Orthogonal Oja algorithm

Abed-Meraim, Karim; Attallah, S.; Chkeif, A.; Hua, Yingbo

doi:10.1109/97.841157

Cited by 66 publications

(26 citation statements)

References 8 publications

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“…At first, we consider the simplest (and hence cheapest) algorithm for the least eigenvector extraction, namely the OOja [3] which is a gradient type method of linear complexity. The estimate of the least…”

Section: Mns-oojamentioning

confidence: 99%

“…This problem is known for many decades and several solutions exist in the literature including the Oja (gradient) like techniques of linear complexity [3,4,5] (i.e, of complexity O(nm) flops per iteration where n is the size of the observation vector and m is the rank of the desired minor subspace) and the power like techniques (YAST, PAST) of quadratic complexity O(n 2 ) [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Minor subspace tracking using MNS technique

Thameri

Abed-Meraim

Belouchrani

2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper introduces new minor (noise) subspace tracking (MST) algorithms based on the minimum noise subspace (MNS) technique. The latter has been introduced as a computationally efficient subspace method for blind system identification. We exploit here the principle of the MNS, to derive the most efficient algorithms for MST. The proposed method joins the advantages of low complexity and fast convergence rate. Moreover, this method is highly parallelizable and hence its computational cost can be easily reduced to a very low level when parallel architectures are available. Different implementations are proposed for different contexts and they are compared via numerical simulations.

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Section: Mns-oojamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minor subspace tracking using MNS technique

Thameri

Abed-Meraim

Belouchrani

2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…The OOjaH algorithm proposes to use as H(i) the inverse square root of the matrix I + β 2 p 2 y(i)y H (i) [6]. However, such an approach diverges slowly from orthonormality in the case of noise subspace tracking.…”

Section: Fast Orthogonal Ojamentioning

confidence: 98%

“…Recently, an orthogonalization step of the weight matrix has been introduced to the Oja algorithm in order to have more stability. The new algorithm is called OOjaH [6] (H stands for Householder) and is summarized in Table 1. …”

Section: Orthogonal Ojamentioning

confidence: 99%

Principal and Minor Subspace Tracking: Algorithms & Stability Analysis

Bartelmaos¹,

Abed-Meraim²

2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings

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We consider the problem of tracking the minor or principal subspace of a positive Hermitian covariance matrix. We first propose a fast and numerically robust implementation of Oja algorithm (FOOja: Fast Orthogonal Oja). The latter is said fast in the sense that its computational cost is of order O(np) flops per iteration where n is the size of the observation vector and p < n is the number of minor or principal eigenvectors we need to estimate. FOOja guarantees the orthogonality of the weight matrix at each iteration. Moreover, this algorithm is analyzed and compared with two other fast algorithms (OOjaH and FDPM) with respect to their numerical stability. Simulation results highlights the relatively good stability behavior of FOOja.

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“…Recently it was shown in [1] that an orthonormal basis of the column space of W (i + 1) can be obtained by reflecting the (orthonormal) columns of W (i) with respect to a hyperplane specified by a certain Householder vector h(i), ||h(i)|| 2 = 1. The iteration has the form…”

Section: Introductionmentioning

confidence: 99%

A Note on the Derivation of Orthogonal Gradient Algorithm for Subspace Estimation

Bojańczyk

Fourth IEEE Workshop on Sensor Array and Multichannel Processing, 2006.

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The purpose of this note is to present an alternative derivation of orthogonal subspace estimation algorithms from elementary geometric properties of reflections. This derivation leads to an entire class of equivalent reflection based algorithms. The cost and performance of these algorithms are essentially the same as those presented earlier by other researchers, and can be superior in the case of high SNRs.

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Orthogonal Oja algorithm

Cited by 66 publications

References 8 publications

Minor subspace tracking using MNS technique

Minor subspace tracking using MNS technique

Principal and Minor Subspace Tracking: Algorithms & Stability Analysis

A Note on the Derivation of Orthogonal Gradient Algorithm for Subspace Estimation

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