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Online Dictionary Learning for Dependent and Multimodal Data Samples: Convergence, Complexity, and Applications

相关和多模态数据样本的在线字典学习：收敛性、复杂性和应用

基本信息

批准号：
2206296
负责人：
Hanbaek Lyu
金额：
$ 30万
依托单位：
University of Wisconsin-Madison
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2206296&HistoricalAwards=false
关键词：
Online Dictionary Learning Dependent Multimodal

项目摘要

One of the remarkable human capabilities is the ability to extract essential patterns from a constantly evolving stream of information that shapes everyday decision-making. Online dictionary learning (ODL) is a mathematical formulation that emulates the human ability to extract patterns in real time. ODL has found fruitful applications in various domains such as text analysis, image reconstruction and denoising, medical imaging, and bioinformatics. However, existing theories and algorithms for ODL are facing significant challenges in coping with modern streaming data. This project will advance both the theoretical understanding and algorithmic capacities of existing ODL methods. More specifically, the project will address challenges in handling streaming data with multi-modal attributes, partial labels for further classification or inference tasks, and heterogeneous structure in the form of networks. This project will also involve interdisciplinary collaboration and provide research opportunities for students at all levels. The project aims to advance the theory and algorithms of ODL in the following aspects: 1) Obtain the worst-case rate of convergence and iteration complexity of generalized ODL algorithms to stationary points for a stream of structured signals under Markovian dependence; 2) Devise supervised ODL algorithms for learning class-discriminating dictionaries from labeled streaming data with provable convergence guarantees and rate of convergence; 3) Use the theory and algorithm for supervised ODL with tensor-valued signals to develop methods of supervised and temporal network dictionary learning, where the former will learn discriminative basis subgraphs from network data for network classification and denoising applications and the latter will learn basis subgraphs and their time-evolution for reconstructing given temporal or multilayer networks. A key element is the development of stochastic majorization-minimization type algorithms that can handle complex surrogate functions depending on data type using block-minimization and regularization techniques. This project will also provide students with research experiences in optimization, machine learning, and network science. Specific topics for undergraduate research experience will include generating a repository of optimal network dictionaries for various real-world networks, network-level regression and inference experiments with biological networks, and temporal brain network analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

人类最了不起的能力之一就是能够从不断演变的信息流中提取基本模式，这些信息流影响着日常决策。在线词典学习（ODL）是一种数学公式，它模拟了人类在真实的时间内提取模式的能力。ODL在文本分析、图像重建和去噪、医学成像和生物信息学等领域都有着丰富的应用。然而，现有的ODL理论和算法在处理现代流数据时面临着重大挑战。该项目将推进现有ODL方法的理论理解和算法能力。更具体地说，该项目将解决处理具有多模态属性的流数据，用于进一步分类或推理任务的部分标签以及网络形式的异构结构的挑战。该项目还将涉及跨学科合作，并为各级学生提供研究机会。本项目的主要目标是在以下几个方面推进ODL的理论和算法：1）获得广义ODL算法在马尔可夫依赖下到达稳定点的最坏情况下的收敛速度和迭代复杂度; 2）设计有监督的ODL算法，用于从标记的流数据中学习具有可证明的收敛保证和收敛速度的类别区分字典; 3）使用张量值信号的监督ODL的理论和算法来开发监督和时态网络字典学习的方法，其中前者将从网络数据中学习用于网络分类和去噪应用的判别基子图，后者将学习基子图及其时间演化以重建给定的时态或多层网络。一个关键因素是随机优化最小化类型的算法，可以处理复杂的代理函数依赖于数据类型，使用块最小化和正则化技术的发展。该项目还将为学生提供优化，机器学习和网络科学方面的研究经验。本科生研究经验的具体主题将包括为各种真实世界的网络生成最佳网络字典库，生物网络的网络级回归和推理实验，以及时间脑网络分析。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。