Casewise en Cellwise Robuuste Methoden voor Tensor Data Analyse

In many research fields data dimension reduction techniques are widely used. Fields such as chemometrics, signal processing, and video compression, try to deal with these issues with tools that transform high-dimensional data to lower dimensions where the meaningful properties of the data are retained. Principal Component Analysis (PCA) is a widely used tool for dimension reduction. However, it is known that PCA is not robust against outliers. Most robust PCA methods are developed to deal with rowwise outliers, which are observations that deviate from the majority. The MacroPCA method can additionally deal with outlying cells and missing values. These methods however can only be applied to two-dimensional data matrices. For multiway data, models such as parallel factor analysis (PARAFAC) have been developed to reduce their dimension. Available robust PARAFAC methods can only deal with rowwise outliers and missing values. The goal of this research is to develop and study methods that can simultaneously deal with rowwise outliers, cellwise outliers, and missing values in multiway data. Application to real-life datasets will also be considered, especially in chemometrics.