Large-Scale Machine Learning: Sparse Representations for Signal/Image Processing and System Modeling

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Rapid advances in computer based technologies such as energy grid networks, web services, bioinformatics, and sensor networks, create a great demand for new pattern recognition/machine learning algorithms able to cope with massive data sets, multiple hypothesis, and data of high dimensionality. This defines the field referred to as large-scale machine learning. In this proposal, I wish to extend my current research on nonparametric/semiparametric learning methods to large-scale machine learning problems. This challenge includes not only the development of new mathematical techniques, but also to verify them in the framework of signal/image processing and system modeling tasks. Testing of the proposed methods in concrete applications within the areas of power engineering, microscopic imaging and multiple change-point detection for biological and network signals is also planned. Our research proposal relies on the idea of blending the modern nonparametric/semiparametric learning methodology with the concept of sparse representations of a given process. The sparsity is roughly defined as a solution to the examined problem based on the representation using a small number of dominating terms. The key is to discover a sparse (low-dimensional) representation and its form in a given setting. Thus far, sparse learning algorithms have mostly focused on parametric (finite dimensional) linear models, where an observed data point is expressed as a linear combination of a small number of vectors of the representation matrix (dictionary). In this proposal we aim at developing a class of nonparametric and semiparametric learning algorithms that utilize the inherent sparsity of a given object. Hence, we wish to go beyond the thus far used linear and finite dimensional sparsity models and apply these findings to problems stemming from multidimensional systems, computational symmetry and multiple change-point detection problems. We believe that the proposed sparse object representation methodology can substantially enlarge a scope of machine learning applications and improve the existing algorithms within the context of proposed case studies.