| This thesis addresses the problem of learning manifold from time series. We use the mixtures of probabilistic principal component analyzers (MPPCA) to model the nonlinear manifold. In addition, we extend the MPPCA model by aligning the PCA coefficients from each mixture component in a global coordinated system. We call these aligned coefficients 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 efficiently learns this DBN for particular data sets. Our analysis proves that our inference algorithm is as efficient as the Kalman filter.; 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. |
