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Issue No.04 - April (2012 vol.34)
pp: 654-669
S. Sclaroff , Dept. of Comput. Sci., Boston Univ., Boston, MA, USA
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 learned 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. A divide, conquer, and coordinate method is proposed. The solution approximates the nonlinear manifold and dynamics using simple piecewise linear models. The interactions and coordinations 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 overfitting. 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.
INDEX TERMS
video signal processing, approximation theory, Bayes methods, image classification, image motion analysis, image reconstruction, time series, tracking, human motion tracking, globally coordinated switching linear dynamical system, informative representation, high-dimensional time series, low-dimensional manifold, dynamical process modeling, complementary relationship, dimensionality reduction, nonlinear model, time series complexity, divide method, conquer method, coordinate method, nonlinear manifold approximation, dynamics approximation, piecewise linear model, graphical model, model structure setup, parameter learning, variational Bayesian approach, automatic Bayesian model structure selection, overfitting problem, inference algorithm, dimensionality reconstruction, synthetic time series, video synthesis, dynamic texture database, human motion synthesis, human motion classification, Time series analysis, Manifolds, Computational modeling, Biological system modeling, Humans, Bayesian methods, Graphical models, human motion., Bayesian learning, nonlinear manifold, nonlinear dynamical model, dynamic texture
CITATION
S. Sclaroff, "Divide, Conquer and Coordinate: Globally Coordinated Switching Linear Dynamical System", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.34, no. 4, pp. 654-669, April 2012, doi:10.1109/TPAMI.2011.152
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