多类分类的粗、细尺度几何信息含量及隐含的数据驱动智能
Coarse- and fine-scale geometric information content of Multiclass Classification and implied Data-driven Intelligence
摘要：
在由特征集指定的标记点云集合定义的任何多类分类（MCC）设置下，我们仅从所有可能的点云三元组中提取随机偏序，而无需显式测量三个云到云的距离。我们证明了这样一个集体的偏序可以有效地计算一个标签嵌入树的几何标签空间。这棵树反过来又产生了一个预测图，或一个具有精确加权链接的网络。这两个多尺度的几何形状被认为是MCC的粗尺度信息内容。它们确实共同揭示了关于标签为什么以及如何产生的可解释知识，并通过数据支持的潜在多个候选标签促进了无错误预测。为了揭示标签内的异质性，我们进一步进行标记自然发现的集群内的每个点云，同样派生多尺度几何作为其精细尺度的信息内容包含在数据中。这种精细尺度的努力表明，我们的计算建议确实是可扩展的MCC设置具有较大的标签空间。总的来说，计算出的数据驱动模式和知识的多尺度集合将作为构建关于感兴趣系统的可见和可解释的主题智能的基础。
英文摘要：
Under any Multiclass Classification (MCC) setting defined by a collection of labeled point-cloud specified by a feature-set, we extract only stochastic partial orderings from all possible triplets of point-cloud without explicitly measuring the three cloud-to-cloud distances. We demonstrate that such a collective of partial ordering can efficiently compute a label embedding tree geometry on the Label-space. This tree in turn gives rise to a predictive graph, or a network with precisely weighted linkages. Such two multiscale geometries are taken as the coarse scale information content of MCC. They indeed jointly shed lights on explainable knowledge on why and how labeling comes about and facilitates error-free prediction with potential multiple candidate labels supported by data. For revealing within-label heterogeneity, we further undergo labeling naturally found clusters within each point-cloud, and likewise derive multiscale geometry as its fine-scale information content contained in data. This fine-scale endeavor shows that our computational proposal is indeed scalable to a MCC setting having a large label-space. Overall the computed multiscale collective of data-driven patterns and knowledge will serve as a basis for constructing visible and explainable subject matter intelligence regarding the system of interest.
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。
