This work bridges the gap between two popular methodologies for data partitioning: kernel clustering and regularization-based segmentation. While addressing closely related practical problems, these general methodologies may seem very different based on how they are covered in the literature. The differences may show up in motivation, formulation, and optimization, e.g. spectral relaxation versus max-flow. We explain how regularization and kernel clustering can work together and why this is useful. Our joint energy combines standard regularization, e.g. MRF potentials, and kernel clustering criteria like normalized cut. Complementarity of such terms is demonstrated in many applications using our bound optimization Kernel Cut algorithm for the joint energy (code is publicly available). While detailing combinatorial move-making, our main focus are new linear kernel and spectral bounds for kernel clustering criteria allowing their integration with any regularization objectives with existing discrete or continuous solvers.

中文翻译：

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Kernel Cuts: Kernel and Spectral Clustering 满足正则化

这项工作弥合了两种流行的数据分区方法之间的差距：内核聚类和基于正则化的分割。在解决密切相关的实际问题时，这些一般方法可能看起来非常不同，这取决于它们在文献中的涵盖方式。差异可能会出现在动机、公式和优化中，例如频谱松弛与最大流量。我们解释了正则化和内核聚类如何协同工作以及为什么这很有用。我们的联合能量结合了标准正则化（例如 MRF 电位）和核聚类标准（如归一化切割）。使用我们针对联合能量的边界优化核切割算法（代码是公开可用的）在许多应用程序中证明了这些术语的互补性。在详述组合动作的同时，