Multispectral and hyperspectral images are increasingly popular in different
research fields, such as remote sensing, astronomical imaging, or precision
agriculture. However, the amount of free data available to perform machine
learning tasks is relatively small. Moreover, artificial intelligence models
developed in the area of spectral imaging require input images with a fixed
spectral signature, expecting the data to have the same number of spectral
bands or the same spectral resolution. This requirement significantly reduces
the number of usable sources that can be used for a given model. The scope of
this study is to introduce a methodology for spectral image data fusion, in
order to allow machine learning models to be trained and/or used on data from a
larger number of sources, thus providing better generalization. For this
purpose, we propose different interpolation techniques, in order to make
multisource spectral data compatible with each other. The interpolation
outcomes are evaluated through various approaches. This includes direct
assessments using surface plots and metrics such as a Custom Mean Squared Error
(CMSE) and the Normalized Difference Vegetation Index (NDVI). Additionally,
indirect evaluation is done by estimating their impact on machine learning
model training, particularly for semantic segmentation.

通过使用插值技术，介绍了一种光谱图像数据融合的方法，以允许机器学习模型在更多数据源上进行训练和使用，从而提供更好的泛化能力。通过使用表面绘图和指标（如 CMSE 和 NDVI），评估了插值结果，并通过估计对语义分割等机器学习模型训练的影响进行间接评估。

多源数据增强的光谱图像数据融合

Spectral Image Data Fusion for Multisource Data Augmentation

Effective verification and validation techniques for modern scientific
machine learning workflows are challenging to devise. Statistical methods are
abundant and easily deployed, but often rely on speculative assumptions about
the data and methods involved. Error bounds for classical interpolation
techniques can provide mathematically rigorous estimates of accuracy, but often
are difficult or impractical to determine computationally. In this work, we
present a best-of-both-worlds approach to verifiable scientific machine
learning by demonstrating that (1) multiple standard interpolation techniques
have informative error bounds that can be computed or estimated efficiently;
(2) comparative performance among distinct interpolants can aid in validation
goals; (3) deploying interpolation methods on latent spaces generated by deep
learning techniques enables some interpretability for black-box models. We
present a detailed case study of our approach for predicting lift-drag ratios
from airfoil images. Code developed for this work is available in a public
Github repository.

验证和验证现代科学机器学习工作流程的有效技术是很具挑战性的。本研究通过展示（1）多个标准插值技术具有信息丰富的误差界限，可以进行高效计算或估计；（2）不同插值器之间的比较性能有助于验证目标；（3）在深度学习技术生成的潜在空间上部署插值方法，使得黑匣子模型具有一定的可解释性。我们提供了一个详细的案例研究，用于从飞翼图像预测升阻比。本研究的代码可在公共 Github 存储库中获取。

利用插值模型和误差界提高可验证的科学机器学习

Leveraging Interpolation Models and Error Bounds for Verifiable  Scientific Machine Learning

An $\varepsilon$-approximate quantile sketch over a stream of $n$ inputs
approximates the rank of any query point $q$ - that is, the number of input
points less than $q$ - up to an additive error of $\varepsilon n$, generally
with some probability of at least $1 - 1/\mathrm{poly}(n)$, while consuming
$o(n)$ space. While the celebrated KLL sketch of Karnin, Lang, and Liberty
achieves a provably optimal quantile approximation algorithm over worst-case
streams, the approximations it achieves in practice are often far from optimal.
Indeed, the most commonly used technique in practice is Dunning's t-digest,
which often achieves much better approximations than KLL on real-world data but
is known to have arbitrarily large errors in the worst case. We apply
interpolation techniques to the streaming quantiles problem to attempt to
achieve better approximations on real-world data sets than KLL while
maintaining similar guarantees in the worst case.

应用插值技术解决流数据的分位数草图问题，以在保持最坏情况下相似保证的同时，尝试获得比 KLL 在实际数据集上更好的近似。