Extended Vision techniques are ubiquitous in physics. However, the data cubes
steaming from such analysis often pose a challenge in their interpretation, due
to the intrinsic difficulty in discerning the relevant information from the
spectra composing the data cube.
Furthermore, the huge dimensionality of data cube spectra poses a complex
task in its statistical interpretation; nevertheless, this complexity contains
a massive amount of statistical information that can be exploited in an
unsupervised manner to outline some essential properties of the case study at
hand, e.g.~it is possible to obtain an image segmentation via (deep) clustering
of data-cube's spectra, performed in a suitably defined low-dimensional
embedding space.
To tackle this topic, we explore the possibility of applying unsupervised
clustering methods in encoded space, i.e. perform deep clustering on the
spectral properties of datacube pixels. A statistical dimensional reduction is
performed by an ad hoc trained (Variational) AutoEncoder, in charge of mapping
spectra into lower dimensional metric spaces, while the clustering process is
performed by a (learnable) iterative K-Means clustering algorithm.
We apply this technique to two different use cases, of different physical
origins: a set of Macro mapping X-Ray Fluorescence (MA-XRF) synthetic data on
pictorial artworks, and a dataset of simulated astrophysical observations.

扩展视觉技术在物理学中非常普遍，然而由于数据立方体的光谱构成对其解释提出了挑战。为了解决这个问题，我们探索了在编码空间中应用无监督聚类方法的可能性，通过数据立方体像素的光谱属性进行深层聚类，该过程由经过训练的变分自动编码器进行统计降维，同时聚类过程由可学习的迭代 K 均值聚类算法执行。我们将这一技术应用于两个不同的物理起源用例：一组关于绘画艺术品的宏观映射 X 射线荧光（MA-XRF）合成数据和模拟天体观测的数据集。

基于深度光谱聚类的数据立方体分割

Datacube segmentation via Deep Spectral Clustering

We give a statistical interpretation of entropic optimal transport by showing
that performing maximum-likelihood estimation for Gaussian deconvolution
corresponds to calculating a projection with respect to the entropic optimal
transport distance. This structural result gives theoretical support for the
wide adoption of these tools in the machine learning community.

我们通过说明高斯反卷积的最大似然估计与判别式最优传输距离的计算相对应来给出熵最优传输的统计解释。这一结构性结果为机器学习社区广泛采用这些工具提供理论支持。