Here, the authors propose a novel two-phase clustering algorithm with a density exploring distance （DED） measure. In the first phase, the fast global K-means clustering algorithm is used to obtain the cluster number...Here, the authors propose a novel two-phase clustering algorithm with a density exploring distance （DED） measure. In the first phase, the fast global K-means clustering algorithm is used to obtain the cluster number and the prototypes. Then, the prototypes of all these clusters and representatives of points belonging to these clusters are regarded as the input data set of the second phase. Afterwards, all the prototypes are clustered according to a DED measure which makes data points locating in the same structure to possess high similarity with each other. In experimental studies, the authors test the proposed algorithm on seven artificial as well as seven UCI data sets. The results demonstrate that the proposed algorithm is flexible to different data distributions and has a stronger ability in clustering data sets with complex non-convex distribution when compared with the comparison algorithms.展开更多
Many image inverse problems are ill-posed for no unique solutions. Most of them have incommensurable or mixed-type objectives. In this study, a multi-objective optimization framework is introduced to model such ill-po...Many image inverse problems are ill-posed for no unique solutions. Most of them have incommensurable or mixed-type objectives. In this study, a multi-objective optimization framework is introduced to model such ill-posed inverse problems. The conflicting objectives are designed according to the properties of ill-posedness and certain techniques. Multi-objective evolutionary algorithms have capability to optimize multiple objectives simultaneously and obtain a set of trade-off solutions. For that reason, we use multi-objective evolutionary algorithms to keep the trade-off between these objectives for image ill-posed problems. Two case studies of sparse reconstruction and change detection are imple- mented. In the case study of sparse reconstruction, the measurement error term and the sparsity term are optimized by multi-objective evolutionary algorithms, which aims at balancing the trade-off between enforcing sparsity and reducing measurement error. In the case study of image change detection, two conflicting objectives are constructed to keep the trade-off between robustness to noise and preserving the image details. Experimental results of the two case studies confirm the multi-objective optimization framework for ill-posed inverse problems in image processing is effective.展开更多
Ill-posed problems are widely existed in signat processing. In this paper, we review popular regularization models such as truncated singular value decomposi- tion regularization, iterative regularization, variational...Ill-posed problems are widely existed in signat processing. In this paper, we review popular regularization models such as truncated singular value decomposi- tion regularization, iterative regularization, variational regularizafion. Meanwhile, we also retrospect popular optimiza- tion approaches and regularization parameter choice meth- ods. In fact, the regularization problem is inherently a multi- objective problem. The traditional methods usually combine the fidelity term and the regularization term into a single- objective with regularization parameters, which are difficult to tune. Therefore, we propose a multi-objective framework for ill-posed problems, which can handle complex features of problem such as non-convexity, discontinuity. In this framework, the fidelity term and regularization term are optimized simultaneously to gain more insights into the ill-posed prob- lems. A case study on signal recovery shows the effectiveness of the multi-objective framework for ill-posed problems.展开更多
文摘Here, the authors propose a novel two-phase clustering algorithm with a density exploring distance （DED） measure. In the first phase, the fast global K-means clustering algorithm is used to obtain the cluster number and the prototypes. Then, the prototypes of all these clusters and representatives of points belonging to these clusters are regarded as the input data set of the second phase. Afterwards, all the prototypes are clustered according to a DED measure which makes data points locating in the same structure to possess high similarity with each other. In experimental studies, the authors test the proposed algorithm on seven artificial as well as seven UCI data sets. The results demonstrate that the proposed algorithm is flexible to different data distributions and has a stronger ability in clustering data sets with complex non-convex distribution when compared with the comparison algorithms.
基金This work was supported by the National Natural Science Foundation of China （Grant no. 61273317 and 61422209）, the National Top Youth Talents Program of China, the Specialized Research Fund for the Doctoral Program of Higher Education （Grant no. 20130203110011） and the Fundamental Research Fund for the Central Universities （Grant no. K5051202053）.
文摘Many image inverse problems are ill-posed for no unique solutions. Most of them have incommensurable or mixed-type objectives. In this study, a multi-objective optimization framework is introduced to model such ill-posed inverse problems. The conflicting objectives are designed according to the properties of ill-posedness and certain techniques. Multi-objective evolutionary algorithms have capability to optimize multiple objectives simultaneously and obtain a set of trade-off solutions. For that reason, we use multi-objective evolutionary algorithms to keep the trade-off between these objectives for image ill-posed problems. Two case studies of sparse reconstruction and change detection are imple- mented. In the case study of sparse reconstruction, the measurement error term and the sparsity term are optimized by multi-objective evolutionary algorithms, which aims at balancing the trade-off between enforcing sparsity and reducing measurement error. In the case study of image change detection, two conflicting objectives are constructed to keep the trade-off between robustness to noise and preserving the image details. Experimental results of the two case studies confirm the multi-objective optimization framework for ill-posed inverse problems in image processing is effective.
文摘Ill-posed problems are widely existed in signat processing. In this paper, we review popular regularization models such as truncated singular value decomposi- tion regularization, iterative regularization, variational regularizafion. Meanwhile, we also retrospect popular optimiza- tion approaches and regularization parameter choice meth- ods. In fact, the regularization problem is inherently a multi- objective problem. The traditional methods usually combine the fidelity term and the regularization term into a single- objective with regularization parameters, which are difficult to tune. Therefore, we propose a multi-objective framework for ill-posed problems, which can handle complex features of problem such as non-convexity, discontinuity. In this framework, the fidelity term and regularization term are optimized simultaneously to gain more insights into the ill-posed prob- lems. A case study on signal recovery shows the effectiveness of the multi-objective framework for ill-posed problems.
