CAREER: Updating Problems in Information Retrieval and a Mathematical Dissection Lab

查尔斯顿大学艾米·朗维尔信息检索更新问题和数学剖析实验室这项建议是关于信息检索的，这是一个组织信息以检索与特定信息需求有关的文件的领域。信息检索分为两类：从Web集合检索和从较小的、非链接的文档集合检索，称为传统集合。这两种类型的检索，无论是网络检索还是传统检索，都至少有一个共同的问题：更新问题。每当文档集合发生更改时，都必须更新几个项，包括性能测量、存储文件和内存指针。文档修改、添加或删除文档时不可避免地会发生这种情况。在许多类型的更新问题中，此建议涉及数学更新问题。本文将研究一个对任何应用都有影响的网络检索的数学更新问题，如人口建模、网页排序、图论度量和电子邮件分析，它使用一个大的、稀疏的、非负的矩阵的主导特征向量。对于传统的信息检索，该项目将研究所谓的非负矩阵分解(NMF)的更新问题，该问题对NMF已应用到的许多其他领域产生影响，包括图像处理、指纹查询处理、音乐处理、信号处理、电影动画、机器学习、数据挖掘和音频和视频数据的摘要提取。这项研究将通过与印第安纳州SAS研究所的合作得到加强。该项目的教育阶段提出了一个数学设备解剖实验室的设计和实施。拟议中的实验室在精神上类似于许多工程学校的机械解剖实验室，旨在解决学生对数学的一个共同问题：学生认为数学只是关于计算，而不是概念。为了纠正这一点，拟议中的实验室允许学生以动手、交互的方式剖析虚拟数学设备，这些设备演示基本概念的使用。该实验室要求学生小组自学，因此模仿了现实世界中所需的搜索技能。本实验与本项目的研究阶段有关，因为三个实验中的九个模块将来自上面的信息检索研究。每个模块描述一个虚拟的数学装置。例如最小二乘法，信息检索的向量空间模型，以及Googles的网页排序方法。所有模块必须能够在低维空间中描述，这样学生才能将想法形象化，然后他们将理解数学的力量，使其能够扩展到更高维空间。当学生将简单的模型扩展到更大的问题时，模块还包含科学计算组件。每个单元将张贴在一个网站上，使这些单元可供全世界传播和改编。此外，该实验室还将用于几个外展项目。该实验室的目标之一是通过揭开数学发明过程的神秘面纱来改变学生对数学的态度，向他们表明数学不仅仅是计算，它是一个具有广泛应用的创造性过程。

ABSTRACT0546622Amy LangvilleCollege of CharlestonUpdating Problems in Information Retrieval and a Mathematical Dissection LabThis proposal is about information retrieval, the field of organizing information in order to retrievedocuments relating to a specific information need. Information retrieval is divided into two categories: re-trieval from web collections and retrieval from smaller, nonlinked document collections, called traditionalcollections. Both types of retrieval, web and traditional, share at least one common problem: the updatingproblem. Any time a document collection changes, which inevitably happens often as documents are mod-ified, added, or deleted, several items must be updated, including performance measures, storage files, andmemory pointers. Of the many types of updating problems, this proposal deals with mathematical updatingproblems. A mathematical updating problem for web retrieval that has impact for any application, such aspopulation modeling, webpage ranking, graph theoretic measures, and email analysis, that uses the domi-nant eigenvector of a large, sparse, nonnegative matrix will be studied. For traditional information retrieval,the project will study an updating problem regarding the so-called nonnegative matrix factorization (NMF),which has impact on the many other fields to which the NMF has been applied including image processing,fingerprint query processing, music processing, signal processing, movie animations, machine learning, datamining, and summary extraction for audio and video data. This research will be enhanced by a partnershipwith SAS Institute, Inc.The Education Phase of this project proposes the design and implementation of a Mathematical DeviceDissection Lab. The proposed lab, which is similar in spirit to the mechanical dissection labs found in manyengineering schools, aims to solve a common problem with students perception of mathematics: studentsthink mathematics is merely about calculation, not concepts. To remedy this, the proposed lab allowsstudents to dissect in a hands-on, interactive manner virtual mathematical devices that demonstrate theuse of fundamental concepts. The lab requires self-study by groups of students, and as such, mimics theresearch skills needed in the real world. This lab relates to the Research Phase of this project as three ofthe labs nine modules will come from the above research in information retrieval. Each module describesa virtual mathematical device. Examples include least squares, the vector space model of informationretrieval, and Googles method of ranking webpages. All modules must be able to be described in lowdimensional space, so that students can visualize the ideas, after which point, they will understand thepower of mathematics to enable extensions to higher dimensional space. Modules also contain a scientificcomputation component as the students extend the simple models to much larger problems. Each modulewill be posted on a website, making the modules available for worldwide dissemination and adaptation. Inaddition, the lab will be used in several outreach projects. One of the labs goals is to change studentsattitudes towards mathematics by demystifying the process of mathematical invention, showing them thatmathematics is more than mere calculation, it is a creative process with broad applications.