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最能代表给定数据集主要特征的主成分向量，对数据分析和数据特征提取的变革性/破坏性思想进行基础性工作，即使存在错误/缺失/离群数据。基于这一想法，将开发一个算法框架，以支持几个有针对性的应用，如数据处理在社交网络，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，生物信息学。该项目工作的潜在影响是巨大的，并可能远远超出这些应用程序，以涵盖任何领域的科学和工程，传统的数据特征提取已在过去使用的technologically来说，调查的目的是重写在过去的世纪的巨大回报章L2-范数（特征向量和奇异向量分解）的数据分析。正在开发最佳L1规范数据分析，其本质上可以抵抗数据污染，并且与“干净”数据的L2规范分析一样好。L1-norm数据主成分分析已经看到了有限的量以前的研究，是不存在的教育/教科书。基于L1范数的主成分分析（PCA）和标准L2范数PCA之间的几个深刻差异，迄今为止，阻碍了基于L1的PCA的理论理解（从而设计有效的算法解决方案）的进展。 该项目旨在开发一种新的方法降维下的L1规范处理离群倾向/污染？大数据？（大量的高维数据）通过将基本的L1范数主成分优化问题解释为等价的二进制域最大化问题，并且在这样的开放频谱中潜在的新的分析和算法技术。项目目标包括：（i）关于最大L1范数投影数据特征的精确计算的基本算法研究;（ii）对L1范数测量数据降维的基本理解和执行;以及（iii）样本空间缩减。

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.