Learning Nonlinear Manifolds from Time Series

Abstract. There has been growing interest in developing nonlinear dimensionality reduction algorithms for vision applications. Although progress has been made in recent years, conventional nonlinear dimensionality reduction algorithms have been designed to deal with stationary, or independent and identically distributed data. In this paper, we present a novel method that learns nonlinear mapping from time series data to their intrinsic coordinates on the underlying manifold. Our work extends the recent advances in learning nonlinear manifolds within a global coordinate system to account for temporal correlation inherent in sequential data. We formulate the problem with a dynamic Bayesian network and propose an approximate algorithm to tackle the learning and inference problems. Numerous experiments demonstrate the proposed method is able to learn nonlinear manifolds from time series data, and as a result of exploiting the temporal correlation, achieve superior results.

• Type: Conference
• Year: 2006
• Where: ECCV
• Authors: Ruei-Sung Lin, Che-Bin Liu, Ming-Hsuan Yang, Narendra Ahuja, Stephen E. Levinson
• Keywords: Computer Vision, Conventional Nonlinear Dimensionality, Dimensionality Reduction Algorithms, ECCV 2006, Nonlinear Dimensionality Reduction, Nonlinear Manifolds, Time Series Data