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Doctor of Philosophy with a Major in Computer Science

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    Nonnegative matrix and tensor factorizations, least squares problems, and applications
    (Georgia Institute of Technology, 2011-11-14) Kim, Jingu
    Nonnegative matrix factorization (NMF) is a useful dimension reduction method that has been investigated and applied in various areas. NMF is considered for high-dimensional data in which each element has a nonnegative value, and it provides a low-rank approximation formed by factors whose elements are also nonnegative. The nonnegativity constraints imposed on the low-rank factors not only enable natural interpretation but also reveal the hidden structure of data. Extending the benefits of NMF to multidimensional arrays, nonnegative tensor factorization (NTF) has been shown to be successful in analyzing complicated data sets. Despite the success, NMF and NTF have been actively developed only in the recent decade, and algorithmic strategies for computing NMF and NTF have not been fully studied. In this thesis, computational challenges regarding NMF, NTF, and related least squares problems are addressed. First, efficient algorithms of NMF and NTF are investigated based on a connection from the NMF and the NTF problems to the nonnegativity-constrained least squares (NLS) problems. A key strategy is to observe typical structure of the NLS problems arising in the NMF and the NTF computation and design a fast algorithm utilizing the structure. We propose an accelerated block principal pivoting method to solve the NLS problems, thereby significantly speeding up the NMF and NTF computation. Implementation results with synthetic and real-world data sets validate the efficiency of the proposed method. In addition, a theoretical result on the classical active-set method for rank-deficient NLS problems is presented. Although the block principal pivoting method appears generally more efficient than the active-set method for the NLS problems, it is not applicable for rank-deficient cases. We show that the active-set method with a proper starting vector can actually solve the rank-deficient NLS problems without ever running into rank-deficient least squares problems during iterations. Going beyond the NLS problems, it is presented that a block principal pivoting strategy can also be applied to the l1-regularized linear regression. The l1-regularized linear regression, also known as the Lasso, has been very popular due to its ability to promote sparse solutions. Solving this problem is difficult because the l1-regularization term is not differentiable. A block principal pivoting method and its variant, which overcome a limitation of previous active-set methods, are proposed for this problem with successful experimental results. Finally, a group-sparsity regularization method for NMF is presented. A recent challenge in data analysis for science and engineering is that data are often represented in a structured way. In particular, many data mining tasks have to deal with group-structured prior information, where features or data items are organized into groups. Motivated by an observation that features or data items that belong to a group are expected to share the same sparsity pattern in their latent factor representations, We propose mixed-norm regularization to promote group-level sparsity. Efficient convex optimization methods for dealing with the regularization terms are presented along with computational comparisons between them. Application examples of the proposed method in factor recovery, semi-supervised clustering, and multilingual text analysis are presented.
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    An integrative framework of time-varying affective robotic behavior
    (Georgia Institute of Technology, 2011-04-04) Moshkina, Lilia V.
    As robots become more and more prevalent in our everyday life, making sure that our interactions with them are natural and satisfactory is of paramount importance. Given the propensity of humans to treat machines as social actors, and the integral role affect plays in human life, providing robots with affective responses is a step towards making our interaction with them more intuitive. To the end of promoting more natural, satisfying and effective human-robot interaction and enhancing robotic behavior in general, an integrative framework of time-varying affective robotic behavior was designed and implemented on a humanoid robot. This psychologically inspired framework (TAME) encompasses 4 different yet interrelated affective phenomena: personality Traits, affective Attitudes, Moods and Emotions. Traits determine consistent patterns of behavior across situations and environments and are generally time-invariant; attitudes are long-lasting and reflect likes or dislikes towards particular objects, persons, or situations; moods are subtle and relatively short in duration, biasing behavior according to favorable or unfavorable conditions; and emotions provide a fast yet short-lived response to environmental contingencies. The software architecture incorporating the TAME framework was designed as a stand-alone process to promote platform-independence and applicability to other domains. In this dissertation, the effectiveness of affective robotic behavior was explored and evaluated in a number of human-robot interaction studies with over 100 participants. In one of these studies, the impact of Negative Mood and emotion of Fear was assessed in a mock-up search-and-rescue scenario, where the participants found the robot expressing affect more compelling, sincere, convincing and "conscious" than its non-affective counterpart. Another study showed that different robotic personalities are better suited for different tasks: an extraverted robot was found to be more welcoming and fun for a task as a museum robot guide, where an engaging and gregarious demeanor was expected; whereas an introverted robot was rated as more appropriate for a problem solving task requiring concentration. To conclude, multi-faceted robotic affect can have far-reaching practical benefits for human-robot interaction, from making people feel more welcome where gregariousness is expected to making unobtrusive partners for problem solving tasks to saving people's lives in dangerous situations.