Sparse Signal Processing and Modeling of High Dimensional Spatio-Temporal Data

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Big high-dimensional spatio-temporal datasets, where the number of measured variables is larger than the sample size, are widely seen in real-world applications (e.g., functional magnetic resonance imaging (fMRI) signals and microarray gene expression time series data). Statistical estimation and inference in high-dimensional situations is fundamentally different from that in the classical setting (with large sample size and smaller number of variables) and many problems are largely open, requiring new statistical signal processing theory and methods involved in regression, clustering, prediction, classification and other statistical problems of high-dimensional data. Generally speaking, estimation and inference in high-dimensional data is not possible without assuming special low-rank (e.g., sparse) structures in the data. With this vision, the current research program will focus on sparse signal processing and modeling of high-dimensional data by both establishing theoretical foundations and developing application-specific novel algorithms. ******More specifically, the proposed research program will pursue the following main technical objectives: 1.) Investigating sparsity-aware estimation and inference problems for high-dimensional time series data. We aim to establish the theory and develop novel algorithms for 2nd-order inference of high-dimensional processes that can be non-iid (independent and identically distributed), non-stationary and non-Gaussian; 2.) Developing novel online sparse Principal Component Analysis (PCA) and online sparse Independent Component Analysis (ICA) algorithms for dimensionality reduction, since PCA and ICA are probably the most popular dimension reduction approaches; and 3.) Investigating motivating real-world health applications, including real-time fMRI based neurofeedback for Parkinson's Disease patients, video-based cardiac physiological monitoring, and Kinect/iPad based serious games for supporting elderly people's cognitive rehabilitation. ******The significance of this research lies in its focus on both the theory and practice of sparse modeling of high dimensional spatio-temporal data. The outcome of this research program will make significant contributions to both the theory and applications of big data analytics. Indeed, the notion “data analytics” is a more attractive capital-lite business than that related to hardware. As one key innovation accelerator in the so-called 3rd Platform era, big data analytics is reshaping many industries and revolutionizing many research areas. The proposed research will help take this vision one tiny step further. The research program will provide an opportunity for the graduate students to be trained in related cutting-edge technologies.