Combined with weight of samples and kernel function, fuzzy clustering method with generalized entropy is studied. Objective function for fuzzy clustering with generalized entropy based on sample weighting is obtained. Following that, fuzzy clustering algorithm with generalized entropy based on sample weighting is presented. In addition, by introducing kernel into the presented objective functio...

The technology of support vector machines (SVM) is being widely used in many research fields at present, but standard SVM does not provide posterior probability that is needed in many uncertain classification problems. To solve this problem, a probability SVM model is built firstly, then the cross entropy and relative cross entropy model for classification problems are built. Finally, the metho...

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingl...

Shannon entropy is increasingly used in many applications. In this article, an estimator of the entropy of a continuous random variable is proposed. Consistency and scale invariance of variance and mean squared error of the proposed estimator is proved and then comparisons are made with Vasicek's (1976), van Es (1992), Ebrahimi et al. (1994) and Correa (1995) entropy estimators. A simulation st...

We show that the entropy of fluctuating two-charge supertubes placed in three-charge scaling microstate solutions depends on their "effective" charges, which in strong magnetic fields can be much larger than their charges. This leads to a much larger entropy than one naively would expect. Since fluctuating supertubes source smooth geometries in certain duality frames, we propose that such an en...

In this paper we analyze the maximum entropy image deconvolution. We show that given the Lagrange multiplier a closed form can be obtained for the image parameters. Using this solution we are able to provide better understanding of some of the known behavior of the maximum entropy algorithm. The solution also yields a very efficient implementation of the maximum entropy deconvolution technique ...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

In this paper we present an entropy based method to analyze complex systems. Systems are treated as black boxes, which only expose information by some specified parameters. To decide whether a system shows self-organizing behavior in terms of the specified parameters, the calculated entropy values are preprocessed using low-pass filters. The time derivative of the smoothed entropy curve is used...

[1] This paper develops a sequential entropy filter for disaggregating nonpoint sources from ambient data. A numerical simulation based on sediment loading is provided to illustrate the ability of the sequential entropy filter to recover the underlying parameters and optimally disaggregate ambient sediment load among nonpoint sources. In the process we show the equivalence of this sequential en...