Twinned Principal Curves

Abstract

In this chapter, we develop methods for combining information from two data sources which have some underlying correlation or dependency where this dependency may not be best viewed as a linear dependency. Our inspiration is biological information processing: sensory information from a single organism is sent to our brains via different sensory channels; however, at some stage we are able to integrate this information so that we can re-create much of the original sensory information from memory when we have a new input from a single sensory stream. We can view this as a form of forecasting - before we taste the orange we can visualise how it will taste. However, our main aim is to develop an engineering application in which extracting structure from two data sets simultaneously is, in some way, easier than extracting information from the individual data sets separately. Traditional statistics has thoroughly investigated linear correlations between two data sets (CCA); however, it is our aim to develop methods which do not rely on the underlying relationship between the data sets being linear.