Journal Article10.1109/97.928678
Fast algorithms for subspace tracking
Samir Attallah,Karim Abed-Meraim +1 more
97
TL;DR: Two normalized versions of Oja's (1992) algorithm (NOja and NOOja), which can be used for the estimation of minor and principal subspaces of a vector sequence, offer a faster convergence, orthogonality, and a better numerical stability.
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Abstract: We present two normalized versions of Oja's (1992) algorithm (NOja and NOOja), which can be used for the estimation of minor and principal subspaces of a vector sequence. The new algorithms offer, as compared to Oja, a faster convergence, orthogonality, and a better numerical stability with a slight increase in computational complexity.
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References
Projection approximation subspace tracking
TL;DR: A novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem is presented, and it is shown that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation.
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Original Contribution: Principal components, minor components, and linear neural networks
TL;DR: The Stochastic Gradient Ascent neural network is proposed and shown to be closely related to the Generalized Hebbian Algorithm (GHA), and the SGA behaves better for extracting the less dominant eigenvectors.
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Orthogonal Oja algorithm
TL;DR: An orthogonalized version of the Oja algorithm (OOja) is proposed that can be used for the estimation of minor and principal subspaces of a vector sequence and offers advantages as orthogonality of the weight matrix.
75
Revisiting adaptive signal subspace estimation based on Rayleigh's quotient
Samir Attallah
- 07 May 2001
TL;DR: A new adaptive algorithm for subspace estimation and tracking that is based on Rayleigh's quotient that has a number of interesting properties such as a low computational complexity, a fast convergence, orthogonality of the subspace vectors which is ensured at each iteration and a good numerical stability.
9
A unified algorithm for principal and minor components extraction
TL;DR: A unified algorithm which can be used to extract both principal and minor component eigenvectors is proposed and if altered simply by the sign, it can also serve as a true minor components extractor.