Exploring hyperspectral imaging data sets with topological data analysis.

Analytical chemistry is rapidly changing. Indeed we acquire always more data in order to go ever further in the exploration of complex samples. Hyperspectral imaging has not escaped this trend. It quickly became a tool of choice for molecular characterisation of complex samples in many scientific domains. The main reason is that it simultaneously provides spectral and spatial information. As a result, chemometrics has provided many exploration tools (PCA, clustering, MCR-ALS …) well-suited for such data structure at early stage. However we are today facing a new challenge considering the always increasing number of pixels in the data cubes we have to manage. The idea is therefore to introduce a new paradigm of Topological Data Analysis in order explore hyperspectral imaging data sets highlighting its nice properties and specific features. With this paper, we shall also point out the fact that conventional chemometric methods are often based on variance analysis or simply impose a data model which implicitly defines the geometry of the data set. Thus we will show that it is not always appropriate in the framework of hyperspectral imaging data sets exploration.