Modern data are often of multiway type which means that each observation is not just a vector, but is a tensor with two or more dimensions, called modes. Some examples are grey scale images where each image can be represented by a matrix with the gray scale (ranging from black to white) of the image at each of its pixels. Similarly, a color image can be represented by a three-dimensional tensor where the first two dimensions are again the pixel values and the third dimension contains the values of the Red, Blue and Green component of each pixel. Multiway data appear in a variety of other applications such as climate data, chemometrics data, video data, etc.

 

When analyzing tensor data, a common starting point is to apply a dimension reduction technique to extract the most relevant information from the data. In this talk Multilinear Principal Component Analysis (MPCA) is considered. It performs dimension reduction similar to PCA for multivariate data. However, similarly to classical PCA, 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. To overcome this drawback of standard MPCA, a novel robust MPCA method is proposed that can handle both casewise and cellwise outliers simultaneously, and can cope with missing values as well.

 

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 real datasets. The first real data example is a surveillance video, the second example is the Dorrit data, a well-known data set in chemometrics.

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