Theoretical derivation of interval principal component analysis

Principal Component Analysis is a well-known method that can be used for dimensionality reduction, a useful technique in the Big Data era. There have been a series of proposed adaptations of the Principal Component Analysis method for interval-valued symbolic data, all of which have the downside of having intermediate steps that deal with conventional data. In this work, we put forward an interval Principal Component Analysis that only deals with symbolic data by developing a theoretical framework that allows for the definition of symbolic principal components. This framework provides the mathematical tools needed to use the symbolic principal components to transform the original data in a way that is mathematically coherent with the remainder of the framework and defines the principal components as solutions to maximisation problems, similarly to what is done in conven-tional Principal Component Analysis. After the theoretical foundations are laid down, we explore real-world data from the telecommunications sector, in an attempt to detect Internet redirection attacks in real-time. In particular, we use our symbolic method to improve and simplify an anomaly detection method that has been proposed in the litera-ture for conventional data. (c) 2022 Published by Elsevier Inc.

Automated summary

In this study, a novel interval Principal Component Analysis method is proposed which only deals with symbolic data. A theoretical framework is developed to define symbolic principal components, allowing for the transformation of the original data coherent with the framework. Real-world data from the telecommunications sector is explored to detect Internet redirection attacks in real-time and improve an existing anomaly detection method.