计算机科学 ›› 2021, Vol. 48 ›› Issue (7): 137-144.doi: 10.11896/jsjkx.200800190
赵敏, 刘惊雷
ZHAO Min, LIU Jing-lei
摘要： 聚类是将给定的样本分成几个不同的簇,它在机器学习、数据挖掘等领域得到了广泛应用,并受到研究人员的广泛关注。但是,传统的聚类方法仍然存在3个方面的不足。首先,由于一些数据中存在噪声和异常值,传统的聚类方法容易产生误差较大的目标函数。其次,传统的聚类方法没有使用监督信息来指导构建相似矩阵。最后,加入图正则的聚类方法在计算相似度矩阵时,邻居关系都是确定的,一旦计算错误就会导致构造图的质量低,进而影响聚类性能。因此,提出了一种基于高斯场和自适应图正则化的半监督聚类(SCGFAG)模型。该模型通过高斯场及谐波函数法引入监督信息,来指导构建相似度矩阵,实现半监督学习,还引入稀疏误差矩阵来表示稀疏噪声,如脉冲噪声、死线和条纹,并且使用l1范数来缓解稀疏噪声。此外,所提模型还引入l2,1范数来处理异常值的影响。因此,SCGFAG对数据噪声和异常值不敏感。更重要的是,SCGFAG通过引入自适应图的正则化提高了聚类性能。为了实现优化聚类的目标,提出了一种迭代更新算法—增广拉格朗日法(Augmented Lagrangian Method,ALM),分别对优化变量进行更新。在4个数据集上进行的实验表明,所提方法优于相比较的8种经典聚类方法获得了更好的聚类性能。
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