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 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.

Fusion of infrared polarization and intensity images using support value transform and fuzzy combination rules

Infrared polarization and intensity imagery provide complementary and discriminative information in image understanding and interpretation. In this paper, a novel fusion method is proposed by effectively merging the information with various combination rules. It makes use of both low-frequency and highfrequency images components from support value transform (SVT), and applies fuzzy logic in the combination process. Images (both infrared polarization and intensity images) to be fused are firstly decomposed into low-frequency component images and support value image sequences by the SVT. Then the low-frequency component images are combined using a fuzzy combination rule blending three sub-combination methods of (1) region feature maximum, (2) region feature weighting average, and (3) pixel value maximum; and the support value image sequences are merged using a fuzzy combination rule fusing two sub-combination methods of (1) pixel energy maximum and (2) region feature weighting. With the variables of two newly defined features, i.e. the low-frequency difference feature for low-frequency component images and the support-value difference feature for support value image sequences, trapezoidal membership functions are proposed and developed in tuning the fuzzy fusion process. Finally the fused image is obtained by inverse SVT operations. Experimental results of visual inspection and quantitative evaluation both indicate the superiority of the proposed method to its counterparts in image fusion of infrared polarization and intensity images.

A genetic algorithm for the design of a fuzzy controller for active queue management

Active queue management (AQM) policies are those policies of router queue management that allow for the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. This paper proposes the adoption of a fuzzy proportional integral (FPI) controller as an active queue manager for Internet routers. The analytical design of the proposed FPI controller is carried out in analogy with a proportional integral (PI) controller, which recently has been proposed for AQM. A genetic algorithm is proposed for tuning of the FPI controller parameters with respect to optimal disturbance rejection. In the paper the FPI controller design metodology is described and the results of the comparison with random early detection (RED), tail drop, and PI controller are presented.

Depth by The Rule

This note corrects a previous treatment of algorithms for the metric DTR, Depth by the Rule.

A fuzzy approach for the network congestion problem

In the recent years, the unpredictable growth of the Internet has moreover pointed out the congestion problem, one of the problems that historicallyha ve affected the network. This paper deals with the design and the evaluation of a congestion control algorithm which adopts a FuzzyCon troller. The analogyb etween Proportional Integral (PI) regulators and Fuzzycon trollers is discussed and a method to determine the scaling factors of the Fuzzycon troller is presented. It is shown that the Fuzzycon troller outperforms the PI under traffic conditions which are different from those related to the operating point considered in the design.

Parallel genetic algorithms for the tuning of a fuzzy AQM controller

This paper presents the results of the application of a parallel Genetic Algorithm (GA) in order to design a Fuzzy Proportional Integral (FPI) controller for active queue management on Internet routers. The Active Queue Management (AQM) policies are those policies of router queue management that allow the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. Two different parallel implementations of the genetic algorithm are adopted to determine an optimal configuration of the FPI controller parameters. Finally, the results of several experiments carried out on a forty nodes cluster of workstations are presented.