Clustering has been extensively explored in pattern recognition and data mining in order to facilitate various applications. Due to the presence of data noise, traditional clustering approaches may become vulnerable and unreliable, thereby degrading clustering performance. In this paper, we propose a robust spectral clustering approach, termed Non-negative Low-rank Self-reconstruction (NLS), which simultaneously a) explores the nonnegative low-rank properties of data correlation as well as b) adaptively models the structural sparsity of data noise. Specifically, in order to discover the intrinsic correlation among data, we devise a self-reconstruction approach to jointly consider the nonnegativity and low-rank property of data correlation matrix. Meanwhile, we propose to model data noise via a structural norm, i.e., ℓ_p,2-norm, which not only naturally conforms to genuine patterns of data noise in real-world situations, but also provides more adaptivity and flexibility to different noise levels. Extensive experiments on various real-world datasets illustrate the advantage of the proposed robust spectral clustering approach compared to existing clustering methods.

中文翻译：

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探索非负和低秩相关性以抗噪声频谱聚类

为了方便各种应用，已经在模式识别和数据挖掘中广泛研究了聚类。由于数据噪声的存在，传统的群集方法可能变得脆弱和不可靠，从而降低了群集性能。在本文中，我们提出了一种鲁棒的频谱聚类方法，称为非负低秩自重构（NLS），同时a）探索数据相关性的非负低秩属性，以及b）自适应地建模数据噪声的结构稀疏性。具体来说，为了发现数据之间的内在相关性，我们设计了一种自重构方法来共同考虑数据相关矩阵的非负性和低秩性质。同时，我们通过一个结构规范，即建议模型数据噪声ℓ _p，2范数，这不仅自然符合数据的真正模式噪声真实世界的情况下，也提供了更多的适应性和灵活性，以不同的噪声水平。在各种实际数据集上的大量实验说明了与现有聚类方法相比，所提出的鲁棒频谱聚类方法的优势。