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The novel single index fuzzy neural network models are proposed in this paper for general machine learning problems. The proposed models are different from the usual fuzzy neural network models in that the output nodes of the networks are replaced by (nonparametric) single index models. Specifically, instead of pre-specifying the output activation functions as in the usual models, they are re-estimated adaptively during the training process via “Loess” (“LOcal regrESSion”), a powerful (nonparametric) scatterplot smoother. These estimated activation functions are not necessarily the usual sigmoidal or identity functions. It is interesting to find that in many cases the estimated output activation functions are well approximated by simple polynomial or generalized hyperbolic tangent functions. These problem-tailored simple functions can, if necessary, then be used as the actual output activation functions for neural network training and prediction. Particle swarm optimization, a commonly used evolutionary computation technique, is adopted in this study to search the optimal connection weights of the neural networks. The main advantages of the single index fuzzy neural network models are that they are well suited in situations when one lacks the information about the probability distribution of the response and it is not necessary to specify the output activation functions of the neural networks. Simulation results show that the proposed models usually provide better fits than the usual models for the data at hand.

Acyclic multistate information network (AMIN), a variant of multistate information network (MIN) that is not dependent on the conservation laws of flow, plays an important role in the current-day network communications because many modern network structures are based on AMIN, e.g., social networks, local area networks (LANs), and 4G/5G networks. An effective evaluation of the network reliability of an AMIN serves as a major and primary metric for determining the performance and quality of the overall network. The network reliability, which was shown to be NP-hard, has been successfully resolved by the universal generation function method (UGFM). However, the UGFM can only address small-scale problems owing to the limitations of the current-day computer memories. To overcome this problem, an improved and enhanced binary-addition tree algorithm (BAT) is proposed in this study to effectively evaluate and analyze the reliability of the AMIN. The performance of the proposed BAT is validated via a few examples.

Robust template design for cellular neural networks (CNNs) implementing an arbitrary Boolean function is currently an active research area. If the given Boolean function is linearly separable, a single robust uncoupled CNN can be designed preferably as a maximal margin classifier to implement the Boolean function. On the other hand, if the linearly separable Boolean function has a small geometric margin or the Boolean function is not linearly separable, a popular approach is to find a sequence of robust uncoupled CNNs implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are usually restricted to assume only a given finite set of integers. In this study, we try to remove this unnecessary restriction. NXOR- or XOR-based decomposition algorithm utilizing the soft margin and maximal margin support vector classifiers is proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

In this paper, least trimmed squares (LTS) estimators, frequently used in robust (or resistant) linear parametric regression problems, will be generalized to nonparametric LTS neural networks for nonlinear regression problems. Emphasis is put particularly on the robustness against outliers. This provides alternative learning machines when faced with general nonlinear learning problems. Simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) algorithms will be provided. The important parameter of trimming percentage for the data at hand can be determined by cross validation. Some simulated and real-world data will be used to illustrate the use of LTS neural networks. We will compare the robustness against outliers for usual neural networks with least squares criterion and the proposed LTS neural networks. Simulation results show that the LTS neural networks proposed in this paper have good robustness against outliers. Nonparametric least trimmed squares neural networks are proposed.We emphasize the issue of robustness against outliers.The trimming percentage for the data at hand is determined by cross validation.

The object tracking problem is an important research topic in computer vision. For real applications such as vehicle tracking and face tracking, there are many efficient and real-time algorithms. In this study, we will focus on the Lucas-Kanade (LK) algorithm for object tracking. Although this method is time consuming, it is effective in tracking accuracy and environment adaptation. In the standard LK method, the sum of squared errors is used as the cost function, while least trimmed squares is adopted as the cost function in this study. The resulting estimator is robust against outliers caused by noises and occlusions in the tracking process. Simulations are provided to show that the proposed algorithm outperforms the standard LK method in the sense that it is robust against the outliers in the object tracking problems.

The well-known sequential minimal optimization (SMO) algorithm is the most commonly used algorithm for numerical solutions of the support vector learning problems. At each iteration in the traditional SMO algorithm, also called 2PSMO algorithm in this paper, it jointly optimizes only two chosen parameters. The two parameters are selected either heuristically or randomly, whilst the optimization with respect to the two chosen parameters is performed analytically. The 2PSMO algorithm is naturally generalized to the three-parameter sequential minimal optimization (3PSMO) algorithm in this paper. At each iteration of this new algorithm, it jointly optimizes three chosen parameters. As in 2PSMO algorithm, the three parameters are selected either heuristically or randomly, whilst the optimization with respect to the three chosen parameters is performed analytically. Consequently, the main difference between these two algorithms is that the optimization is performed at each iteration of the 2PSMO algorithm on a line segment, whilst that of the 3PSMO algorithm on a two-dimensional region consisting of infinitely many line segments. This implies that the maximum can be attained more efficiently by 3PSMO algorithm. Main updating formulae of both algorithms for each support vector learning problem are presented. To assess the efficiency of the 3PSMO algorithm compared with the 2PSMO algorithm, 14 benchmark datasets, 7 for classification and 7 for regression, will be tested and numerical performances are compared. Simulation results demonstrate that the 3PSMO outperforms the 2PSMO algorithm significantly in both executing time and computation complexity.

In this paper, M-estimators, where M stands for maximum likelihood, used in robust regression theory for linear parametric regression problems will be generalized to nonparametric maximum likelihood fuzzy neural networks (MFNNs) for nonlinear regression problems. Emphasis is put particularly on the robustness against outliers. This provides alternative learning machines when faced with general nonlinear learning problems. Simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) will be derived. Some numerical examples will be provided to compare the robustness against outliers for usual fuzzy neural networks (FNNs) and the proposed MFNNs. Simulation results show that the MFNNs proposed in this paper have good robustness against outliers.

In this paper, a genetic algorithm with a hybrid select mechanism is proposed to speed up the fractal encoder. First, all of the image blocks including domain blocks and range blocks are classified into three classes: smooth; horizontal/vertical edge; and diagonal/sub-diagonal edge, according to their discrete cosine transformation (DCT) coefficients. Then, during the GA evolution, the population of every generation is separated into two clans: a superior clan and an inferior clan, according to whether the chromosome type is the same as that of the range block to be encoded or not. The hybrid select mechanism proposed by us is used to select appropriate parents from the two clans in order to reduce the number of MSE computations and maintain the retrieved image quality. Experimental results show that, since the number of MSE computations in the proposed GA method is about half of the traditional GA method, the encoding time for the proposed GA method is less than that of the traditional GA method. For retrieved image quality, the proposed GA method is almost the same as the traditional GA method or only has a little decay. Moreover, in comparison with the full search method, the encoding speed of the proposed GA method is some 130 times faster than that of the full search method, whereas the retrieved image quality is still relatively acceptable.

In this paper, a general problem of the robust template decomposition with restricted weights for cellular neural networks (CNNs) implementing an arbitrary Boolean function is investigated. First, the geometric margin of a linear classifier with respect to a training data set is used to define the robustness of an uncoupled CNN implementing a linearly separable Boolean function. Second, maximal margin classifiers, i.e. robust CNNs, for such Boolean functions can be designed via support vector machines (SVMs). Third, some general properties of robust CNNs with or without restricted weights are discussed. Moreover, all robust CNNs with restricted weights are characterized. Finally, for an arbitrarily given Boolean function, we propose an algorithm, which is the generalized version of the well-known CFC algorithm, to find a sequence of robust uncoupled CNNs implementing the given Boolean function. Several illustrative examples demonstrate the efficiency of the proposed method. It will be seen that, in general, the tradeoff between the complexity regarding the number of terms in the decomposition and the guaranteed robustness regarding the geometric margins of the resulting CNNs must be made in the robust template decomposition with restricted weights.

The object tracking problem is an important research topic in computer vision. For real applications such as vehicle tracking and face tracking, there are many efficient and real-time algorithms. In this study, we will focus on the Lucas-Kanade (LK) algorithm for object tracking. In the standard LK method, sum of squared errors is used as the cost function, while least trimmed squares is adopted as the cost function in this study. The resulting estimator is robust against outliers caused by noises in the tracking process. Simulation is provided to show that the proposed algorithm outperforms the standard LK method in the sense that it is robust against the outliers in the object tracking problem.

If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

In this paper, an improved version of CFC algorithm is proposed. The main contribution is the reduction of a dimension in the search space. Moreover, the elements in the reduced search space are entries of control templates of uncoupled CNNs and the corresponding linearly separable Boolean functions are robust in the sense of maximal geometric margin. Illustrative examples demonstrate the efficiency of the proposed method.

In this paper, some similarity measures for fractal image compression (FIC) are introduced, which are robust against noises. In the proposed methods, robust estimation technique from statistics is embedded into the encoding procedure of the fractal inverse problem to find the parameters. When the original image is corrupted by noises, we hope that the proposed scheme is insensitive to those noises presented in the corrupted image. This leads to a new concept of robust estimation of fractal inverse problem. The proposed least absolute derivation (LAD), least trimmed squares (LTS), and Wilcoxon FIC are the first attempt toward the design of robust fractal image compression which can remove the noises in the encoding process. The main disadvantage of the robust FIC is the computational cost. To overcome this drawback, particle swarm optimization (PSO) technique is utilized to reduce the searching time. Simulation results show that the proposed FIC is robust against the outliers in the image. Also, the PSO method can effectively reduce the encoding time while retaining the quality of the retrieved image.

In this paper, an edge property-based neighborhood region search method is proposed to speedup the fractal encoder. The method searches for the best matched solution in the frequency domain. A coordinate system is constructed using the two lowest discrete cosine transformation (DCT) coefficients of image blocks. Image blocks with similar edge shapes will be concentrated in some specific regions. Therefore the purpose of speedup can be reached by limiting the search space. Moreover, embedding the edge property of block into the proposed search method, the speedup rate can be lifted further. Experimental results show that, under the condition of the same PSNR, the encoding time of the proposed method is only about two-fifth of Duh’s classification method. Compared with Tseng’s method, the proposed method is near or superior to the performance of their method. Moreover, the encoding speed of the proposed method is about 120 times faster than that of the full search method, while the penalty of retrieved image quality is only decaying 0.9 dB.