Simultaneous Learning of Non-Linear Manifold and Dynamical Models for High-Dimensional Time Series

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dc.contributor.author Li, Rui en_US
dc.date.accessioned 2011-10-20T04:58:51Z
dc.date.available 2011-10-20T04:58:51Z
dc.date.issued 2009-08-10 en_US
dc.identifier.uri http://hdl.handle.net/2144/1751
dc.description.abstract The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. The model structure setup and parameter learning are done using a variational Bayesian approach, which enables automatic Bayesian model structure selection, hence solving the problem of over-fitting. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance. en_US
dc.description.sponsorship National Science Foundation (IIS-0713168, CNS-0202067, IIS-0308213, IS-0208876) en_US
dc.language.iso en_US en_US
dc.publisher Boston University Computer Science Department en_US
dc.relation.ispartofseries BUCS Technical Reports;BUCS-TR-2009-027 en_US
dc.title Simultaneous Learning of Non-Linear Manifold and Dynamical Models for High-Dimensional Time Series en_US
dc.type Technical Report en_US
etd.degree.name Doctor of Philosophy
etd.degree.level doctoral
etd.degree.discipline Computer Science
etd.degree.grantor Boston University

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