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Title:Manifold Learning From Time Series
Author(s):Lin, Ruei-Sung
Subject(s):computer science
Abstract:This thesis addresses the problem of learning manifold from time series. We use the mixtures of probabilistic principal component analyzers (MPPCA) to model the nonliner manifold. In addition, we extend the MPPCA model by aligning the PCA coe.cients from each mixture component in a global coordinated system. We call these aligned coe.cients the global coordinates. Global coordinates enable us to expand our manifold model along time axis to become a dynamic Bayesian network (DBN) on which temporal constraints among the global coordinates can be imposed. The exact inference on this DBN is intractable, but we propose an approximate inference and learning algorithm that e.ciently learns this DBN for particular data sets. Our analysis proves that our inference algorithm is as e.cient as the Kalman .lter. We apply our manifold learning algorithm to synthetic data and real world applications. The experiment on synthetic data clearly demonstrates that by taking temporal dependency among global coordinates into consideration our proposed algorithm achieves superior learning results than other manifold learning algorithms that treat samples in the training data set as independent, identical, distributed (i.i.d). In addition, we demonstrate that our algorithm is capable of solving complicated real world problems including appearance-based object tracking and robot map learning.
Issue Date:2006-05
Genre:Technical Report
Type:Text
URI:http://hdl.handle.net/2142/11177
Other Identifier(s):UIUCDCS-R-2006-2624
Rights Information:You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS:2009-04-20


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