使用传输变换划分信号类用于数据分析和机器学习
Partitioning signal classes using transport transforms for data analysis and machine learning
摘要：
一组相对较新的基于传输的变换（CDT，R-CDT，LOT）已经显示出它们在各种图像和数据处理任务中的实力和巨大潜力，例如参数信号估计，分类，癌症检测等。因此，这是值得阐明的一些数学属性，解释成功的这些变换时，它们被用作数据分析，信号处理或数据分类的工具。特别是，我们给出的条件下，由代数生成模型创建的信号类被转换成凸集的运输变换。当在变换域中观察时，类的这种凸化简化了分类和其他数据分析和处理问题。更具体地说，我们研究了代数生成建模框架下的凸化能力，这些变换的程度和限制。我们希望本文将作为这些变换的介绍，并将鼓励数学家和其他研究人员进一步探索理论基础和算法工具，这将有助于理解这些变换的成功，并为进一步的成功应用奠定基础。
英文摘要：
A relatively new set of transport-based transforms (CDT, R-CDT, LOT) have shown their strength and great potential in various image and data processing tasks such as parametric signal estimation, classification, cancer detection among many others. It is hence worthwhile to elucidate some of the mathematical properties that explain the successes of these transforms when they are used as tools in data analysis, signal processing or data classification. In particular, we give conditions under which classes of signals that are created by algebraic generative models are transformed into convex sets by the transport transforms. Such convexification of the classes simplify the classification and other data analysis and processing problems when viewed in the transform domain. More specifically, we study the extent and limitation of the convexification ability of these transforms under an algebraic generative modeling framework. We hope that this paper will serve as an introduction to these transforms and will encourage mathematicians and other researchers to further explore the theoretical underpinnings and algorithmic tools that will help understand the successes of these transforms and lay the groundwork for further successful applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
