SIAM Journal on Imaging Sciences, Volume 13, Issue 2, Page 1015-1048, January 2020.
The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a nontrivial task of practical importance. In image analysis this manifests for example in anomaly detection and target detection. The traditional spectral clustering algorithm, which relies on the leading $K$ eigenvectors to detect $K$ clusters, fails in such cases. In this paper we propose the spectral embedding norm which sums the squared values of the first $I$ normalized eigenvectors, where $I$ can be significantly larger than $K$. We prove that this quantity can be used to separate clusters from the background in unbalanced settings, including extreme cases such as outlier detection. The performance of the algorithm is not sensitive to the choice of $I$, and we demonstrate its application on synthetic and real-world remote sensing and neuroimaging datasets.

中文翻译：

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谱嵌入范数：深入研究图拉普拉斯算子的谱

SIAM 影像科学杂志，第 13 卷，第 2 期，第 1015-1048 页，2020 年 1 月。
从包含多个聚类和重要背景成分的数据集中提取聚类是一项具有实际重要性的重要任务。在图像分析中，这体现在例如异常检测和目标检测中。传统的谱聚类算法依赖于前导的 $K$ 个特征向量来检测 $K$ 个簇，在这种情况下会失败。在本文中，我们提出了谱嵌入范数，它对第一个 $I$ 归一化特征向量的平方值求和，其中 $I$ 可以显着大于 $K$。我们证明该数量可用于在不平衡设置中将集群与背景分开，包括异常值检测等极端情况。算法的性能对$I$的选择不敏感，