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.

中文翻译：

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通过拓扑数据分析探索高光谱成像数据集

分析化学正在迅速变化。事实上，我们总是获得更多的数据，以便在复杂样本的探索中走得更远。高光谱成像也未能摆脱这种趋势。它很快成为许多科学领域复杂样品分子表征的首选工具。主要原因是它同时提供光谱和空间信息。因此，化学计量学在早期提供了许多非常适合此类数据结构的探索工具（PCA、聚类、MCR-ALS……）。然而，考虑到我们必须管理的数据立方体中的像素数量不断增加，我们今天面临着新的挑战。因此，我们的想法是引入拓扑数据分析的新范式，以探索突出其良好属性和特定特征的高光谱成像数据集。在本文中，我们还将指出一个事实，即传统的化学计量学方法通常基于方差分析或简单地强加一个隐含定义数据集几何形状的数据模型。因此，我们将证明它在高光谱成像数据集探索的框架中并不总是合适的。