EAGER-DynamicData: A new paradigm for data analytics: L1-norm based Learning and Processing

该项目旨在通过新定义和计算的主成分向量来开展数据分析和数据特征提取的变革/颠覆性思想的基础工作，这些主成分向量最好地代表给定数据集的主要特征，即使存在错误/缺失/异常数据。基于这一想法，将开发一个算法框架来支持几个目标应用，如社交网络中的数据处理、图像处理和视频库、无线传感器网络数据融合、经济学、基因组学和蛋白质组学以及生物信息学。该项目工作的潜在影响是巨大的，可能会远远超出这些应用范围，覆盖过去使用传统数据特征提取的任何科学和工程领域。从技术上讲，这项研究的目的是重写过去一个世纪以来关于l2 -范数（特征向量和奇异向量分解）数据分析的巨大成果。最优的l1规范数据分析正在开发中，它固有地抵抗数据污染，并且与l2规范分析在“干净”数据上一样好。l1范数数据主成分分析在之前的研究中数量有限，到目前为止在教育/教科书中还不存在。迄今为止，基于l1范数的主成分分析（PCA）与标准l2范数的主成分分析之间的几个深刻差异阻碍了基于l1的主成分分析的理论理解（以及有效算法解决方案的设计）的进展。该项目寻求在L1规范下开发一种新颖的降维方法，以处理异常值易发/受污染？大数据?（大量高维数据），通过将基本的l1范数主成分优化问题解释为等效的二元场最大化问题，并在这样的情况下打开了一系列潜在的新分析和算法技术。项目目标包括：(i)关于精确计算最大l1范数投影数据特征的基础算法研究；（ii）基本理解和执行l1规范测量的数据降维；(3)样本空间约简。

This project aims to carry out fundamental work on the transformative/disruptive idea of data analytics and data-feature extraction by newly defined and calculated principal-component vectors that best represent the main features of a given data set, even in the presence of faulty/missing/outlier data. Based on this idea, an algorithmic framework will be developed to support several targeted applications, such as data processing in social networks, image processing and video libraries, wireless-sensor-network data fusion, economics, genomics and proteomics, and bioinformatics. The potential impact of the project work is immense and may extend well beyond these applications to cover any field of science and engineering where conventional data feature extraction has been used in the past.Technically speaking, the investigation aims at rewriting the enormously rewarding over the past century chapter on L2-norm (eigen-vector and singular-vector decomposition) data analysis. Optimal L1-norm data analytics are being developed that are inherently resistant to data contamination and as good as L2-norm analytics on "clean" data. L1-norm data principal component analysis has seen a limited amount of previous research and is non-existent so far in education/textbooks. Several profound differences between L1-norm based principle component analysis (PCA) and standard L2-norm PCA have, to date, blocked progress in the theoretical understanding (and thus in the design of efficient algorithmic solutions) of L1-based PCA. The project seeks the development of a novel approach toward dimensionality reduction under the L1 norm to deal with processing of outlier-prone/contaminated ?big data? (large amount of high-dimensional data) by interpreting the fundamental L1-norm principal-components optimization problem as an equivalent binary-field maximization problem, and in such opening a spectrum of potentially new analytical and algorithmic techniques. The project goals include: (i) Fundamental algorithmic research on the exact calculation of maximum-L1-norm-projection data features; (ii) fundamental understanding and execution of L1-norm-measured data dimensionality reduction; and (iii) sample-space reduction.