On a Class of Orthonormal Algorithms for Principal and Minor Subspace Tracking
Journal of VLSI Signal Processing Systems
Optimal Linear Representations of Images for Object Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Data Complexity Analysis: Linkage between Context and Solution in Classification
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Tools for application-driven linear dimension reduction
Neurocomputing
Optimal linear projections for enhancing desired data statistics
Statistics and Computing
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This paper presents a geometric approach to estimating subspaces as elements of the complex Grassmann-manifold, with each subspace represented by its unique, complex projection matrix. Variation between the subspaces is modeled by rotating their projection matrices via the action of unitary matrices [elements of the unitary group U(n)]. Subspace estimation or tracking then corresponds to inferences on U(n). Taking a Bayesian approach, a posterior density is derived on U(n), and certain expectations under this posterior are empirically generated. For the choice of the Hilbert-Schmidt norm on U(n), to define estimation errors, an optimal MMSE estimator is derived. It is shown that this estimator achieves a lower bound on the expected squared errors associated with all possible estimators. The estimator and the bound are computed using (Metropolis-adjusted) Langevin's-diffusion algorithm for sampling from the posterior. For use in subspace tracking, a prior model on subspace rotation, that utilizes Newtonian dynamics, is suggested