We propose a family of Markov chain Monte Carlo methods whose performance is unaffected by affine tranformations of space. These algorithms are easy to construct and require little or no additional computational overhead. They should be particularly useful for sampling badly scaled distributions. Computational tests show that the affine invariant methods can be significantly faster than standard MCMC methods on highly skewed distributions.

/pdf/ensemble-samplers-with-affine-invariance-4t8yddl1e2.pdf

Ensemble samplers with affine invariance

Edited by the people who were forerunners in creating the field, together with contributions from 34 leading international experts, this handbook provides the definitive reference on Blind Source Separation, giving a broad and comprehensive description of all the core principles and methods, numerical algorithms and major applications in the fields of telecommunications, biomedical engineering and audio, acoustic and speech processing. Going beyond a machine learning perspective, the book reflects recent results in signal processing and numerical analysis, and includes topics such as optimization criteria, mathematical tools, the design of numerical algorithms, convolutive mixtures, and time frequency approaches. This Handbook is an ideal reference for university researchers, RD algebraic identification of under-determined mixtures, time-frequency methods, Bayesian approaches, blind identification under non negativity approaches, semi-blind methods for communicationsShows the applications of the methods to key application areas such as telecommunications, biomedical engineering, speech, acoustic, audio and music processing, while also giving a general method for developing applications

https://ie.technion.ac.il/~mcib/Gribonval_Zibulevsky_SCA_chapter.pdf

Handbook of Blind Source Separation: Independent Component Analysis and Applications

This article develops methods for determining visually appealing motion transitions using linear blending. Motion transitions are segues between two sequences of animation, and are important components for generating compelling animation streams in virtual environments and computer games. Methods involving linear blending are studied because of their efficiency, computational speed, and widespread use. Two methods of transition specification are detailed, center-aligned and start-end transitions. First, we compute a set of optimal weights for an underlying cost metric used to determine the transition points. We then evaluate the optimally weighted cost metric for generalizability, appeal, and robustness through a cross-validation and user study. Next, we develop methods for computing visually appealing blend lengths for two broad categories of motion. We empirically evaluate these results through user studies. Finally, we assess the importance of these techniques by determining the minimum sensitivity of viewers to transition durations, the just noticeable difference, for both center-aligned and start-end specifications.

Synthesis and evaluation of linear motion transitions

http://users.wfu.edu/plemmons/papers/BBLPP-rev.pdf

Algorithms and applications for approximate nonnegative matrix factorization

A general-purpose MATLAB software program called GPOPS--II is described for solving multiple-phase optimal control problems using variable-order Gaussian quadrature collocation methods. The software employs a Legendre-Gauss-Radau quadrature orthogonal collocation method where the continuous-time optimal control problem is transcribed to a large sparse nonlinear programming problem (NLP). An adaptive mesh refinement method is implemented that determines the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy. The software can be interfaced with either quasi-Newton (first derivative) or Newton (second derivative) NLP solvers, and all derivatives required by the NLP solver are approximated using sparse finite-differencing of the optimal control problem functions. The key components of the software are described in detail and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a useful platform upon which to solve a wide variety of complex constrained optimal control problems.

/pdf/gpops-ii-a-matlab-software-for-solving-multiple-phase-382v6ulw8t.pdf

GPOPS-II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming

Andreas Antoniou

Papers

Practical Optimization