Grouping Objects to Homogeneous Classes Satisfying Requisite Mass

Grouping datasets plays an important role in many scientific researches. Depending on data features and applications, different constrains are imposed on groups, while having groups with similar members is always a main criterion. In this paper, we propose an algorithm for grouping the objects with random labels, nominal features having too many nominal attributes. In addition, the size constraint on groups is necessary. These conditions lead to a mixed integer optimization problem which is not convex nor linear. It is an NP-hard problem and exact solution methods are computationally costly. Our motivation to solve such a problem comes along with grouping insurance data which is essential for fair pricing. The proposed algorithm includes two phases. First, we rank random labels using fuzzy numbers. Afterwards, an adjusted K-means algorithm is used to produce homogenous groups satisfying a cluster size constraint. Fuzzy numbers are used to compare random labels, in both observed values and their chance of occurrence. Moreover, an index is defined to find the similarity of multi-valued attributes without perfect information with those accompanied with perfect information. Since all ranks are scaled into the interval [0,1], the result of ranking random labels does not need rescaling techniques. In the adjusted K-means algorithm, the optimum number of clusters is found using coefficient of variation instead of Euclidean distance. Experiments demonstrate that our proposed algorithm produces fairly homogenous and significantly different groups having requisite mass

Feature base fusion for splicing forgery detection based on neuro fuzzy

Most of image forensics researches have mainly focused on detection of artifacts introduced by a single processing tool. Thus, they have lead in the development of many specialized algorithms looking for one or more particular footprints under distinct settings. Naturally, the performance of such algorithms are not perfect and accordingly the provided output they might be noisy, inaccurate and only partially correct. Furthermore, in practical scenarios, a forged image is often the result of utilizing several tools made available by the image-processing softwares. Therefore, reliable tamper detection requires developing several tools to deal with various tampering scenarios. Fusion of forgery detection tools based on Fuzzy Inference System has been used before for addressing this problem. Adjusting the Membership Functions and defining proper fuzzy rules for getting optimal results are a time consuming processes. This can be accounted as main disadvantage of Fuzzy Inference Systems. In this study, a Neuro Fuzzy Inference System for fusion of forgery detection tools is developed. The Neural Network characteristic of Neuro Fuzzy Inference Systems provide appropriate tool for automatically adjusting Membership Functions. Moreover, initial Fuzzy inference system is generated based on fuzzy clustering techniques. The purposed framework is implemented and validated on a benchmark image splicing dataset in which three forgery detection tools are fused based on Adaptive Neuro Fuzzy Inference System. The final outcome of the purposed method reveals that applying Neuro Fuzzy Inference systems could be a proper approach for fusion of forgery detection tools. On the best of our knowledge, this is the first time that Neuro Fuzzy Inference Systems employed for fusion of forgery detection tools. Therefore, more researches should be conducted to make it more practical and to increase the effectiveness of methodology

Sensitivity analysis in convex quadratic optimization: Simultaneous perturbation of the objective and right-hand-side vectors

In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval are generalized to the case of simultaneous perturbation. Criteria for convexity, concavity or linearity of the optimal value function on invariancy intervals are derived. Furthermore, differentiability of the optimal value function is studied, and linear optimization problems are given to calculate the left and right derivatives. An algorithm, that is capable to compute the transition points and optimal partitions on all invariancy intervals, is outlined. We specialize the method to Linear Optimization problems and provide a practical example of simultaneous perturbation parametric quadratic optimization problem from electrical engineering