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.

现实世界的数据越来越多地具有许多维度或特征，但不是均匀地填充所有维度，而是分布在内在维度低得多的表面上或其附近。例如，fMRI数据以及自然图像和视频数据集。这项研究将把层次结构融入数据的“稀疏字典表示”中，从而突破目前在分析如此庞大的数据集方面所能达到的极限。结果将包括对机器学习方法的基本智力贡献和有助于调查复杂现实世界数据的计算进步。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底层结构的特征。在许多应用中，包括人脸识别和对象识别，稀疏词典表示已被证明对此目的有效。然而，由于求解大规模稀疏表示问题的代价非常高，该方法通常仅限于中等规模的问题。这项研究将该方法重新表述为一个增量的、多阶段的、分层次的词典学习过程。该方法以增量方式从数据中提取信息，并使用该信息以有组织的分层方式改进数据表示。这使得能够以计算高效的方式构建大规模词典。因此，该方法将稀疏词典表示方法的能力扩展到更广泛的现实世界应用。它还具有结合现有最先进的稀疏编码算法作为基本解算器的灵活性，因此可以将现有稀疏编码算法的功能扩展到多阶段、分层词典学习。