Greedy Dictionary Learning Algorithms For Sparse Surrogate Modelling
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Greedy Dictionary Learning Algorithms for Sparse Surrogate Modelling
In the field of engineering design, numerical simulations are commonly used to forecast system performance before physical prototypes are built and tested. However the fidelity of predictive models has outpaced advances in computer hardware and numerical methods, making it impractical to directly apply numerical optimization algorithms to the design of complex engineering systems modelled with high fidelity. A promising approach for dealing with this computational challenge is the use of surrogate models, which serve as approximations of the high-fidelity computational models and can be evaluated very cheaply. This makes surrogates extremely valuable in design optimization and a wider class of problems: inverse parameter estimation, machine learning, uncertainty quantification, and visualization. This thesis is concerned with the development of greedy dictionary learning algorithms for efficiently constructing sparse surrogate models using a set of scattered observational data. The central idea is to define a dictionary of basis functions either a priori or a posteriori in light of the dataset and select a subset of the basis functions from the dictionary using a greedy search criterion. In this thesis, we first develop a novel algorithm for sparse learning from parameterized dictionaries in the context of greedy radial basis function learning (GRBF). Next, we develop a novel algorithm for general dictionary learning (GGDL). This algorithm is presented in the context of multiple kernel learning with heterogenous dictionaries. In addition, we present a novel strategy, based on cross-validation, for parallelizing greedy dictionary learning and a randomized sampling strategy to significantly reduce approximation costs associated with large dictionaries. We also employ our GGDL algorithm in the context of uncertainty quantification to construct sparse polynomial chaos expansions. Finally, we demonstrate how our algorithms may be adapted to approximate gradient-enhanced datasets. Numerical studies are presented for a variety of test functions, machine learning datasets, and engineering case studies over a wide range of dataset size and dimensionality. Compared to state-of-the-art approximation techniques such as classical radial basis function approximations, Gaussian process models, and support vector machines, our algorithms build surrogates which are significantly more sparse, of comparable or improved accuracy, and often offer reduced computational and memory costs.
Sparse Representation, Modeling and Learning in Visual Recognition
This unique text/reference presents a comprehensive review of the state of the art in sparse representations, modeling and learning. The book examines both the theoretical foundations and details of algorithm implementation, highlighting the practical application of compressed sensing research in visual recognition and computer vision. Topics and features: describes sparse recovery approaches, robust and efficient sparse representation, and large-scale visual recognition; covers feature representation and learning, sparsity induced similarity, and sparse representation and learning-based classifiers; discusses low-rank matrix approximation, graphical models in compressed sensing, collaborative representation-based classification, and high-dimensional nonlinear learning; includes appendices outlining additional computer programming resources, and explaining the essential mathematics required to understand the book.
Advances in Visual Computing
The two volume set LNCS 8887 and 8888 constitutes the refereed proceedings of the 10th International Symposium on Visual Computing, ISVC 2014, held in Las Vegas, NV, USA. The 74 revised full papers and 55 poster papers presented together with 39 special track papers were carefully reviewed and selected from more than 280 submissions. The papers are organized in topical sections: Part I (LNCS 8887) comprises computational bioimaging, computer graphics; motion, tracking, feature extraction and matching, segmentation, visualization, mapping, modeling and surface reconstruction, unmanned autonomous systems, medical imaging, tracking for human activity monitoring, intelligent transportation systems, visual perception and robotic systems. Part II (LNCS 8888) comprises topics such as computational bioimaging , recognition, computer vision, applications, face processing and recognition, virtual reality, and the poster sessions.