Fuzzy clustering is an essential algorithm in image segmentation, and most of them are based on fuzzy c-mean algorithms. However, it sensitive to noise, center point selection, cluster number, distance metric. To address this problem, we propose a new method low-rank representation (LRR) for which integrates structure with theory. First, improve the morphological reconstruction superpixel edge ...

In a class of piecewise-constant image segmentation models, we propose to incorporate weighted difference anisotropic and isotropic total variation (AITV) regularize the partition boundaries in an image. particular, replace regularization Chan--Vese model fuzzy region competition by proposed AITV. To deal with nonconvex nature AITV, apply difference-of-convex algorithm (DCA), which subproblems ...

Clustering algorithms with deep neural network has attracted wide attention to scholars. A fuzzy K-means clustering algorithm model on adaptive loss function and entropy regularization (DFKM) is proposed by combining automatic encoder algorithm. Although it introduces improve the robustness of model, its segmentation effect not ideal for high noise. The research purpose this paper focus anti-no...

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. This pap...

cozero maps are generalized forms of cozero elements. two particular cases of cozero maps, slim and regular cozero maps, are significant. in this paper we present methods to construct slim and regular cozero maps from a given  cozero map. the construction of the slim and the regular cozero map from a cozero map are called slimming and regularization of the cozero map, respectively. also, we pro...

Recently, the design of group sparse regularization has drawn much attentions in group sparse signal recovery problem. Two of the most popular group sparsity inducing regularization are the l1,2 and l1,∞ regularization, defined as the sum of l2 and l∞ norms respectively. Nevertheless, they may fail to simultaneously consider the intra-group and intergroup sparsity characteristic of the signal. ...

We investigate chiral anomaly for fermions in fundamental representation on noncommutative (fuzzy) 2-sphere. In spite that this system is realized by finite dimensional matrices and no regularization is necessary for either UV or IR, we can reproduce the correct chiral anomaly which is consistent with the calculations done in flat noncommutative space. Like the flat case, there are ambiguities ...

In medical datasets classification, support vector machine (SVM) is considered to be one of the most successful methods. However, most of the real-world medical datasets usually contain some outliers/noise and data often have class imbalance problems. In this paper, a fuzzy support machine (FSVM) for the class imbalance problem (called FSVM-CIP) is presented, which can be seen as a modified cla...