Current anomaly detection (AD) algorithms are typically challenged by either accuracy or efficiency. More accurate nonlinear detectors are typically slow and not scalable. In this letter, we propose two families of techniques to improve the efficiency of the standard kernel Reed–Xiaoli (KRX) method for AD by approximating the kernel function with either the data-independent random Fourier features or the data-dependent basis with the Nyström approach. We compare all methods for both real multi- and hyperspectral images. We show that the proposed efficient methods have a lower computational cost, and they perform similar to (or outperform) the standard KRX algorithm thanks to their implicit regularization effect. Last but not least, the Nyström approach has an improved power of detection.

中文翻译：

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高效的非线性 RX 异常检测器

当前的异常检测 (AD) 算法通常面临准确性或效率的挑战。更准确的非线性检测器通常很慢且不可扩展。在这封信中，我们提出了两类技术，通过使用与数据无关的随机傅立叶特征或使用 Nyström 的数据相关基础逼近核函数，来提高用于 AD 的标准核 Reed-Xiaoli (KRX) 方法的效率。方法。我们比较了真实多光谱和高光谱图像的所有方法。我们表明，所提出的有效方法具有较低的计算成本，并且由于其隐式正则化效果，它们的性能类似于（或优于）标准 KRX 算法。最后但并非最不重要的是，Nyström 方法具有改进的检测能力。