Nonlinear Latent Variable Models for Video Sequences
Many high-dimensional time-varying signals can be modeled as a sequence of noisy nonlinear observations of a low-dimensional dynamical process. Given high-dimensional observations and a distribution describing the dynamical process, we present a computationally inexpensive approximate algorithm...
| Main Authors: | , , |
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| Language: | en_US |
| Published: |
2005
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/30552 |
| _version_ | 1811077329018945536 |
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| author | rahimi, ali recht, ben darrell, trevor |
| author_facet | rahimi, ali recht, ben darrell, trevor |
| author_sort | rahimi, ali |
| collection | MIT |
| description | Many high-dimensional time-varying signals can be modeled as a sequence of noisy nonlinear observations of a low-dimensional dynamical process. Given high-dimensional observations and a distribution describing the dynamical process, we present a computationally inexpensive approximate algorithm for estimating the inverse of this mapping. Once this mapping is learned, we can invert it to construct a generative model for the signals. Our algorithm can be thought of as learning a manifold of images by taking into account the dynamics underlying the low-dimensional representation of these images. It also serves as a nonlinear system identification procedure that estimates the inverse of the observation function in nonlinear dynamic system. Our algorithm reduces to a generalized eigenvalue problem, so it does not suffer from the computational or local minimum issues traditionally associated with nonlinear system identification, allowing us to apply it to the problem of learning generative models for video sequences. |
| first_indexed | 2024-09-23T10:41:13Z |
| id | mit-1721.1/30552 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:41:13Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | mit-1721.1/305522019-04-10T16:54:59Z Nonlinear Latent Variable Models for Video Sequences rahimi, ali recht, ben darrell, trevor AI Manifold learning,nonlinear system identification unsupervised learning Many high-dimensional time-varying signals can be modeled as a sequence of noisy nonlinear observations of a low-dimensional dynamical process. Given high-dimensional observations and a distribution describing the dynamical process, we present a computationally inexpensive approximate algorithm for estimating the inverse of this mapping. Once this mapping is learned, we can invert it to construct a generative model for the signals. Our algorithm can be thought of as learning a manifold of images by taking into account the dynamics underlying the low-dimensional representation of these images. It also serves as a nonlinear system identification procedure that estimates the inverse of the observation function in nonlinear dynamic system. Our algorithm reduces to a generalized eigenvalue problem, so it does not suffer from the computational or local minimum issues traditionally associated with nonlinear system identification, allowing us to apply it to the problem of learning generative models for video sequences. 2005-12-22T02:32:35Z 2005-12-22T02:32:35Z 2005-06-06 MIT-CSAIL-TR-2005-041 AIM-2005-021 http://hdl.handle.net/1721.1/30552 en_US Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory 11 p. 13801637 bytes 2196348 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | AI Manifold learning,nonlinear system identification unsupervised learning rahimi, ali recht, ben darrell, trevor Nonlinear Latent Variable Models for Video Sequences |
| title | Nonlinear Latent Variable Models for Video Sequences |
| title_full | Nonlinear Latent Variable Models for Video Sequences |
| title_fullStr | Nonlinear Latent Variable Models for Video Sequences |
| title_full_unstemmed | Nonlinear Latent Variable Models for Video Sequences |
| title_short | Nonlinear Latent Variable Models for Video Sequences |
| title_sort | nonlinear latent variable models for video sequences |
| topic | AI Manifold learning,nonlinear system identification unsupervised learning |
| url | http://hdl.handle.net/1721.1/30552 |
| work_keys_str_mv | AT rahimiali nonlinearlatentvariablemodelsforvideosequences AT rechtben nonlinearlatentvariablemodelsforvideosequences AT darrelltrevor nonlinearlatentvariablemodelsforvideosequences |