CAREER: Exploiting low-dimensional structure in data for more effective, efficient and interactive machine intelligence

传感器数据的快速增长正在给技术、国防和科学发现的许多领域带来革命性的变化。幸运的是，尽管数据是高维的，但数据的各个方面经常可以被描述为具有低维几何结构。这项研究项目通过利用这种几何结构来显著提高机器智能，以实现更有效、更高效和更交互的数据分析系统。作为对这些技术目标的补充，该项目还旨在通过开发新的课程和宣传材料，说明如何在信息系统中使用数学，从而吸引、招募和教育各类学生从事STEM职业。这个项目的潜在好处在数据发挥基础作用的领域是广泛的。提高机器智能需要了解如何最好地利用给定类型的数据中的底层低维结构，该项目以三个研究目标为指导。第一个目标通过利用相同现象的多个观测通常通过沿流形的运动相关这一事实来提高机器效率，特别关注不变对象识别的规范计算机视觉问题。第二个目标旨在通过开发流形模型数据的降维技术来提高计算效率，该技术保留了关于非线性特征空间映射的信息。第三个目标寻求利用互动性，在从人类专家那里学习低维信息(主动学习范式的延伸)的同时，完全关闭人与机器之间的环路。该项目还追求两个教育目标，包括开发大学前推广课程模块和将神经系统内容纳入欧洲经委会课程，以说明量化方法与智能系统之间的联系。

The rapid increase in sensor data is revolutionizing many areas of technology, defense, and scientific discovery. Fortunately, despite data being high-dimensional, various aspects of the data can frequently be characterized as having low-dimensional geometric structure. This research project dramatically improves machine intelligence by exploiting this geometric structure for more effective, efficient and interactive data analysis systems. Complementary to these technical objectives, this project also aims to engage, recruit, and educate a diverse collection of students to STEM careers by developing novel curricular and outreach materials that illustrate how mathematics can be used in information systems. The potential benefits of this project are wide ranging in areas where data plays a fundamental role.Improving machine intelligence requires understanding how to best exploit the underlying low-dimensional structure in data for a given type of task, and this project is guided by three research objectives toward this goal. The first objective enhances machine effectiveness by exploiting the fact that multiple observations of the same phenomenon are often related by movement along a manifold, with a particular focus on the canonical computer vision problem of invariant object recognition. The second objective seeks to improve computational efficiency by developing dimensionality reduction techniques for manifold-modeled data that preserves information about nonlinear feature-space mappings. The third objective seeks to leverage interactivity to fully "close the loop" between between humans and machines while learning low-dimensional information from a human expert (an extension of the active learning paradigm). The project also pursues two educational objectives, including developing curriculum modules for pre-college outreach and integrating neural systems content into the ECE curriculum to illustrate the connections between quantitative methods and intelligent systems.