III-COR: Collaborative Research: Mining Biomedical and Network Data Using Tensors

IIS 0705359，IIS 0705215 III-COR：协作研究：使用张量Christos Faloutsos(Christos@cs.cmu.edu)挖掘生物医学和网络数据CMU Vasileios Megalooikonomou(Vasilis@cis.temple.edu)Temple University。考虑到一大批功能磁共振(FMR)图像随着时间的推移，如何找到模式和相关性？同样，假设网络流量信息流源源不断，如何监控异常、入侵和潜在故障？这个建议背后的主要思想是用张量理论来处理这两个问题。尽管这两种设置看起来差异很大，但归根结底，它们都是在多维阵列中寻找模式，无论是稀疏的还是密集的。张量是矩阵的精确推广，大致对应于数据挖掘的“数据立方体”。矩阵分析和分解是数据挖掘标准工具箱的一部分，提供了降维、模式发现和“隐藏变量”发现的方法。将这些工具扩展到更高的维度是有价值的，张量提供了进行这种概括的工具。然而，这些工具还没有在海量数据挖掘中投入使用。这是这项建议的主要贡献。研究人员建议(A)设计适用于大型数据集的张量分解算法，特别关注稀疏数据集和永无止境的数据流，以及(B)将其应用于两个驱动应用：fMRI数据分析和网络数据分析。研究人员建议分析执行以下子任务的大量fMRI数据：对给定对象和/或任务或跨对象和/或任务聚类具有相似行为的体素，对大脑活动模式进行分类，并检测fMRI时间序列之间的滞后相关性和时空模式。调查人员还建议对数千兆字节的网络流量数据执行以下相互关联的任务：异常检测、模式发现和压缩。这些应用程序对医学、健康管理、计算机和国家安全都很重要。对功能磁共振数据的分析可以帮助理解大脑的功能，大脑的哪些部分与其他哪些部分合作，以及不同的受试者和与任务相关的活动是否存在差异。对于网络流量监控设置，快速检测异常非常重要，以发现恶意软件、端口扫描尝试和普通的非恶意故障。教育目标包括将研究成果纳入芝加哥大学(15-826)和坦普尔(9664-9665)的高级研究生课程，并在数据库、数据挖掘和生物信息学音频的领先会议上提出教程。有关更多信息，请参阅网页：http://knight.cis.temple.edu/~vasilis/research/tensors.html

IIS 0705359, IIS 0705215III-COR: Collaborative Research: Mining Biomedical and Network Data Using Tensors Christos Faloutsos (christos@cs.cmu.edu) CMU Vasileios Megalooikonomou (vasilis@cis.temple.edu) Temple Univ.Given a large collection of functional Magnetic Resonance (fMR) images over time,how can one find patterns and correlations? Similarly, given a never-ending stream of network traffic information, how can one monitor for anomalies, intrusions, and potential failures? The main idea behind this proposal is to treat both problems using the theory of tensors. Despite the seemingly wide differences in the two settings, they both boil down to finding patterns in multidimensional arrays, sparse or dense. Tensors are exactly generalizations of matrices, and correspond roughly to ``DataCubes'' of data mining. Matrix analysis and decompositions are part of the standard toolbox for data mining, providing methods for dimensionality reduction, pattern discovery and``hidden variable'' discovery. Extending these tools to higher dimensionalities is valuable and tensors provide the tools to do this generalization. However, these tools have not yet been put to use in large volume data mining. This is the main contribution of this proposal. The investigators propose (a) to design tensor decomposition algorithms that scale for large datasets,with special attention to sparse datasets, and to never-ending streams of data and (b) to apply them on two driving applications, fMRI data analysis and networkdata analysis. The investigators propose to analyze large volumes of fMRI data performingthe following sub-tasks: cluster voxels with similar behavior over time fora given subject and/or task or across subjects and/or tasks, classify patterns of brain activity, and detect lag correlationsand spatio-temporal patterns among fMRI time sequences. The investigators also propose to perform the following inter-related tasks on multiple GigaBytes of network flow data: anomaly detection, pattern discovery, and compression.Both of these applications are important for medicine, health management,and for computer and national security. Analysis of fMRI data can help understandinghow the brain functions, which parts of the brain collaborate with what other parts, and whether there are variations across subjects and across task-related activities. For the network traffic monitoring setting, fast detection of anomalies is important,to spot malware, port-scanning attempts, and just plain non-malicious failures.The educational goals include incorporating the research findings in advanced graduate courses at CMU (15-826) and at Temple (9664, 9665)and proposing tutorials in leading conferences in databases, data mining and bio-informatics audiences.For further information see the web page: http://knight.cis.temple.edu/~vasilis/research/tensors.html