The use of the Higher Order Singular Value Decomposition of the 4-cumulant's tensors in features selection and outlier detection

We use the High Order Singular Value Decomposition (HOSVD) of higher order cumulant tensors to perform features selection and outlier detection on multivariate data. In both cases, a target subset of data (outlier subset) has higher-order dependencies. In our case, those dependencies are modeled by the t-Student copula. Apart from a target subset, ordinary data are modeled by a Gaussian multivariate distribution. This scenario is a typical setting in real life data processing, where the Central Limit Theorem holds in general but breaks for unusual events (outliers). In the presented approach, we collect information about higher order dependencies utilizing the 4th cumulant's tensor. It makes the approach more general comparing with recently developed 3rd cumulant's tensor approach. If the 3rd cumulant's tensor of data is non-zero in most cases the 4th should be non-zero as well. However, the opposite is not true in many cases, consider the t-Student copula model as an example. In this paper, through experiment we show the superiority of our method over the Reed-Xiaoli (RX) Detector, that is a well-known outlier detector and can be used as a benchmark. We present the application of our method in a real life financial data analysis. We demonstrate that our method has advantage for detecting outliers being a increases of shares prices during a crisis. Our algorithms are implemented in the modern open source Julia programming language and available on the GitHub.