Classification of dynamics on Riemannian manifold
Permanent URL:
http://hdl.handle.net/2047/D20290581
Camps, Octavia (Committee member)
Dy, Jennifer (Committee member)
Ioannidis, Stratis (Committee member)
For simple dynamical sequences, we embed the sequences into a Riemannian manifold by using positive definite regularized Gram matrices of their Hankelets. It captures better the underlying geometry than directly comparing the sequences or their Hankel matrices. Moreover, Gram matrices inherit desirable properties from the underlying Hankel matrices: their rank measures the complexity of the underlying dynamics, and the order and the coefficients of the associated regressive models are invariant to affine transformations and varying initial conditions.
For complex temporal sequences that contain dynamics switches, we consider the problem of switched Wiener system identification from a Kernel based manifold embedding perspective. We show that a computationally efficient solution can be obtained using a polynomial optimization approach that allows for exploiting the underlying sparse structure of the problem and provides optimality certificates. As an alternative, we provide a low complexity algorithm for the case where the affine part of the system switches only between two sub models.
The benefits of this framework are illustrated using both academic examples and real data examples in system identification, action recognition, activity segmentation and multi-camera motion segmentation.
efficient
embedding
motion segmentation
Riemannian manifold
switched system identification
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