解模糊约束软子空间聚类

Defuzzification Constraint Soft Subspace Clustering

摘要: 在现有的大多数软子空间聚类算法中都是基于簇内的信息开发的，忽略了簇间信息，造成信息严重丢失，算法性能受到较大程度的限制。本文在现有的软子空间聚类算法的目标函数上集成了簇内的信息以及簇间信息，同时为了提升算法的鲁棒性，我们采用解模糊化约束权重策略，结合模糊加权以及熵加权的思想构造了一个新的权重约束函数，据此构建了一个新的目标函数，并推导了DCSSC (Defuzzification Constraint Soft Subspace Clustering)算法。利用人工合成数据集以及UCI数据集进行实验，对该算法的性能评估。在与几种现有的软子空间聚类算法的对比实验中，DCSSC算法在性能和稳定性上均表现出优势。最后利用Friedman检验验证了新提出的算法的性能与现有的软子空间的性能存在显著性差异，并且这种差异具有统计意义。

Abstract: The development of most existing soft subspace clustering algorithms is based on information within clusters, while information between clusters is ignored, resulting in severe information loss and considerably limiting the performance of the algorithms. In this paper, information within clusters and information between clusters are integrated into the objective function of existing soft subspace clustering algorithms. Meanwhile, to improve the robustness of the algorithm, we adopt a defuzzification constraint weight strategy and combine the ideas of fuzzy weighting and entropy weighting to construct a new weight constraint function. On this basis, a new objective function is constructed, and the DCSSC (Defuzzification Constraint Soft Subspace Clustering) algorithm is derived. Experiments were conducted using artificial synthetic datasets and UCI datasets to evaluate the performance of the algorithm. In comparative experiments with several existing soft subspace clustering algorithms, the DCSSC algorithm shows advantages in both performance and stability. Finally, the Friedman test is used to verify that the performance of the newly proposed algorithm is significantly different from that of existing soft subspace algorithms, and that this difference is statistically significant.