In this paper, we first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be NP-complete. However, they are unknown for supergrid graphs. The Hamiltonian cycle (path) problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines. In this paper, we will prove that the Hamiltonian cycle problem for supergrid graphs is NP-complete. It is easily derived from the Hamiltonian cycle result that the Hamiltonian path problem on supergrid graphs is also NP-complete. We then show that two subclasses of supergrid graphs, including rectangular (parallelism) and alphabet, always contain Hamiltonian cycles.

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In this paper we propose a modified framework of support vector machines, called Oblique Support Vector Machines(OSVMs), to improve the capability of classification. The principle of OSVMs is joining an orthogonal vector into weight vector in order to rotate the support hyperplanes. By this way, not only the regularized risk function is revised, but the constrained functions are also modified. Under this modification, the separating hyperplane and the margin of separation are constructed more precise. Moreover, in order to apply to large-scale data problem, an iterative learning algorithm is proposed. In this iterative learning algorithm, three different schemes for training can be found in this literature, including pattern-mode learning, semi-batch mode learning and batch mode learning. Besides, smooth technique is adopted in order to convert the constrained nonlinear programming problem into unconstrained optimum problem. Consequently, experimental results and comparisons are given to demonstrate that the performance of OSVMs is better than that of SVMs and SSVMs.

Support vector machines (SVMs), a classification algorithm for the machine learning community, have been shown to provide higher performance than traditional learning machines. In this paper, the technique of SVMs is introduced into the design of weighted order statistics (WOS) filters. WOS filters are highly effective, in processing digital signals, because they have a simple window structure. However, due to threshold decomposition and stacking property, the development of WOS filters cannot significantly improve both the design complexity and estimation error. This paper proposes a new designing technique which can improve the learning speed and reduce the complexity of designing WOS filters. This technique uses a dichotomous approach to reduce the Boolean functions from 255 levels to two levels, which are separated by an optimal hyperplane. Furthermore, the optimal hyperplane is gotten by using the technique of SVMs. Our proposed method approximates the optimal weighted order statistics filters more rapidly than the adaptive neural filters.

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