, we
demonstrate applications to microphone position calibration, ultrasound
tomography, room reconstruction from echoes and phase retrieval. By spelling
out the essential algorithms, we hope to fast-track the readers in applying
EDMs to their own problems. Matlab code for all the described algorithms, and
to generate the figures in the paper, is available online. Finally, we suggest
directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine
- change of title in the last revisio
A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data: With applications in machine learning and signal processing
This article presents a powerful algorithmic framework for big data optimization, called the block successive upper-bound minimization (BSUM). The BSUM includes as special cases many well-known methods for analyzing massive data sets, such as the block coordinate descent (BCD) method, the convex-concave procedure (CCCP) method, the block coordinate proximal gradient (BCPG) method, the nonnegative matrix factorization (NMF) method, the expectation maximization (EM) method, etc. In this article, various features and properties of the BSUM are discussed from the viewpoint of design flexibility, computational efficiency, parallel/distributed implementation, and the required communication overhead. Illustrative examples from networking, signal processing, and machine learning are presented to demonstrate the practical performance of the BSUM framework
Divide-and-Conquer Method for Instanton Rate Theory
Ring-polymer instanton theory has been developed to simulate the quantum
dynamics of molecular systems at low temperatures. Chemical reaction rates can
be obtained by locating the dominant tunneling pathway and analyzing
fluctuations around it. In the standard method, calculating the fluctuation
terms involves the diagonalization of a large matrix, which can be unfeasible
for large systems with a high number of ring-polymer beads. Here we present a
method for computing the instanton fluctuations with a large reduction in
computational scaling. This method is applied to three reactions described by
fitted, analytic and on-the-fly ab initio potential-energy surfaces and is
shown to be numerically stable for the calculation of thermal reaction rates
even at very low temperature
IK-FA, a new heuristic inverse kinematics solver using firefly algorithm
In this paper, a heuristic method based on Firefly Algorithm is proposed for inverse kinematics problems in articulated robotics. The proposal is called, IK-FA. Solving inverse kinematics, IK, consists in finding a set of joint-positions allowing a specific point of the system to achieve a target position. In IK-FA, the Fireflies positions are assumed to be a possible solution for joints elementary motions. For a robotic system with a known forward kinematic model, IK-Fireflies, is used to generate iteratively a set of joint motions, then the forward kinematic model of the system is used to compute the relative Cartesian positions of a specific end-segment, and to compare it to the needed target position. This is a heuristic approach for solving inverse kinematics without computing the inverse model. IK-FA tends to minimize the distance to a target position, the fitness function could be established as the distance between the obtained forward positions and the desired one, it is subject to minimization. In this paper IK-FA is tested over a 3 links articulated planar system, the evaluation is based on statistical analysis of the convergence and the solution quality for 100 tests. The impact of key FA parameters is also investigated with a focus on the impact of the number of fireflies, the impact of the maximum iteration number and also the impact of (a, Ăź, Âż, d) parameters. For a given set of valuable parameters, the heuristic converges to a static fitness value within a fix maximum number of iterations. IK-FA has a fair convergence time, for the tested configuration, the average was about 2.3394 Ă— 10-3 seconds with a position error fitness around 3.116 Ă— 10-8 for 100 tests. The algorithm showed also evidence of robustness over the target position, since for all conducted tests with a random target position IK-FA achieved a solution with a position error lower or equal to 5.4722 Ă— 10-9.Peer ReviewedPostprint (author's final draft
Application of the Genetic Algorithm at Initial Stages of Ships Design
The main tasks for which the genetic algorithm is currently applied in shipbuilding are shown. The possibility of applying the genetic algorithm for determining the optimal characteristics of ships at the initial stages of design is considered.The formulation of the problem of parametric optimization for the initial stages of design is given. The features of such a problem and possible approaches to its solution are considered. Using the example of the problem of parametric optimization of small waterplane area twin hull ships, it is shown that the traditional methods of non-linear programming are not very effective. It is shown that one of the possible options for increasing the efficiency of searching for the optimal solution is the application of genetic algorithms. The mathematical bases of GA are considered and the scheme for finding the optimal solution using this method is described. The examples of test functions show the effectiveness of the genetic algorithm in comparison with traditional optimization methods. The results of solving the problem of parametric optimization of high-speed SWATH passenger ships are presented
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
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