Robust Identification of a Class of Structured Systems with High Dimensional Outputs and Applications

具有高维输出和应用的一类结构化系统的鲁棒识别

• 批准号: 0901433
• 负责人: Mario Sznaier
• 金额: $ 41.53万
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901433&HistoricalAwards=false
• 关键词: Robust; Identification; Class; Structured; Systems

The objective of this research program is to develop a comprehensive framework for robust identification of a class of multidimensional systems arising in diverse domains ranging from image processing to nano-systems. Its transformative impact and novelty reside in recasting problems that require extracting information sparsely encoded in high dimensional data streams as multidimensional systems identification problems, establishing a new connection between dynamical systems theory, image processing and machine learning.Intellectual Merit: Recent exponential growth in sensing capabilities poses a serious challenge to identification theory. Simply put, existing techniques are ill-equipped to deal with the overwhelming volume of data. The present proposal seeks to develop a comprehensive robust modeling (identification, reduction, validation) framework specifically tailored to address this challenge. Advantages over existing techniques include the abilities to directly accommodate structural constraints (such as periodicity), exploit correlations in the data to accomplish substantial dimensionality reduction and exploit recent results in optimization to furnish tractable solutions to problems that challenge current techniques, due to poor scaling properties. Examples (known to be generically NP-hard) are (i) robust identification of piecewise affine hybrid systems, (ii) robust identification of Hammerstein/Wiener systems and (iii) semi-blind (in)validation.Broader Impact: Enhanced data collection and analysis capabilities can profoundly impact society, with benefits ranging from safer, self aware environments, to enhanced image-based therapies. A major impediment to realizing this vision stems from the curse of dimensionality. The proposed research exploits a hidden commonality --underlying dynamical models having a far simpler representation than the dimension of the data-- to recast key problems, e.g. data segmentation, reconstruction and classification, into a tractable form, significantly advancing the state of the art in several domains. Examples include (but are not limited to) biomedical image processing, building safety, nano-systems and aging civil-infrastructure monitoring. Translation of these results to society and the economy will proceed by actively engaging our partners in bio-medical image processing and building security. The proposed research also has the potential for significant cross--fertilization with other branches of engineering and applied mathematics. An example is the connection between nonlinear dimensionality reduction methods and manifold discovery (both hallmarks of machine learning) and nonlinear identification.

该研究计划的目标是开发一个全面的框架，用于对从图像处理到纳米系统等不同领域中产生的一类多维系统进行鲁棒识别。它的变革性的影响和新奇在于重铸的问题，需要提取信息稀疏编码在高维数据流的多维系统识别问题，建立一个新的连接之间的动力系统理论，图像处理和机器learning.Intellectual优点：最近指数增长的传感能力提出了一个严重的挑战，识别理论。 简单地说，现有的技术不足以处理大量的数据。本提案旨在制定一个全面的强大的建模（识别，减少，验证）框架，专门针对这一挑战。与现有技术相比的优点包括直接适应结构约束（例如周期性）的能力，利用数据中的相关性来实现大幅降维，以及利用优化中的最新结果来为挑战当前技术的问题提供易于处理的解决方案，这是由于缩放特性差。例子（已知一般是NP-困难的）是（i）分段仿射混合系统的鲁棒识别，（ii）Hammerstein/Wiener系统的鲁棒识别和（iii）半盲（在）validation.Broader影响：增强的数据收集和分析能力可以深刻地影响社会，从更安全、自我意识的环境到增强的基于图像的治疗。实现这一愿景的一个主要障碍来自维度灾难。 拟议的研究利用了一个隐藏的共性-潜在的动态模型具有比数据维度简单得多的表示-将关键问题（例如数据分割，重建和分类）重新转换为易于处理的形式，显着推进了几个领域的最新技术。例子包括（但不限于）生物医学图像处理，建筑安全，纳米系统和老化的民用基础设施监测。将这些成果转化为社会和经济将通过积极参与我们的合作伙伴在生物医学图像处理和建筑安全。拟议中的研究也有可能显着的交叉-施肥与工程和应用数学的其他分支。 一个例子是非线性降维方法和流形发现（机器学习的两个标志）和非线性识别之间的联系。