An Improved Spectral Clustering Algorithm Based on Axiomatic Fuzzy Set
ZHAO Xiaoqiang①②③ LIU Xiaoli①
①(College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China) ②(Key Laboratory of Gansu Advanced Control for Industrial Processes, Lanzhou 730050, China) ③(National Experimental Teaching Center of Electrical and Control Engineering, Lanzhou University of Technology, Lanzhou 730050, China)
摘要 谱聚类算法通常是采用高斯核作为相似性度量，并利用所有可用的特征来构建具有欧氏距离的相似度矩阵，数据集复杂度会影响其谱聚类性能，因此该文提出一种基于公理化模糊子集(AFS)的改进谱聚类算法。首先结合A F S算法，利用识别特征来衡量更合适的数据成对相似性，生成更强大的亲合矩阵；再有效地利用 Nyström采样算法，计算采样点间以及采样点和剩余点间的相似度矩阵去降低计算的复杂度；最后通过在不同数据集以及图像分割上进行实验，证明了提出算法的有效性。
Abstract：Gaussian kernel is usually used as the similarity measure in spectral clustering algorithm, and all the available features are used to construct the similarity matrix with Euclidean distance. The complexity of the data set would affect its spectral clustering performance. Therefore, an improved spectral clustering algorithm
based on Axiomatic Fuzzy Set (AFS) is proposed. Firstly, AFS algorithm is combined to measure the similarity of more suitable data by recognizing features, and the stronger affinity matrix is generated. Then Nyström sampling algorithm is used to calculate the similarity matrix between the sampling points and the sampling points and the remaining points to reduce the computational complexity. Finally, the experiment is carried out by using different data sets and image segmentations, the effectiveness of the proposed algorithm are proved.
