9825053
M-estimator and D-optimality model construction using orthogonal forward regression
This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.
28248774
Dual-orthogonal radial basis function networks for nonlinear time series prediction
A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.
6169265
Automatic Kernel Regression Modelling Using Combined Leave-One-Out Test Score and Regularised Orthogonal Least Squares
This paper introduces an automatic robust nonlinear identification algorithm using the leave-one-out test score also known as the PRESS (Predicted REsidual Sums of Squares) statistic and regularised orthogonal least squares. The proposed algorithm aims to achieve maximised model robustness via two effective and complementary approaches, parameter regularisation via ridge regression and model optimal generalisation structure selection. The major contributions are to derive the PRESS error in a regularised orthogonal weight model, develop an efficient recursive computation formula for PRESS errors in the regularised orthogonal least squares forward regression framework and hence construct a model with a good generalisation property. Based on the properties of the PRESS statistic the proposed algorithm can achieve a fully automated model construction procedure without resort to any other validation data set for model evaluation.
12285484
Kernel Density Construction Using Orthogonal Forward Regression
An automatic algorithm is derived for constructing kernel density estimates based on a regression approach that directly optimizes generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. Local regularization is incorporated into the density construction process to further enforce sparsity. Examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample Parzen window density estimate.
18316871
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.
2411991
Robust nonlinear model identification methods using forward regression
In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.
2137876
Achieving Anonymity in Mobile Ad Hoc Networks Using Fuzzy Position Information
Traditionally the anonymity of an entity of interest can be achieved by hiding it among a group of other entities with similar characteristics, i.e., an anonymity set. In mobile ad hoc networks, generating and maintaining such an anonymity set for any ad hoc node are challenging because of the node mobility and consequently of the dynamic network topology. In this paper, we address the problem of the destination anonymity. We propose protocols that use fuzzy destination position to generate a geographic area called anonymity zone (AZ). A packet for a destination is delivered to all the nodes in the AZ, which, consequently, make up the anonymity set. The size of the anonymity set may decrease because nodes are mobile, yet the corresponding management on anonymity set is simple. We design techniques to further improve node anonymity. We use extensive simulation to study the node anonymity and routing performance, and to determine the parameters that most impact the anonymity level that can be achieved by our protocol.
2606413
A Mobility Framework for Ad Hoc Wireless Networks
Mobility management in ad hoc wireless networks faces many challenges. Mobility constantly causes the network topology to change. In order to keep accurate routes, the routing protocols must dynamically readjust to such changes. Thus, routing update traffic overhead is significantly high. Different mobility patterns have in general different impact on a specific network protocol or application. Consequently the network performance will be strongly influenced by the nature of the mobility pattern. In the past, mobility models were rather casually used to evaluate network performance under different routing protocols. Here, we propose a universal mobility framework, Mobility Vector Model, which can be used for recreating the various mobility patterns produced in different applications. Case studies on optimal transmission range as a function of mobility and on network performance under various mobility models are presented in the paper. Simulation results show that excessively large transmission range will not improve network performance significantly because of the increased collisions. There is an optimal range between 1.5 - 2 times the mean node distance for free space channel. Also, simulation results show that different mobility models will have different impact on the network performance for a variety of routing protocols (AODV, DSR, FSR). When choosing routing protocols for ad hoc network applications, performance studies under multiple mobility models are recommended. The Mobility Vector model can provide a realistic and flexible framework for reproducing various models.