Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

The application of Prony’s method to time-domain waveform data modeling in the presence of noise

In this paper,the Prony's method is applied to the time-domain waveform data modelling in the presence of noise.The following three problems encountered in this work are studied:(1)determination of the order of waveform;(2)de-termination of numbers of multiple roots;(3)determination of the residues.The methods of solving these problems are given and simulated on the computer.Finally,an output pulse of model PG-10N signal generator and the distorted waveform obtained by transmitting the pulse above mentioned through a piece of coaxial cable are modelled,and satisfactory results are obtained.So the effectiveness of Prony's method in waveform data modelling in the presence of noise is confirmed.

Data management for the ocean sciences - perspectives for the next decade

There is remarkable agreement in expectations today for vastly improved ocean data management a decade from now -- capabilities that will help to bring significant benefits to ocean research and to society. Advancing data management to such a degree, however, will require cultural and policy changes that are slow to effect. The technological foundations upon which data management systems are built are certain to continue advancing rapidly in parallel. These considerations argue for adopting attitudes of pragmatism and realism when planning data management strategies. In this paper we adopt those attitudes as we outline opportunities for progress in ocean data management. We begin with a synopsis of expectations for integrated ocean data management a decade from now. We discuss factors that should be considered by those evaluating candidate “standards”. We highlight challenges and opportunities in a number of technical areas, including “Web 2.0” applications, data modeling, data discovery and metadata, real-time operational data, archival of data, biological data management and satellite data management. We discuss the importance of investments in the development of software toolkits to accelerate progress. We conclude the paper by recommending a few specific, short term targets for implementation, that we believe to be both significant and achievable, and calling for action by community leadership to effect these advancements.

Adaptive modelling, estimation and fusion from data: a neurofuzzy approach

In a world of almost permanent and rapidly increasing electronic data availability, techniques of filtering, compressing, and interpreting this data to transform it into valuable and easily comprehensible information is of utmost importance. One key topic in this area is the capability to deduce future system behavior from a given data input. This book brings together for the first time the complete theory of data-based neurofuzzy modelling and the linguistic attributes of fuzzy logic in a single cohesive mathematical framework. After introducing the basic theory of data-based modelling, new concepts including extended additive and multiplicative submodels are developed and their extensions to state estimation and data fusion are derived. All these algorithms are illustrated with benchmark and real-life examples to demonstrate their efficiency. Chris Harris and his group have carried out pioneering work which has tied together the fields of neural networks and linguistic rule-based algortihms. This book is aimed at researchers and scientists in time series modeling, empirical data modeling, knowledge discovery, data mining, and data fusion.

Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

Case study of the use of remotely sensed data for modeling flood inundation on the river Severn, UK.

A methodology for using remotely sensed data to both generate and evaluate a hydraulic model of floodplain inundation is presented for a rural case study in the United Kingdom: Upton-upon-Severn. Remotely sensed data have been processed and assembled to provide an excellent test data set for both model construction and validation. In order to assess the usefulness of the data and the issues encountered in their use, two models for floodplain inundation were constructed: one based on an industry standard one-dimensional approach and the other based on a simple two-dimensional approach. The results and their implications for the future use of remotely sensed data for predicting flood inundation are discussed. Key conclusions for the use of remotely sensed data are that care must be taken to integrate different data sources for both model construction and validation and that improvements in ground height data shift the focus in terms of model uncertainties to other sources such as boundary conditions. The differences between the two models are found to be of minor significance.

Dynamic causal modeling applied to fMRI data shows high reliability

Sensitivity, specificity, and reproducibility are vital to interpret neuroscientific results from functional magnetic resonance imaging (fMRI) experiments. Here we examine the scan–rescan reliability of the percent signal change (PSC) and parameters estimated using Dynamic Causal Modeling (DCM) in scans taken in the same scan session, less than 5 min apart. We find fair to good reliability of PSC in regions that are involved with the task, and fair to excellent reliability with DCM. Also, the DCM analysis uncovers group differences that were not present in the analysis of PSC, which implies that DCM may be more sensitive to the nuances of signal changes in fMRI data.

First structural analysis of a naphthalene-based poly(ether ketone): Crystal and molecular simulation from X-ray powder data and diffraction modeling

Polycondensation of 2,6-dihydroxynaphthalene with 4,4'-bis(4"-fluorobenzoyl)biphenyl affords a novel, semicrystalline poly(ether ketone) with a melting point of 406 degreesC and glass transition temperature (onset) of 168 degreesC. Molecular modeling and diffraction-simulation studies of this polymer, coupled with data from the single-crystal structure of an oligomer model, have enabled the crystal and molecular structure of the polymer to be determined from X-ray powder data. This structure-the first for any naphthalene-containing poly(ether ketone)-is fully ordered, in monoclinic space group P2(1)/b, with two chains per unit cell. Rietveld refinement against the experimental powder data gave a final agreement factor (R-wp) of 6.7%.

Efficient modeling and inference for event-related fMRI data

Event-related functional magnetic resonance imaging (efMRI) has emerged as a powerful technique for detecting brains' responses to presented stimuli. A primary goal in efMRI data analysis is to estimate the Hemodynamic Response Function (HRF) and to locate activated regions in human brains when specific tasks are performed. This paper develops new methodologies that are important improvements not only to parametric but also to nonparametric estimation and hypothesis testing of the HRF. First, an effective and computationally fast scheme for estimating the error covariance matrix for efMRI is proposed. Second, methodologies for estimation and hypothesis testing of the HRF are developed. Simulations support the effectiveness of our proposed methods. When applied to an efMRI dataset from an emotional control study, our method reveals more meaningful findings than the popular methods offered by AFNI and FSL. (C) 2008 Elsevier B.V. All rights reserved.

Modeling data with structural and temporal correlation using lower level and higher level multilevel models

Novel imaging techniques are playing an increasingly important role in drug development, providing insight into the mechanism of action of new chemical entities. The data sets obtained by these methods can be large with complex inter-relationships, but the most appropriate statistical analysis for handling this data is often uncertain - precisely because of the exploratory nature of the way the data are collected. We present an example from a clinical trial using magnetic resonance imaging to assess changes in atherosclerotic plaques following treatment with a tool compound with established clinical benefit. We compared two specific approaches to handle the correlations due to physical location and repeated measurements: two-level and four-level multilevel models. The two methods identified similar structural variables, but higher level multilevel models had the advantage of explaining a greater proportion of variation, and the modeling assumptions appeared to be better satisfied.

Model estimation of cerebral hemodynamics between blood flow and volume changes: A data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

A new data set of soil mineralogy for dust-cycle modeling

The mineralogy of airborne dust affects the impact of dust particles on direct and indirect radiative forcing, on atmospheric chemistry and on biogeochemical cycling. It is determined partly by the mineralogy of the dust-source regions and partly by size-dependent fractionation during erosion and transport. Here we present a data set that characterizes the clay and silt-sized fractions of global soil units in terms of the abundance of 12 minerals that are important for dust–climate interactions: quartz, feldspars, illite, smectite, kaolinite, chlorite, vermiculite, mica, calcite, gypsum, hematite and goethite. The basic mineralogical information is derived from the literature, and is then expanded following explicit rules, in order to characterize as many soil units as possible. We present three alternative realizations of the mineralogical maps, taking the uncertainties in the mineralogical data into account. We examine the implications of the new database for calculations of the single scattering albedo of airborne dust and thus for dust radiative forcing.

Probabilistic downscaling of remote sensing data with applications for multi-scale biogeochemical flux modeling

Upscaling ecological information to larger scales in space and downscaling remote sensing observations or model simulations to finer scales remain grand challenges in Earth system science. Downscaling often involves inferring subgrid information from coarse-scale data, and such ill-posed problems are classically addressed using regularization. Here, we apply two-dimensional Tikhonov Regularization (2DTR) to simulate subgrid surface patterns for ecological applications. Specifically, we test the ability of 2DTR to simulate the spatial statistics of high-resolution (4 m) remote sensing observations of the normalized difference vegetation index (NDVI) in a tundra landscape. We find that the 2DTR approach as applied here can capture the major mode of spatial variability of the high-resolution information, but not multiple modes of spatial variability, and that the Lagrange multiplier (γ) used to impose the condition of smoothness across space is related to the range of the experimental semivariogram. We used observed and 2DTR-simulated maps of NDVI to estimate landscape-level leaf area index (LAI) and gross primary productivity (GPP). NDVI maps simulated using a γ value that approximates the range of observed NDVI result in a landscape-level GPP estimate that differs by ca 2% from those created using observed NDVI. Following findings that GPP per unit LAI is lower near vegetation patch edges, we simulated vegetation patch edges using multiple approaches and found that simulated GPP declined by up to 12% as a result. 2DTR can generate random landscapes rapidly and can be applied to disaggregate ecological information and compare of spatial observations against simulated landscapes.

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.