CIF: Small: Fast Stagewise Learning of Sparse Hierarchical Data Representations

CIF：小型：稀疏分层数据表示的快速分阶段学习

• 批准号: 1116208
• 负责人: Peter Ramadge
• 金额: $ 37.2万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1116208&HistoricalAwards=false
• 关键词: CIF; Small; Fast; Stagewise; Learning

Increasingly, real-world data has many dimensions or features but rather than filling out all dimensions equally, the data distributed on or near a surface of much lower intrinsic dimension. Examples include fMRI data and natural image and video data sets. This research will push the boundary of what is currently possible in the analysis of such large data sets by incorporating hierarchical structure into what is known as a "sparse dictionary representation" of the data. The results will include both basic intellectual contributions to machine learning methods and computational advancements that will aid the investigation of complex real world data. A fundamental problem in learning the structure of complex data is how to effectively extract a set of features that reflects the underlying structure of the data. In many applications, including face recognition and object recognition, sparse dictionary representations have proved effective for this purpose. However, since solving large-scale sparse representation problems is very expensive, the method is generally limited to problems of moderate scale. This research reformulates the method into an incremental, multi-stage, hierarchical dictionary learning process. This approach incrementally extracts information from the data and uses this to refine the data representation in an organized hierarchical fashion. This enables the building of large-scale dictionaries in a computationally efficient way. The method hence extends the power of sparse dictionary representation methods to a wider variety of real world applications. It also has the flexibility to incorporate an existing state-of-the-art sparse coding algorithm as the basic solver and hence can extend the functionality of existing sparse coding algorithms to multi-stage, hierarchical dictionary learning.

现实世界中的数据越来越多地具有许多维度或功能，但并没有平等地填充所有维度，而是在较低的固有维度表面上分布的数据。示例包括fMRI数据以及自然图像和视频数据集。 这项研究将通过将层次结构纳入所谓的数据的“稀疏字典表示”，从而在分析此类大数据集中的当前可能发生的边界。 结果将包括对机器学习方法和计算进步的基本智力贡献，这些贡献将有助于研究复杂的现实世界数据。 学习复杂数据结构的一个基本问题是如何有效地提取一组反映数据基础结构的功能。在许多应用程序（包括面部识别和对象识别）中，稀疏的词典表示已被证明对此目的有效。但是，由于解决大规模稀疏表示问题非常昂贵，因此该方法通常仅限于中等范围的问题。这项研究将该方法重新定义为一种渐进，多阶段，层次词典学习过程。这种方法从数据中逐步提取信息，并以有组织的层次结构方式来完善数据表示。这样可以以计算上有效的方式构建大型词典。因此，该方法将稀疏词典表示方法的功能扩展到更广泛的现实世界应用。它还具有将现有的最先进的稀疏编码算法作为基本求解器的灵活性，因此可以将现有稀疏编码算法的功能扩展到多阶段的多阶段，层次结构词典学习。