基于拉普拉斯约束的半监督模糊C均值算法

Semi-Supervised Fuzzy C-Means Algorithm Based on Laplace Constraint

摘要: 模糊聚类算法作为经典的无监督算法之一，在未提供先验信息的基础上容易陷入局部最优。为了能够将监督学习与无监督学习相结合，同时利用已标签数据和未标签数据共同进行训练学习，本文通过对目标函数进行拉普拉斯约束，通过验证隶属度的范围始终大于等于零，能够证明该算法是有效的。在其基础上加入先验信息来挖掘大量有用的信息，使之在未提供先验信息的基础上，算法能够合理、有效地利用部分已标识样本的类别信息对未标识样本产生影响，从而提高半聚类算法的聚类性能；最后，将文章中提出的两类改进算法与原始模糊c均值(FCM)进行聚类指标对比，能够显示其具有良好的聚类效果。

Abstract: As one of the classical unsupervised algorithms, fuzzy clustering algorithm is easy to fall into local optimum without providing prior information. In order to combine supervised learning with unsupervised learning and use both labeled and unlabeled data for training learning, this paper proved the effectiveness of the algorithm through Laplace constraint on the objective function and verification that the range of membership is always greater than or equal to zero. On this basis, prior information is added to mine a lot of useful information, so that the algorithm can reasonably and effectively use the category information of part of the identified samples to affect the unidentified samples, so as to improve the clustering performance of the semi-clustering algorithm. Finally, the two improved algorithms proposed in this paper are compared with the original Fuzzy C-means (FCM) for clustering index, and the results show that the proposed algorithm has good clustering effect.