Fully complex-valued radial basis function networks: orthogonal least squares regression and classification

We consider a fully complex-valued radial basis function (RBF) network for regression and classification applications. For regression problems, the locally regularised orthogonal least squares (LROLS) algorithm aided with the D-optimality experimental design, originally derived for constructing parsimonious real-valued RBF models, is extended to the fully complex-valued RBF (CVRBF) network. Like its real-valued counterpart, the proposed algorithm aims to achieve maximised model robustness and sparsity by combining two effective and complementary approaches. The LROLS algorithm alone is capable of producing a very parsimonious model with excellent generalisation performance while the D-optimality design criterion further enhances the model efficiency and robustness. By specifying an appropriate weighting for the D-optimality cost in the combined model selecting criterion, the entire model construction procedure becomes automatic. An example of identifying a complex-valued nonlinear channel is used to illustrate the regression application of the proposed fully CVRBF network. The proposed fully CVRBF network is also applied to four-class classification problems that are typically encountered in communication systems. A complex-valued orthogonal forward selection algorithm based on the multi-class Fisher ratio of class separability measure is derived for constructing sparse CVRBF classifiers that generalise well. The effectiveness of the proposed algorithm is demonstrated using the example of nonlinear beamforming for multiple-antenna aided communication systems that employ complex-valued quadrature phase shift keying modulation scheme. (C) 2007 Elsevier B.V. All rights reserved.

Evolution in software systems: foundations of the SPE classification scheme

The SPE taxonomy of evolving software systems, first proposed by Lehman in 1980, is re-examined in this work. The primary concepts of software evolution are related to generic theories of evolution, particularly Dawkins' concept of a replicator, to the hermeneutic tradition in philosophy and to Kuhn's concept of paradigm. These concepts provide the foundations that are needed for understanding the phenomenon of software evolution and for refining the definitions of the SPE categories. In particular, this work argues that a software system should be defined as of type P if its controlling stakeholders have made a strategic decision that the system must comply with a single paradigm in its representation of domain knowledge. The proposed refinement of SPE is expected to provide a more productive basis for developing testable hypotheses and models about possible differences in the evolution of E- and P-type systems than is provided by the original scheme. Copyright (C) 2005 John Wiley & Sons, Ltd.

Ratio selection for classification models

This paper is concerned with the selection of inputs for classification models based on ratios of measured quantities. For this purpose, all possible ratios are built from the quantities involved and variable selection techniques are used to choose a convenient subset of ratios. In this context, two selection techniques are proposed: one based on a pre-selection procedure and another based on a genetic algorithm. In an example involving the financial distress prediction of companies, the models obtained from ratios selected by the proposed techniques compare favorably to a model using ratios usually found in the financial distress literature.

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems. (C) 2003 Optical Society of America.

A classification system for delirium subtyping with the use of a commercial mobility monitor

The usefulness of motor subtypes of delirium is unclear due to inconsistency in subtyping methods and a lack of validation with objective measures of activity. The activity of 40 patients was measured over 24 h with a commercial accelerometer-based activity monitor. Accelerometry data from patients with DSM-IV delirium that were readily divided into hyperactive, hypoactive and mixed motor subtypes, were used to create classification trees that were Subsequently applied to the remaining cohort to define motoric subtypes. The classification trees used the periods of sitting/lying, standing, stepping and number of postural transitions as measured by the activity monitor as determining factors from which to classify the delirious cohort. The use of a classification system shows how delirium subtypes can be categorised in relation to overall activity and postural changes, which was one of the most discriminating measures examined. The classification system was also implemented to successfully define other patient motoric subtypes. Motor subtypes of delirium defined by observed ward behaviour differ in electronically measured activity levels. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

A continuous wavelet transform and classification method for delirium motoric subtyping

The usefulness of motor subtypes of delirium is unclear due to inconsistency in subtyping methods and a lack of validation with objective measures of activity. The activity of 40 patients was measured over 24 h with a discrete accelerometer-based activity monitor. The continuous wavelet transform (CWT) with various mother wavelets were applied to accelerometry data from three randomly selected patients with DSM-IV delirium that were readily divided into hyperactive, hypoactive, and mixed motor subtypes. A classification tree used the periods of overall movement as measured by the discrete accelerometer-based monitor as determining factors for which to classify these delirious patients. This data used to create the classification tree were based upon the minimum, maximum, standard deviation, and number of coefficient values, generated over a range of scales by the CWT. The classification tree was subsequently used to define the remaining motoric subtypes. The use of a classification system shows how delirium subtypes can be categorized in relation to overall motoric behavior. The classification system was also implemented to successfully define other patient motoric subtypes. Motor subtypes of delirium defined by observed ward behavior differ in electronically measured activity levels.

Characterization and classification of tumor lesions using computerized fractal-based texture analysis and support vector machines in digital mammograms

Objective: This paper presents a detailed study of fractal-based methods for texture characterization of mammographic mass lesions and architectural distortion. The purpose of this study is to explore the use of fractal and lacunarity analysis for the characterization and classification of both tumor lesions and normal breast parenchyma in mammography. Materials and methods: We conducted comparative evaluations of five popular fractal dimension estimation methods for the characterization of the texture of mass lesions and architectural distortion. We applied the concept of lacunarity to the description of the spatial distribution of the pixel intensities in mammographic images. These methods were tested with a set of 57 breast masses and 60 normal breast parenchyma (dataset1), and with another set of 19 architectural distortions and 41 normal breast parenchyma (dataset2). Support vector machines (SVM) were used as a pattern classification method for tumor classification. Results: Experimental results showed that the fractal dimension of region of interest (ROIs) depicting mass lesions and architectural distortion was statistically significantly lower than that of normal breast parenchyma for all five methods. Receiver operating characteristic (ROC) analysis showed that fractional Brownian motion (FBM) method generated the highest area under ROC curve (A z = 0.839 for dataset1, 0.828 for dataset2, respectively) among five methods for both datasets. Lacunarity analysis showed that the ROIs depicting mass lesions and architectural distortion had higher lacunarities than those of ROIs depicting normal breast parenchyma. The combination of FBM fractal dimension and lacunarity yielded the highest A z value (0.903 and 0.875, respectively) than those based on single feature alone for both given datasets. The application of the SVM improved the performance of the fractal-based features in differentiating tumor lesions from normal breast parenchyma by generating higher A z value. Conclusion: FBM texture model is the most appropriate model for characterizing mammographic images due to self-affinity assumption of the method being a better approximation. Lacunarity is an effective counterpart measure of the fractal dimension in texture feature extraction in mammographic images. The classification results obtained in this work suggest that the SVM is an effective method with great potential for classification in mammographic image analysis.

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.

Classification-based probabilistic modeling of texture transition for fast line search tracking and delineation

We introduce a classification-based approach to finding occluding texture boundaries. The classifier is composed of a set of weak learners, which operate on image intensity discriminative features that are defined on small patches and are fast to compute. A database that is designed to simulate digitized occluding contours of textured objects in natural images is used to train the weak learners. The trained classifier score is then used to obtain a probabilistic model for the presence of texture transitions, which can readily be used for line search texture boundary detection in the direction normal to an initial boundary estimate. This method is fast and therefore suitable for real-time and interactive applications. It works as a robust estimator, which requires a ribbon-like search region and can handle complex texture structures without requiring a large number of observations. We demonstrate results both in the context of interactive 2D delineation and of fast 3D tracking and compare its performance with other existing methods for line search boundary detection.

On improvement of classification accuracy for stochastic discrimination

Stochastic discrimination (SD) depends on a discriminant function for classification. In this paper, an improved SD is introduced to reduce the error rate of the standard SD in the context of a two-class classification problem. The learning procedure of the improved SD consists of two stages. Initially a standard SD, but with shorter learning period is carried out to identify an important space where all the misclassified samples are located. Then the standard SD is modified by 1) restricting sampling in the important space, and 2) introducing a new discriminant function for samples in the important space. It is shown by mathematical derivation that the new discriminant function has the same mean, but with a smaller variance than that of the standard SD for samples in the important space. It is also analyzed that the smaller the variance of the discriminant function, the lower the error rate of the classifier. Consequently, the proposed improved SD improves standard SD by its capability of achieving higher classification accuracy. Illustrative examples are provided to demonstrate the effectiveness of the proposed improved SD.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Land-cover classification from airborne LIDAR data fused with aerial optical images

Airborne LIght Detection And Ranging (LIDAR) provides accurate height information for objects on the earth, which makes LIDAR become more and more popular in terrain and land surveying. In particular, LIDAR data offer vital and significant features for land-cover classification which is an important task in many application domains. In this paper, an unsupervised approach based on an improved fuzzy Markov random field (FMRF) model is developed, by which the LIDAR data, its co-registered images acquired by optical sensors, i.e. aerial color image and near infrared image, and other derived features are fused effectively to improve the ability of the LIDAR system for the accurate land-cover classification. In the proposed FMRF model-based approach, the spatial contextual information is applied by modeling the image as a Markov random field (MRF), with which the fuzzy logic is introduced simultaneously to reduce the errors caused by the hard classification. Moreover, a Lagrange-Multiplier (LM) algorithm is employed to calculate a maximum A posteriori (MAP) estimate for the classification. The experimental results have proved that fusing the height data and optical images is particularly suited for the land-cover classification. The proposed approach works very well for the classification from airborne LIDAR data fused with its coregistered optical images and the average accuracy is improved to 88.9%.

Geodetic mass balance of Azarova glacier, Kodar Mountains, eastern Siberia, and its links to observed and projected climatic change

The Kodar Mountains in eastern Siberia accommodate 30 small, cold-based glaciers with a combined surface area of about 19 km2. Very little is known about these glaciers, with the first survey conducted in the late 1950s. In this paper, we use terrestrial photogrammetry to calculate changes in surface area, elevation, volume and geodetic mass balance of the Azarova Glacier between 1979 and 2007 and relate these to meteorological data from nearby Chara weather station (1938-2007). The glacier surface area declined by 20±6.9% and surface lowered on average by 20±1.8 m (mean thinning: 0.71 m a-1) resulting in a strongly negative cumulative and average mass balance of -18±1.6 m w.e. and -640±60 mm w.e.a-1 respectively. The July-August air temperature increased at a rate of 0.036oC a-1 between 1979 and 2007 and the 1980-2007 period was, on average, around 1oC warmer than 1938-1979. The regional climate projections for A2 and B2 CO2 emission scenarios developed using PRECIS regional climate model indicate that summer temperatures will increase in 2071–2100 by 2.6-4.7°C and 4.9-6.2°C respectively in comparison with 1961–1990. The annual total of solid precipitation will increase by 20% under B2 scenario but decline by 3% under A2 scenario. The length of the ablation season will extend from July–August to June-September. The Azarova Glacier exhibits high sensitivity to climatic warming due to its low elevation, exposure to comparatively high summer temperatures, and the absence of a compensating impact of cold season precipitation. Further summer warming and decline of solid precipitation projected under the A2 scenario will force Azarova to retreat further while impacts of an increase in solid precipitation projected under the B2 scenario require further investigation.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.