逐个案例和单元格鲁棒的多线性主成分分析
Casewise and Cellwise Robust Multilinear Principal Component Analysis
AI总结：
本文提出一种能同时处理案例和单元格异常值的鲁棒多线性主成分分析方法，通过迭代加权最小二乘算法解决缺失值问题，并通过图形工具检测异常值。
摘要：
多线性主成分分析（MPCA）是分析张量数据的重要工具，其通过类似于PCA的方式进行降维。然而，标准MPCA对异常值敏感，易受偏离数据主体的案例异常值和张量中的单元格异常值影响。本文提出一种新的鲁棒MPCA方法，能够同时处理这两种异常值类型，并处理缺失值。该方法使用单一损失函数减少两种异常值的影响。通过迭代加权最小二乘算法求解损失函数最小化问题，并提出图形诊断工具以识别新鲁棒MPCA方法检测到的异常值类型。通过模拟和两个实际数据集评估方法和相关图形展示的性能。
英文摘要：
Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It is highly influenced by observations deviating from the bulk of the data, called casewise outliers, as well as by individual outlying cells in the tensors, so-called cellwise outliers. This latter type of outlier is highly likely to occur in tensor data, as tensors typically consist of many cells. This paper introduces a novel robust MPCA method that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers. The solution that minimizes this loss function is computed using an iteratively reweighted least squares algorithm with a robust initialization. Graphical diagnostic tools are also proposed to identify the different types of outliers that have been found by the new robust MPCA method. The performance of the method and associated graphical displays is assessed through simulations and illustrated on two real datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
