Thompson’s partition of a cyclic subnormal operator into normal and completely non-normal components is combined with a non-commutative calculus for hyponormal operators for separating outliers from the cloud, in rather general point distributions in the plane. The main result provides exact transformation formulas from the power moments of the prescribed point distribution into the moments of the uniform mass carried by the cloud. The proposed algorithm solely depends on the Hessenberg matrix associated to the original data. The robustness of the algorithm is reflected by the insensitivity of the output under trace class, or by a theorem of Voiculescu, under certain Hilbert–Schmidt class, additive perturbations of the Hessenberg matrix.

中文翻译：

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二维异常值布局的光谱分析

Thompson 将循环次正态算子划分为正态分量和完全非正态分量的方法与次正态算子的非交换演算相结合，用于将离群点从云中分离出来，在平面上相当一般的点分布中。主要结果提供了从指定点分布的幂矩到云承载的均匀质量的矩的精确转换公式。所提出的算法仅依赖于与原始数据相关联的 Hessenberg 矩阵。算法的鲁棒性体现在迹类下输出的不敏感性，或者通过Voiculescu 定理，在某些Hilbert-Schmidt 类下，Hessenberg 矩阵的加性扰动。