Peter Filzmoser is a Professor of Statistics at the Vienna University of Technology, Austria. He received his Ph.D. and postdoctoral lecture qualification from the same university. He was a Visiting Professor at Toulouse, France, and Belarus. Furthermore, he has authored more than 200 research articles and several R packages and is a co-author of a book on multivariate methods in chemometrics (CRC Press, 2009), on analyzing environmental data (Wiley, 2008), and on compositional data analysis (Springer, 2018).
Abstract: Outlier detection techniques are well established for multivariate observations (vectors). We extend the ideas to matrix-valued objects, where the measurements are arranged in the rows and columns of a matrix. An example are image data, where the pixel information is presented in a rectangular matrix. The concept of matrix-valued data is not new at all, and a prominent distribution in this context is the matrix normal distribution. There are different proposals in the literature on how to estimate the parameters of this distribution. It is also possible to define a Mahalanobis distance, and the concept of robust covariance estimation can be modified to obtain robust estimators for the matrix-valued case. We present an adaptation of the well-known MCD (Minimum Covariance Determinant) estimator to this situation. Moreover, the concept of Shapley values, which has been successfully used in the context of Explainable AI, is extended in order to explain the reasoning behind the outlyingness. For example, one can identify outlying images and explain which pixels contribute to this outlyingness. A more detailed background, as well as illustrative examples, will be provided in the presentation.