University of Illinois Urbana-Champaign

Manifold Learning From Time Series

Lin, Ruei-Sung

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Manifold Learning From Time Series.pdf

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https://hdl.handle.net/2142/11177

Description

Title
Manifold Learning From Time Series
Author(s)
Lin, Ruei-Sung
Issue Date
2006-05
Keyword(s)
computer science
Date of Ingest
2009-04-20T20:20:13Z
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.
Type of Resource
text
Genre of Resource
Technical Report
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http://hdl.handle.net/2142/11177
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