Correlation clustering detects complex and intricate relationships in high-dimensional data by identifying groups of data points, each characterized by differents correlation among a (sub)set of features. Current correlation clustering methods generally limit themselves to linear correlations only. In this paper, we introduce a method for detecting global non-linear correlated clusters focusing on quadratic relations. We introduce a novel Hough transform for the detection of hyperparaboloids and apply it to the detection of hyperparaboloid correlated clusters in arbitrary high-dimensional data spaces. We further provide a solution for utilizing all available CPU cores on a system. For this we simply split the Hough space among a pre-defined axis into a number of equi-sized partitions. In this paper we show that this most simple way of parallelization already improves the runtime significantly. Non-linear correlation clustering like our method can reveal valuable insights which are not covered by current linear versions. Our empirical results on synthetic and real world data reveal that the proposed method is robust against noise, jitter and irregular densities.

中文翻译：

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检测全局超抛物面相关簇：基于霍夫变换的多核算法

相关聚类通过识别数据点组来检测高维数据中的复杂和错综复杂的关系，每个数据点的特征在于一组（子）特征之间的不同相关性。当前的相关聚类方法通常仅限于线性相关。在本文中，我们介绍了一种检测全局非线性相关簇的方法，该方法侧重于二次关系。我们引入了一种用于检测超抛物面的新型霍夫变换，并将其应用于检测任意高维数据空间中的超抛物面相关簇。我们进一步提供了一种利用系统上所有可用 CPU 内核的解决方案。为此，我们简单地将预定义轴之间的霍夫空间分成许多等大小的分区。在本文中，我们展示了这种最简单的并行化方法已经显着改善了运行时间。像我们的方法这样的非线性相关聚类可以揭示当前线性版本未涵盖的有价值的见解。我们对合成和现实世界数据的实证结果表明，所提出的方法对噪声、抖动和不规则密度具有鲁棒性。