A novel approach to fuzzy clustering for image segmentation is described. The fuzzy C-means objective function is generalized to include a spatial penalty on the membership functions. The penalty term leads to an iterative algorithm that is only slightly different from the original fuzzy C-means algorithm and allows the estimation of spatially smooth membership functions. To determine the stren...

We saw earlier how we can use a concave gap penalty function γ, i.e. one that satisfies γ(x+1)−γ(x) ≤ γ(x)−γ(x−1), as a more realistic model for penalizing gaps. This was at the expense of increasing the time complexity of our dynamic programming algorithm. With a concave gap penalty function, the new DP algorithm requires O(mn + nm) time, as compared to the O(mn) time bound of previous algorit...

We study the asymptotic behavior of the Gerber–Shiu expected discounted penalty function in the renewal risk model. Under the assumption that the claim-size distribution has a convolution-equivalent density function, which allows both heavy-tailed and light-tailed cases, we establish some asymptotic formulas for the Gerber–Shiu function with a fairly general penalty function. These formulas bec...

This paper introduces a global approach to the semi-infinite programming problem that is based upon a generalisation of the g~ exact penalty function. The advantages are that the ensuing penalty function is exact and the penalties include all violations. The merit function requires integrals for the penalties, which provides a consistent model for the algorithm. The discretization is a result o...

although our religious doctrines have given special importance to the execution of legal punishments and penalties for their conventional outcomes, the execution of legal punishments or their suspension in the age of occultation of the infallible imam (a.s.) has been one of the controversial issues in jurisprudence, to the extent that it has created two conflicting fronts; one, a group of disti...

This paper applies genetic optimization with an adaptive penalty function to the shapeconstrained unequal area facility layout problem. We implement a genetic search for unequal area facility layout, and show how optimal solutions are affected by constraints on permitted department shapes, as specified by a maximum allowable aspect ratio for each department. We show how an adaptive penalty func...

In this paper, we study the Nyström type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nyström type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretical analysis of multi-penalty least-square regularization scheme under the general ...

Penalty methods have been commonly used to improve the generalization performance of feedforward neural networks and to control the magnitude of the network weights. Weight boundedness and convergence results are presented for the batch BP algorithm with penalty for training feedforward neural networks with a hidden layer. A key point of the proofs is the monotonicity of the error function with...

The defective renewal equation satisfied by the Gerber-Shiu discounted penalty function in the renewal risk model with arbitrary interclaim times is analyzed. The ladder height distribution is shown to be a mixture of residual lifetime claim severity distributions, which results in an invariance property satisfied by a large class of claim amount models. In particular, when claims are exponenti...

In this paper, we consider a risk model with two independent classes of insurance risks and random incomes. We assume that the two independent claim counting processes are, respectively, the Poisson and the Erlang(2) process. When the individual premium sizes are exponentially distributed, the explicit expressions for the Laplace transforms of the expected discounted penalty functions are deriv...