RI: Small: Explicit and Implicit Regularity Perception

这是一个大数据无处不在的时代，来自各种传感器，如医疗扫描仪，监控摄像头，智能家电和手机。即使配备了最强大的硬件和软件进行数据处理，人们仍然可能迷失在这些大量嘈杂的数据中，错过“只见树木不见森林”。这个项目解决了数据科学中的一个基本问题：我们在一个看似结构不复杂的数据集中寻找什么？基于已被证明的关于对称性的数学理论，并受到人类视觉的启发，研究人员将构建一个路线图，用于发现这些数据集中所有可能的潜在模式，并提供计算有效的工具来发现这些模式，即使是在扭曲和伪装的形式下。这种不懈的模式搜索算法将展示“寻宝”式搜索的力量，促进自动模式发现，填补当前数据分析实践中的空白，从而推动数据科学的发展。该项目的成果将适用于不同领域的数据集，从药物发现、基因图谱和人体运动监测等生物医学领域，到无人驾驶汽车导航、城市场景理解和监视异常活动检测等计算机视觉应用。本研究建立了一个基于对称群理论的正则空间，并为基于规则驱动和人类感知启发的模式搜索算法构建了一个计算平台。由群论指导并从人类感知中学习的正则空间的零状态之间的转换将与贝叶斯概率理论无缝结合。 模式的两个关键成分，最小细胞和细胞间拓扑结构，将在大规模，多模态，高维真实世界的感觉数据上进行广泛的探索。其目的是构建和验证计算工具，促进有效的无监督重复模式发现，其次是恢复几何变换，最后通过定量连接完整的规则感知频谱从规则，近规则到不规则。这个基于群体理论的规律性空间的有限性、唯一性和完整性将为指导一般数据科学中的模式搜索提供一个合理的计算框架。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This is an era of pervasive big data, streaming in from all sorts of sensors such as medical scanners, surveillance cameras, smart appliances and cellphones. Even equipped with the most powerful hardware and software for data processing, one may still get lost in this massive collection of noisy data and miss "seeing the forest for the trees". This project addresses a fundamental issue in the data sciences: what are we looking for in a seemingly structure-less complex data set? Based on proven mathematical theories about symmetry and inspired by human vision, the investigator will construct a roadmap for discovering all possible potential patterns in these datasets and provide computationally effective tools to discover such patterns even in their distorted and disguised forms. Such a relentless pattern-seeking algorithm will illustrate the power of a "treasure hunt" type search, promote automatic pattern discovery, and fill a gap in current practice of data analysis, thus advancing data science. The outcome from this project will be applicable to data sets from diverse fields, from biomedical domains such as drug discovery, gene mapping and human movement monitoring, to computer vision applications like driverless car navigation, urban scene understanding, and anomalous activity detection for surveillance. This research formulates a symmetry group theory-based regularity space and constructs a computational platform for pattern-seeking algorithms that are principle-driven and human perception-inspired. The transitions among zero states of the proposed regularity-space, guided by group theory and learned from human perception, will be governed by a seamless marriage with Bayesian probability theory. The two key ingredients of a pattern, minimum cells and inter-cell topology, will be explored extensively on large scale, multimodality, high dimensional real-world sensory data. The aims are to construct and validate computational tools facilitating effective unsupervised recurring pattern discovery, followed by recovering geometric transformations, and finally by quantitatively linking the full regularity-perception spectrum from regular, near-regular to irregular. The finiteness, uniqueness and completeness of this group theory-based regularity space will provide a sound computational framework to guide pattern seeking in general data science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.