Oates, TimWang, Zhiguang2019-10-112019-10-112016-01-0111511http://hdl.handle.net/11603/15491Most real-world data has a temporal component, whether it is measurements of natural (weather, sound) or man-made (stock market, robotics and even speech and language) phenomena. Analysis of temporal data has been the subject of active research for decades and is still considered to be a challenge in machine learning and data mining, due to the intrinsically structured temporal correlation. In this thesis, we propose three different novel approaches to represent and model time-series. Time-Warping SAX and Pooling SAX are two extensions of the vanilla SAX approach that is used as a symbolic representation of time series. Time-Warping SAX extracts linear temporal dependencies by building a time-delay embedding vector to construct more informative SAX words. Pooling SAX applies a non-parametric weighting scheme to extract significant variables. These are data adaptive models that achieve state-of-the-art accuracy on time-series classification problems. We also propose the Gramian Angular Field (GAF) and Markov Transition Field (MTF) as two novel approaches to encode a time-series as an image. These representations not only demonstrate potential for visual inspection by humans, but when they are combined with deep learning approaches (Convolutional Networks and Denoised Auto-encoders). They achieve state-of-the-art performance compared to other modern algorithms on classification and regression/imputation problems for different type of temporal data and trajectories. GAF and MTF are non-data adaptive approaches that allow us to learn models and extract the abstract representations supported by model-based approaches. Finally, we develop a set of exponential-form based error estimator (NRAE/NAAE) with their learning approaches (Adaptive Training) to attach the non-convex optimization problems in training deep neural networks. Both in theory and practice, they are able to achieve optimality on accuracy and robustness against outliers/noise. They provide another perspectives to debunk the non-convexity of deep learning in high dimensional learning and recurrent architectures and benefit the modeling of high-dimensional temporal data.This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.eduDeep LearningNon-convex OptimizationSymbolic Aggregate ApproximationTime SeriesText