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Collaborative Research: Fast, Low-Memory Embeddings for Tensor Data with Applications

协作研究：使用应用程序快速、低内存嵌入张量数据

基本信息

批准号：
2108479
负责人：
Deanna Needell
金额：
$ 15.64万
依托单位：
University of California-Los Angeles
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2108479&HistoricalAwards=false
关键词：
Collaborative Research Fast Low Memory

项目摘要

Many data processing tasks, such as image, video, and music compression and classification, involve finding compact representations of data files. Compactly representing such files is generally a good idea for many practical reasons. Compressed music and image files (MP3, JPG, etc.) are much faster and cheaper to communicate and store than the originals. In classification applications, a small number of informative file features are often selected from larger categories of data in order to help boost accuracy and efficiency (this is akin to only focusing on the voice in a song when the aim is to identify the singer). In more extreme situations, data signals may be so large or change so rapidly that they cannot be stored or analyzed at all without first being quickly compressed. Many interesting problems of this type exist in research areas related to algorithms for internet data analysis aimed at, for example, quickly detecting particular types of large-scale cyber-attacks. As part of this project, the investigators will develop and implement new faster compression and data analysis techniques for complex data, which can then be used to facilitate faster data processing in a myriad of large-scale data processing applications. The project will also have educational benefits aimed at increasing the representation of students from under-represented and under-served groups in STEM research fields. This will be accomplished by the investigators hosting and mentoring research projects for undergraduate students from diverse backgrounds who will apply the compression and data analysis techniques developed as part of this research to specific application data, for example, to analyze and better understand Lyme disease data.This research includes a rich new class of practical Johnson-Lindenstrauss (JL) maps for vector data that cannot only be applied to vectors faster than Fast Fourier Transform time serially but are also trivially parallelizable. The embeddings will be randomized, and their analysis will be supported by the development of novel concentration inequalities based on generic chaining and supremum of chaos approaches for structured tensor data embeddings. These techniques will then allow, for example, the construction of new fast and memory efficient embeddings with the Tensor Restricted Isometry Property of value in the analysis of large tensor data. In addition, the research will develop new nonlinear bi-Lipchitz extensions of linear modewise JL-maps for tensor data capable of preserving distances between all low rank tensors in a given database and all other lower rank tensors, even outside of the database. These new nonlinear embeddings techniques will allow improved theoretical guarantees for space-constrained learning and classification with polynomial kernels. Finally, these embeddings will also be applied to address data-intensive problems in quantum many-body theory and nuclear physics.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.

许多数据处理任务，如图像、视频和音乐的压缩和分类，都涉及到寻找数据文件的紧凑表示。出于许多实际原因，紧凑地表示此类文件通常是一个好主意。压缩的音乐和图像文件（MP3、JPG等）比原始文件传输和存储起来更快、更便宜。在分类应用程序中，为了帮助提高准确性和效率，通常会从更大的数据类别中选择少量信息文件特征（这类似于在目标是识别歌手时只关注歌曲中的声音）。在更极端的情况下，数据信号可能非常大或变化非常快，如果不首先进行快速压缩，就根本无法存储或分析。这种类型的许多有趣问题存在于与互联网数据分析算法相关的研究领域，例如，快速检测特定类型的大规模网络攻击。作为该项目的一部分，研究人员将为复杂数据开发和实施新的更快的压缩和数据分析技术，这些技术可用于在无数大规模数据处理应用中促进更快的数据处理。该项目还将具有教育效益，旨在增加来自STEM研究领域代表性不足和服务不足群体的学生的代表性。这将由研究人员主持和指导来自不同背景的本科生的研究项目来完成，这些本科生将把作为本研究的一部分开发的压缩和数据分析技术应用于具体的应用数据，例如，分析和更好地理解莱姆病数据。这项研究包含了丰富的新型实用的Johnson-Lindenstrauss （JL）映射，用于向量数据，不仅可以比快速傅里叶变换时间序列更快地应用于向量，而且还可以并行化。嵌入将是随机的，它们的分析将得到基于通用链和结构化张量数据嵌入的混沌最优方法的新型集中不等式的发展的支持。这些技术将允许，例如，在分析大张量数据时，使用张量受限等长属性构建新的快速和内存高效的嵌入。此外，该研究将为张量数据开发新的线性模式jl映射的非线性bi-Lipchitz扩展，能够保持给定数据库中所有低秩张量与所有其他低秩张量之间的距离，甚至在数据库之外。这些新的非线性嵌入技术将为空间约束学习和多项式核分类提供改进的理论保证。最后，这些嵌入也将应用于解决量子多体理论和核物理中的数据密集型问题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。