Department of Mathematics, LStat, Katholieke Universiteit Leuven, Celestijnenlaan 200B, BE-3001 Heverlee, Belgium.
Anal Chim Acta. 2011 Oct 31;705(1-2):155-65. doi: 10.1016/j.aca.2011.04.043. Epub 2011 Jun 16.
To explore multi-way data, different methods have been proposed. Here, we study the popular PARAFAC (Parallel factor analysis) model, which expresses multi-way data in a more compact way, without ignoring the underlying complex structure. To estimate the score and loading matrices, an alternating least squares procedure is typically used. It is however well known that least squares techniques suffer from outlying observations, making the models useless when outliers are present in the data. In this paper, we present a robust PARAFAC method. Essentially, it searches for an outlier-free subset of the data, on which we can then perform the classical PARAFAC algorithm. An outlier map is constructed to identify outliers. Simulations and examples show the robustness of our approach.
为了探索多元数据，已经提出了不同的方法。在这里，我们研究了流行的 PARAFAC（并行因子分析）模型，该模型以更紧凑的方式表示多元数据，同时不会忽略潜在的复杂结构。为了估计得分和加载矩阵，通常使用交替最小二乘法程序。然而，众所周知，最小二乘法技术容易受到异常值的影响，因此当数据中存在异常值时，这些模型将变得毫无用处。在本文中，我们提出了一种鲁棒的 PARAFAC 方法。本质上，它搜索数据中无异常值的子集，然后我们可以在该子集上执行经典的 PARAFAC 算法。构建了一个异常值图来识别异常值。模拟和实例表明了我们方法的稳健性。
