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Interval type-2 fuzzy sets not only have stronger ability to deal with uncertainty, but also have low computational complexity than general type-2 fuzzy set, so they are widely used in fuzzy clustering methods. However, most existing interval type-2 fuzzy clustering methods are still sensitive to noise and lack a certain degree of robustness in segmenting images with noise. Therefore, this paper proposes a novel interval type-2 enhanced kernel possibilistic fuzzy local and non-local information c-means clustering method for segmenting images with high noise. Interval type-2 possibilistic fuzzy clustering with Lambert-W function is first extended to obtain a novel interval type-2 enhanced possibilistic fuzzy clustering with product partition. Then deep local neighborhood information including local and non-local information is used to constrain interval type-2 enhanced possibilistic fuzzy product partition c-means clustering, and a robust interval type-2 enhanced possibilistic fuzzy deep local information clustering with kernel metric is proposed. Experimental results demonstrate that the proposed algorithm significantly outperforms the latest fuzzy clustering-related algorithms in the presence of high noise. [ABSTRACT FROM AUTHOR]

To improve the segmentation performance and anti-noise robustness of existing weighted kernel intuitionistic fuzzy clustering, a robust kernelized total Bregman divergence-based fuzzy local information clustering motivated by intuitionistic fuzzy information is proposed. In this algorithm, a kernelized total Bregman divergence is extended by a polynomial kernel function, and the corresponding intuitionistic kernelized total Bregman divergence is put forward to measure the difference between intuitionistic fuzzy sets. Then, the weighted local information is introduced into the objective function of intuitionistic fuzzy clustering, and the similarity between the current pixel and its neighborhood pixels is constructed to better describe the influence of neighborhood pixels on the current pixel. Finally, the square root of the deviation between the current pixel and the mean value of its neighboring pixels is used to adjust the local spatial information to improve the robustness to noise or outliers and further enhance the anti-noise ability of the algorithm. Experimental results show that the proposed algorithm has better clustering performance and stronger anti-noise robustness than existing state-of-the-art fuzzy clustering-related algorithms. [ABSTRACT FROM AUTHOR]

In the fuzzy clustering process, the clustering number for image or text data to be classified is not easy to determine or unknown. The competitive learning algorithm can automatically determine the optimal clustering number to avoid the problem of inappropriate artificial selection. In this paper, based on the clustering by competitive agglomeration (CA), the idea of the "Competitive Learning Mechanism" is introduced to picture fuzzy clustering to obtain the competitive agglomeration picture fuzzy clustering (CAPFCM). The competitive learning regular term of the CAPFCM objective function is reinterpreted from the perspective of minimizing the entropy, and the general framework of the entropy competitive clustering algorithm is constructed. Moreover, the competitive learning regular term of the objective function is replaced by quadratic entropy, Renyi entropy or Shannon entropy to obtain different entropy competitive clustering. To improve the efficiency of the CAPFCM algorithm, the suppressed factor is introduced to appropriately increase the maximum value of the picture fuzzy partition information for different clusters and suppress all others. In addition, this paper proposes a robust adaptive entropy competitive picture fuzzy clustering segmentation algorithm with neighborhood spatial information constraints to enhance the anti-noise ability of the picture fuzzy clustering algorithm for noise image. Experiments show that robust CAPFCM can automatically determine the clustering number and greatly improve the operation efficiency and segmentation performance. [ABSTRACT FROM AUTHOR]

• An interval type-2 possibilistic fuzzy clustering with local information is proposed. • Deep neighborhood window is used to enhance the adaptive ability of algorithm. • Local and non-local information is used to improve the robustness of algorithm. • Using structural similarity to enhance the influence of local spatial information. • Testing results show that the proposed algorithm has extremely good performance. Type-2 fuzzy set theory has certain potential advantage in processing high-order uncertainty, and has been more and more widely applied in pattern recognition, image processing, and system modeling. Although it has been introduced into robust fuzzy clustering modeling, most clustering methods based on type-2 fuzzy set theory have many obvious shortcomings, such as weak robustness against noise and high sensitivity to initial value. Therefore, this paper presents a novel single fuzzifier interval type-2 kernel-based possibilistic fuzzy local and non-local information c-means clustering, and it is driven by deep neighborhood information for image segmentation in the presence of high noise. Firstly, we construct the novel deep neighborhood window structure, which consists of local neighborhood window around current pixel and deep neighborhood window around the pixel in local neighborhood window around current pixel. Secondly, using the structural similarity between local neighborhood window and deep neighborhood window around current pixel, we construct a novel fuzzy local information factor to tune the impact of local neighborhood information on current pixel clustering. Thirdly, possibility theory and fuzzy local information factor are introduced into interval type-2 kernel-based fuzzy c-means clustering, and a novel single fuzzifier type-2 possibilistic fuzzy clustering with richer local and non-local information and kernel metric is proposed. Experimental results indicate that the proposed algorithm outperforms existing state-of-the-art robust fuzzy clustering-related algorithms, and significantly improve the robustness of robust fuzzy clustering algorithms against noise. [ABSTRACT FROM AUTHOR]