EAGER: Nonlinear and Data-Adaptive Compressive Sampling for Big Data Processing

随着无处不在的传感器不断地从通信、社会和生物网络中收集和记录大量高维数据，以及现代计算机不断增长的存储和处理能力，为挖掘如此大量的信息提供了新的、强大的方法，对梳理这些“大数据”的新型分析工具的需求变得势在必行。该项目的目标是为非线性、数据自适应（去）压缩算法开发新的框架，以学习大规模、不完整或损坏的数据集中的潜在结构，以便压缩和存储基本信息，实时运行分析，推断数据集的缺失部分，并从压缩的情况中重建原始数据。智力上的优点在于探索了丰富但大部分未探索的领域，如流形学习、非线性降维和稀疏感知技术，用于压缩和恢复丢失和受损的测量。利用机器学习和信号处理的最新进展，微分几何、稀疏性和字典学习被认为是关键的推动因素。还将努力开发在线和分布式（非）线性降维算法，以允许使用并行处理器对顺序测量进行流分析。更广泛的影响是有助于开发新的计算方法和工具，用于数据推断，清理，预测和协同过滤，直接影响统计信号处理和机器学习应用于大规模数据分析，包括通信，社会和生物网络。

As pervasive sensors continuously collect and record massive amounts ofhigh-dimensional data from communication, social, and biological networks,and growing storage as well as processing capacities of modern computershave provided new and powerful ways to dig into such huge quantities ofinformation, the need for novel analytic tools to comb through these "bigdata" becomes imperative. The objective of this project is to develop anovel framework for nonlinear, data-adaptive (de)compression algorithms tolearn the latent structure within large-scale, incomplete or corrupteddatasets for compressing and storing only the essential information, forrunning analytics in real time, inferring missing pieces of a dataset, andfor reconstructing the original data from their compressed renditions. The intellectual merit lies in the exploration of the fertile but largelyunexplored areas of manifold learning, nonlinear dimensionality reduction,and sparsity-aware techniques for compression and recovery of missing andcompromised measurements. Capitalizing on recent advances in machinelearning and signal processing, differential geometry, sparsity, anddictionary learning are envisioned as key enablers. Effort will be put alsointo developing online and distributed (non)linear dimensionality reductionalgorithms to allow for streaming analytics of sequential measurementsusing parallel processors. The broader impact is to contribute to the development of novel computational methods and tools useful for data inference, cleansing, forecasting, and collaborative filtering, with direct impact to statistical signal processing and machine learning applicationsto large-scale data analysis, including communication, social, andbiological networks.