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.

显着的人类能力之一是能够从不断发展的信息流中提取基本模式，从而塑造日常决策。在线词典学习（ODL）是一种数学表述，可以实时模拟人类提取模式的能力。 ODL在各种领域中发现了富有成果的应用，例如文本分析，图像重建和降解，医学成像和生物信息学。但是，ODL的现有理论和算法在应对现代流数据方面面临重大挑战。该项目将促进现有ODL方法的理论理解和算法能力。更具体地说，该项目将解决使用多模式属性，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质结构的挑战。该项目还将涉及跨学科的合作，并为各级学生提供研究机会。该项目旨在在以下方面推进ODL的理论和算法：1）获得最差的融合率和广义ODL算法的收敛性和迭代复杂性，以在马尔可夫依赖性下的结构信号流到固定点； 2）设计有监督的ODL算法，用于从具有可证明的收敛保证和收敛速度的标记流数据中学习类歧视字典的词典； 3）使用理论和算法用张量值的信号来监督ODL，以开发监督和时间网络词典学习的方法，其中前者将学习网络分类网络数据的歧视性基础子图，用于网络分类和剥夺应用程序，后者将学习基础的基础术语及其时间 - 用于重新构建给定的临时或多个临时网络。一个关键要素是开发随机大型化最小化类型算法，这些算法可以使用块最小化和正则化技术根据数据类型来处理复杂的替代功能。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。 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.