公理化模糊共享近邻自适应谱聚类算法

针对传统的谱聚类算法通常利用高斯核函数作为相似性度量，且单纯以距离决定相似性不能充分表现原始数据中固有的模糊性、不确定性和复杂性，导致聚类性能降低的问题。提出了一种公理化模糊共享近邻自适应谱聚类算法，首先结合公理化模糊集理论提出了一种模糊相似性度量方法，利用识别特征来衡量更合适的数据成对相似性，然后采用共享近邻的方法发现密集区域样本点分布的结构和密度信息，并且根据每个点所处领域的稠密程度自动调节参数σ，从而生成更强大的亲和矩阵，进一步提高聚类准确率。实验表明，相较于距离谱聚类、自适应谱聚类、模糊聚类方法和地标点谱聚类，所提算法有着更好的聚类性能。

Shared nearest neighbor adaptive spectral clustering algorithm based on axiomatic fuzzy set theory

For the traditional spectral clustering algorithm, the Gaussian kernel function is usually used as the similarity measure. However, the similarity of distance cannot fully express the ambiguity, uncertainty, and complexity inherent in the original data, resulting in the reduction of clustering performance. To solve this problem, we propose an axiomatic fuzzy set shared nearest neighbor adaptive spectral clustering algorithm. First, the proposed algorithm uses a fuzzy similarity measurement method based on axiomatic fuzzy set theory to measure more suitable data pairwise similarity by identifying features. Then, the structure and density information of sample point distribution in a dense area is obtained using the method of sharing the nearest neighbor, and the parameter σ is automatically adjusted according to the density degree of each point in the domain, thereby generating a more powerful affinity matrix to further increase the accuracy rate of clustering. Experimental results show that the proposed algorithm has better clustering performance than distance spectral clustering, adaptive spectral clustering, fuzzy clustering, and landmark spectral clustering.