谱聚类算法中的奇异解问题

The Problem of Singular Solution in Spectral Clustering Algorithm

对谱聚类的奇异解进行了研究。在谱聚类中,由对象相似度的定义,两种属性完全不同或截然相反的对象的类,其类内对象的相似度、类间对象的相似度和与其它类对象的相似度,会出现接近或相同的情况,从而有可能被聚为一类。研究发现,大多数情况下,出现谱聚类的奇异解的主要原因是聚类个数设置不合理和高斯核参数σ估计不准确。本文给出了利用特征值差值分析与特征值累积贡献率来确定聚类个数和估计高斯核参数σ的方法。实验表明,所给聚类个数选择和高斯核参数σ估计的方法有效,可以消除谱聚类结果中存在的奇异解。

In spectral clustering, according to the definition of object similarity, two classes of objects whose properties are completely different or opposite, may be clustered into one class. It is because that the similarity of these objects within class, between different classes and with other classes, can be very close to each other. The study found that in most cases, the main reason of the emergence of singular solutions is the number of clusters is set unreasonable and the Gaussian kernel parameter 6 does not estimate accurately. The method given in this paper is trying to determine the number of clusters and estimate the Gaussian kernel parameter 6, using the difference between two consecutive eigenvalues and the cumulative contribution rate of the eigenvalues of the scaled adjacency matrix of spectral clustering algorithm. Experiments show that this method is effective, which the number of spectral clustering choice and Gaussian kernel parameter ~ estimated, it can eliminate the singularity exists in the spectral clustering.