Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

Additional co-authors: TJ Heaton, AG Hogg, KA Hughen, KF Kaiser, B Kromer, SW Manning, RW Reimer, DA Richards, JR Southon, S Talamo, CSM Turney, J van der Plicht, CE Weyhenmeyer

/pdf/intcal13-and-marine13-radiocarbon-age-calibration-curves-0-4f3vsbzfqx.pdf

IntCal13 and Marine13 radiocarbon age calibration curves 0-50,000 years cal BP

A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

Mean shift: a robust approach toward feature space analysis

A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

/pdf/gaussian-processes-for-machine-learning-40fp9c190d.pdf

Gaussian Processes for Machine Learning

Algorithms for clustering data

Using Kernel Density Estimates to Investigate Multimodality

Preface. Introduction. Approaches to Regression. Roughness Penalties. Extensions of the Roughness Penalty Approach. Computing the Estimates. Further Reading. Interpolating and Smoothing Splines. One-Dimensional Case: Further Topics. Partial Splines. Generalized Linear Models. Extending the Model. Thin Plate Splines. Available Software. Reference. Author Index. Subject Index.

Nonparametric regression and generalized linear models: a roughness penalty approach

Wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level-dependent soft threshold to the coefficients in the wavelet transform. A variety of threshold choices is proposed, including one based on an unbiased estimate of mean-squared error. The practical performance of the method is demonstrated on examples, including data from a neurophysiological context. The theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable `bench-mark', that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity, and more generally is obtained by the use of an `oracle' that provides information that is not actually available in the data. It is shown that the level-dependent threshold estimator performs well relative to the bench-mark risk, and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator. The wavelet domain structure of both short- and long-range dependent noise is considered, and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes, adapting automatically to the regularity properties of the underlying model. The proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem.

Wavelet threshold estimators for data with correlated noise

Estimating the mean and covariance structure nonparametrically when the data are curves

Despite their importance, we are only beginning to understand how mixed communities of bacteria operate. There is a good reason for this: the microbial world is remarkably complex and dynamic so it is difficult to design experiments that ask the right questions. Laboratory microcosms are useful but involve small numbers of species in unreal situations. A natural ecosystem that can be manipulated experimentally is available, however. Rainpools that form in bark-lined depressions at the base of European beech trees are communities of up to 72 species, rather than the thousands found in, say, pond water. In this rainpool ecosystem the number of bacterial species (the biodiversity) strongly influences the rate at which the community provides a particular service (in this case, respiration). On this scale at least, species richness determines the level at which an ecosystem can function. Bacterial communities provide important services. They break down pollutants, municipal waste and ingested food, and they are the primary means by which organic matter is recycled to plants and other autotrophs. However, the processes that determine the rate at which these services are supplied are only starting to be identified. Biodiversity influences the way in which ecosystems function1, but the form of the relationship between bacterial biodiversity and functioning remains poorly understood. Here we describe a manipulative experiment that measured how biodiversity affects the functioning of communities containing up to 72 bacterial species constructed from a collection of naturally occurring culturable bacteria. The experimental design allowed us to manipulate large numbers of bacterial species selected at random from those that were culturable. We demonstrate that there is a decelerating relationship between community respiration and increasing bacterial diversity. We also show that both synergistic interactions among bacterial species and the composition of the bacterial community are important in determining the level of ecosystem functioning.

Bernard W. Silverman

Papers

Using Kernel Density Estimates to Investigate Multimodality

Nonparametric regression and generalized linear models: a roughness penalty approach

Wavelet threshold estimators for data with correlated noise

Estimating the mean and covariance structure nonparametrically when the data are curves

The contribution of species richness and composition to bacterial services