Adaptive constraints for feature tracking

In this paper extensions to an existing tracking algorithm are described. These extensions implement adaptive tracking constraints in the form of regional upper-bound displacements and an adaptive track smoothness constraint. Together, these constraints make the tracking algorithm more flexible than the original algorithm (which used fixed tracking parameters) and provide greater confidence in the tracking results. The result of applying the new algorithm to high-resolution ECMWF reanalysis data is shown as an example of its effectiveness.

Bayesian ranking and selection of fishing boat efficiencies

The steadily accumulating literature on technical efficiency in fisheries attests to the importance of efficiency as an indicator of fleet condition and as an object of management concern. In this paper, we extend previous work by presenting a Bayesian hierarchical approach that yields both efficiency estimates and, as a byproduct of the estimation algorithm, probabilistic rankings of the relative technical efficiencies of fishing boats. The estimation algorithm is based on recent advances in Markov Chain Monte Carlo (MCMC) methods—Gibbs sampling, in particular—which have not been widely used in fisheries economics. We apply the method to a sample of 10,865 boat trips in the US Pacific hake (or whiting) fishery during 1987–2003. We uncover systematic differences between efficiency rankings based on sample mean efficiency estimates and those that exploit the full posterior distributions of boat efficiencies to estimate the probability that a given boat has the highest true mean efficiency.

A sparse kernel density estimation algorithm using forward constrained regression

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward constrained regression manner. The leave-one-out (LOO) test score is used for kernel selection. The jackknife parameter estimator subject to positivity constraint check is used for the parameter estimation of a single parameter at each forward step. As such the proposed approach is simple to implement and the associated computational cost is very low. An illustrative example is employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to that of the classical Parzen window estimate.

Orthogonal forward selection for constructing the radial basis function network with tunable nodes

An orthogonal forward selection (OFS) algorithm based on the leave-one-out (LOO) criterion is proposed for the construction of radial basis function (RBF) networks with tunable nodes. This OFS-LOO algorithm is computationally efficient and is capable of identifying parsimonious RBF networks that generalise well. Moreover, the proposed algorithm is fully automatic and the user does not need to specify a termination criterion for the construction process.

Construction of tunable radial basis function networks using orthogonal forward selection

An orthogonal forward selection (OFS) algorithm based on leave-one-out (LOO) criteria is proposed for the construction of radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines an RBF node, namely, its center vector and diagonal covariance matrix, by minimizing the LOO statistics. For regression application, the LOO criterion is chosen to be the LOO mean-square error, while the LOO misclassification rate is adopted in two-class classification application. This OFS-LOO algorithm is computationally efficient, and it is capable of constructing parsimonious RBF networks that generalize well. Moreover, the proposed algorithm is fully automatic, and the user does not need to specify a termination criterion for the construction process. The effectiveness of the proposed RBF network construction procedure is demonstrated using examples taken from both regression and classification applications.

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.

Fast kernel classifier construction using orthogonal forward selection to minimise leave-one-out misclassification rate

We propose a simple yet computationally efficient construction algorithm for two-class kernel classifiers. In order to optimise classifier's generalisation capability, an orthogonal forward selection procedure is used to select kernels one by one by minimising the leave-one-out (LOO) misclassification rate directly. It is shown that the computation of the LOO misclassification rate is very efficient owing to orthogonalisation. Examples are used to demonstrate that the proposed algorithm is a viable alternative to construct sparse two-class kernel classifiers in terms of performance and computational efficiency.

A neurofuzzy network knowledge extraction and extended gram-Schmidt algorithm for model subspace decomposition

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T-S) inference mechanism and a new extended Gram-Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction of a one to one mapping between a fuzzy rule-base and a model matrix feature subspace using the T-S inference mechanism. This link enables the numerical properties associated with a rule-based matrix subspace, the relationships amongst these matrix subspaces, and the correlation between the output vector and a rule-base matrix subspace, to be investigated and extracted as rule-based knowledge to enhance model transparency. The matrix subspace spanned by a fuzzy rule is initially derived as the input regression matrix multiplied by a weighting matrix that consists of the corresponding fuzzy membership functions over the training data set. Model transparency is explored by the derivation of an equivalence between an A-optimality experimental design criterion of the weighting matrix and the average model output sensitivity to the fuzzy rule, so that rule-bases can be effectively measured by their identifiability via the A-optimality experimental design criterion. The A-optimality experimental design criterion of the weighting matrices of fuzzy rules is used to construct an initial model rule-base. An extended Gram-Schmidt algorithm is then developed to estimate the parameter vector for each rule. This new algorithm decomposes the model rule-bases via an orthogonal subspace decomposition approach, so as to enhance model transparency with the capability of interpreting the derived rule-base energy level. This new approach is computationally simpler than the conventional Gram-Schmidt algorithm for resolving high dimensional regression problems, whereby it is computationally desirable to decompose complex models into a few submodels rather than a single model with large number of input variables and the associated curse of dimensionality problem. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

A comparison between feature-based and EM-based contour tracking

Most active-contour methods are based either on maximizing the image contrast under the contour or on minimizing the sum of squared distances between contour and image 'features'. The Marginalized Likelihood Ratio (MLR) contour model uses a contrast-based measure of goodness-of-fit for the contour and thus falls into the first class. The point of departure from previous models consists in marginalizing this contrast measure over unmodelled shape variations. The MLR model naturally leads to the EM Contour algorithm, in which pose optimization is carried out by iterated least-squares, as in feature-based contour methods. The difference with respect to other feature-based algorithms is that the EM Contour algorithm minimizes squared distances from Bayes least-squares (marginalized) estimates of contour locations, rather than from 'strongest features' in the neighborhood of the contour. Within the framework of the MLR model, alternatives to the EM algorithm can also be derived: one of these alternatives is the empirical-information method. Tracking experiments demonstrate the robustness of pose estimates given by the MLR model, and support the theoretical expectation that the EM Contour algorithm is more robust than either feature-based methods or the empirical-information method. (c) 2005 Elsevier B.V. All rights reserved.

Application of Gaussian multi-scale representation to feature tracking in meteorological satellite imagery

Gaussian multi-scale representation is a mathematical framework that allows to analyse images at different scales in a consistent manner, and to handle derivatives in a way deeply connected to scale. This paper uses Gaussian multi-scale representation to investigate several aspects of the derivation of atmospheric motion vectors (AMVs) from water vapour imagery. The contribution of different spatial frequencies to the tracking is studied, for a range of tracer sizes, and a number of tracer selection methods are presented and compared, using WV 6.2 images from the geostationary satellite MSG-2.

Selection of funding schemes by a borrowing decision model: a Hong Kong case study

In financial decision-making, a number of mathematical models have been developed for financial management in construction. However, optimizing both qualitative and quantitative factors and the semi-structured nature of construction finance optimization problems are key challenges in solving construction finance decisions. The selection of funding schemes by a modified construction loan acquisition model is solved by an adaptive genetic algorithm (AGA) approach. The basic objectives of the model are to optimize the loan and to minimize the interest payments for all projects. Multiple projects being undertaken by a medium-size construction firm in Hong Kong were used as a real case study to demonstrate the application of the model to the borrowing decision problems. A compromise monthly borrowing schedule was finally achieved. The results indicate that Small and Medium Enterprise (SME) Loan Guarantee Scheme (SGS) was first identified as the source of external financing. Selection of sources of funding can then be made to avoid the possibility of financial problems in the firm by classifying qualitative factors into external, interactive and internal types and taking additional qualitative factors including sovereignty, credit ability and networking into consideration. Thus a more accurate, objective and reliable borrowing decision can be provided for the decision-maker to analyse the financial options.

Givens rotation based fast backward elimination algorithm for RBF neural network pruning

A fast backward elimination algorithm is introduced based on a QR decomposition and Givens transformations to prune radial-basis-function networks. Nodes are sequentially removed using an increment of error variance criterion. The procedure is terminated by using a prediction risk criterion so as to obtain a model structure with good generalisation properties. The algorithm can be used to postprocess radial basis centres selected using a k-means routine and, in this mode, it provides a hybrid supervised centre selection approach.

Neural network basis function center selection using cluster analysis

This paper deals with the selection of centres for radial basis function (RBF) networks. A novel mean-tracking clustering algorithm is described as a way in which centers can be chosen based on a batch of collected data. A direct comparison is made between the mean-tracking algorithm and k-means clustering and it is shown how mean-tracking clustering is significantly better in terms of achieving an RBF network which performs accurate function modelling.

Application of a hybrid tracking algorithm to motion analysis

An algorithm for tracking multiple feature positions in a dynamic image sequence is presented. This is achieved using a combination of two trajectory-based methods, with the resulting hybrid algorithm exhibiting the advantages of both. An optimizing exchange algorithm is described which enables short feature paths to be tracked without prior knowledge of the motion being studied. The resulting partial trajectories are then used to initialize a fast predictor algorithm which is capable of rapidly tracking multiple feature paths. As this predictor algorithm becomes tuned to the feature positions being tracked, it is shown how the location of occluded or poorly detected features can be predicted. The results of applying this tracking algorithm to data obtained from real-world scenes are then presented.