An edge property-based neighborhood region search strategy for fractal image compression

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.     

NXOR- or XOR-based robust template decomposition for cellular neural networks implementing an arbitrary Boolean function via support vector classifiers

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.

     

Genetic algorithm with a hybrid select mechanism for fractal image compression

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.     

Three-parameter sequential minimal optimization for support vector machines

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.     

Study on semiparametric Wilcoxon fuzzy neural networks

Fuzzy neural network (FNN) has long been recognized as an efficient and powerful learning machine for general machine learning problems. Recently, Wilcoxon fuzzy neural network (WFNN), which generalizes the rank-based Wilcoxon approach for linear parametric regression problems to nonparametric neural network, was proposed aiming at improving robustness against outliers. FNN and WFNN are nonparametric models in the sense that they put no restrictions, except possibly smoothness, on the functional form of the regression function. However, they may be difficult to interpret and, even worse, yield poor estimates with high computational cost when the number of predictor variables is large. To overcome this drawback, semiparametric models have been proposed in statistical regression theory. A semiparametric model keeps the easy interpretability of its parametric part and retains the flexibility of its nonparametric part. Based on this, semiparametric FNN and semiparametric WFNN will be proposed in this paper. The learning rules are based on the backfitting procedure frequently used in semiparametric regression. Simulation results show that the semiparametric models perform better than their nonparametric counterparts.