BIGDATA: F: DKA: Learning a Union of Subspaces from Big and Corrupted Data

BIGDATA：F：DKA：从大数据和损坏数据中学习子空间并集

• 批准号: 1447822
• 负责人: Rene Vidal
• 金额: $ 60万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1447822&HistoricalAwards=false
• 关键词: BIGDATA; DKA; Learning; Union; Subspaces

This project develops theory and algorithms for automatically discovering multiple low-dimensional structures in high-dimensional data, and evaluates these algorithms in image clustering applications. The developed techniques enhance our ability to handle big data problems from multiple sources and modalities, and advance the knowledge on how to interpret massive amounts of complex high-dimensional data. The techniques developed in this project can significantly broaden the applicability of existing results in sparse representation theory to subspace clustering problems, which have found widespread applications in image processing (e.g., image denoising, compression, representation, and segmentation), computer vision (e.g., motion segmentation and face clustering) and dynamical systems (e.g., hybrid system identification). This research develops provably correct and scalable algorithms for learning a union of low-dimensional subspaces from big and corrupted data. The algorithms are based on the so-called self-expressiveness property of the data, which states that an uncorrupted data point can be well approximated by an affine combination of other uncorrupted data points. This research shows that by imposing a structured sparse and low-rank prior on the coefficients, one can discover multiple structures in the data. In the case of uncorrupted data, the research team studies conditions on the data under which a perfect clustering is possible. In the case of data corrupted by outliers, the research team studies conditions under which perfect clustering and outlier rejection are possible. In the case of data with missing entries, the research team studies conditions under which perfect clustering and data completion are possible. The project also develops efficient and scalable algorithms that benefit from distributed and high-performance computing for solving the various subspace clustering problems. These algorithms enable solving large-scale problems in computer vision, including image clustering.

该项目开发了自动在高维数据中自动发现多个低维结构的理论和算法，并在图像群集应用中评估了这些算法。开发的技术增强了我们从多种来源和方式处理大数据问题的能力，并促进了如何解释大量复杂高维数据的知识。该项目中开发的技术可以显着扩大现有结果在稀疏表示理论中对子空间聚类问题的适用性，这些问题在图像处理中发现了广泛的应用（例如，图像降低，压缩，表示，表示和分段），计算机视觉，计算机视觉（例如，运动序列和面部群集聚类和动态系统）和动态系统（例如，类型的系统识别）。这项研究开发了可证明正确且可扩展的算法，用于从大数据和损坏的数据中学习低维子空间的结合。该算法基于数据的所谓自表达性能，该算法指出，通过其他未腐败的数据点的仿射组合可以很好地近似数据点。这项研究表明，通过在系数上施加结构化稀疏和低级别的先验，人们可以发现数据中的多个结构。在未腐败的数据的情况下，研究团队研究了可能进行完美聚类的数据。在异常值损坏的数据中，研究团队研究了可能的聚类和异常值拒绝的条件。对于缺少条目的数据，研究团队研究了完美的聚类和数据完成的条件。该项目还开发了有效且可扩展的算法，这些算法受益于分布式和高性能计算，以解决各种子空间聚类问题。这些算法可以解决计算机视觉中的大规模问题，包括图像群集。