Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
The O.D. E. Method for Convergence of Stochastic Approximation and Reinforcement Learning
SIAM Journal on Control and Optimization
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
Q-Learning for Risk-Sensitive Control
Mathematics of Operations Research
Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost
Mathematics of Operations Research
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
Control Techniques for Complex Networks
Control Techniques for Complex Networks
An information-theoretic framework to aggregate a Markov chain
ACC'09 Proceedings of the 2009 conference on American Control Conference
Global convergence of Oja's subspace algorithm for principal component extraction
IEEE Transactions on Neural Networks
Convergence analysis of a deterministic discrete time system of Oja's PCA learning algorithm
IEEE Transactions on Neural Networks
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Given a positive definite matrix M and an integer N"m=1, Oja's subspace algorithm will provide convergent estimates of the first N"m eigenvalues of M along with the corresponding eigenvectors. It is a common approach to principal component analysis. This paper introduces a normalized stochastic-approximation implementation of Oja's subspace algorithm, as well as new applications to the spectral decomposition of a reversible Markov chain. Recall that this means that the stationary distribution satisfies the detailed balance equations (Meyn & Tweedie, 2009). Equivalently, the statistics of the process in steady state do not change when time is reversed. Stability and convergence of Oja's algorithm are established under conditions far milder than that assumed in previous work. Applications to graph clustering, Markov spectral decomposition, and multiplicative ergodic theory are surveyed, along with numerical results.