A Matrix Pseudoinversion Lemma and Its Application to Block-Based Adaptive Blind Deconvolution for MIMO Systems

Kohno, Kiyotaka; Kawamoto, Mitsuru; Inouye, Yasushi

doi:10.1109/tcsi.2010.2050222

Cited by 13 publications

(19 citation statements)

References 19 publications

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“…Some non iterative procedures based on the evaluation of generalized pseudoinverse matrices have been recently proposed as novel learning algorithms for SLFNs: among them the method to improve performance of multilayer perceptron by Halawa [2], the extreme learning machine (elm) [3] and some studies more application oriented [4,5,6]. Usually, input weights (linking input and hidden layers) are randomly chosen, and output weights (linking hidden and output layers) are analytically determined by the Moore-Penrose (MP) generalized inverse (or pseudoinverse).…”

Section: Introductionmentioning

confidence: 99%

Matrix Pseudoinversion for Image Neural Processing

Cancelliere

Gai²,

Artières

et al. 2012

Neural Information Processing

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Abstract.Recently some novel strategies have been proposed for training of Single Hidden Layer Feedforward Networks, that set randomly the weights from input to hidden layer, while weights from hidden to output layer are analytically determined by Moore-Penrose generalised inverse. Such non-iterative strategies are appealing since they allow fast learning, but some care may be required to achieve good results, mainly concerning the procedure used for matrix pseudoinversion. This paper proposes a novel approach based on original determination of the initialization interval for input weights, a careful choice of hidden layer activation functions and on critical use of generalised inverse to determine output weights. We show that this key step suffers from numerical problems related to matrix invertibility, and we propose a heuristic procedure for bringing more robustness to the method. We report results on a difficult astronomical image analysis problem of chromaticity diagnosis to illustrate the various points under study.

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Section: Introductionmentioning

confidence: 99%

Matrix Pseudoinversion for Image Neural Processing

Cancelliere

Gai²,

Artières

et al. 2012

Neural Information Processing

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“…Differently from the EVM in [5], (13) means that i w  is modified iteratively by the value of the right-hand side of (13) …”

Section: The Proposed Algorithmmentioning

confidence: 99%

“…Therefore, our proposed algorithm for achieving the BD is that the vector i w  is modified by using the value i d R † in (13), and then the modified vector, that is, i w  in the left-hand side of (13) is normalized by (14).…”

Section: The Proposed Algorithmmentioning

confidence: 99%

“…We treat P(k) as , † R and i w  is iteratively modified using (13) and (14), where i  in (13) is assumed to be fixed to 1 and : (13) is estimated by using…”

Section: The Proposed Algorithmmentioning

confidence: 99%

“…(33) is the first step of the SEM with respect to i w [8]．In the SEM, the second step, that is, the normalization step is implemented using (14). Therefore, (13) and (14) are nothing but the iterative algorithm of the SEM. This completes the proof.…”

Section: Appendixmentioning

confidence: 99%

See 2 more Smart Citations

A modified eigenvector method for blind deconvolution of MIMO systems using the matrix pseudo-inversion lemma

Kawamoto

Kono

Inouye

et al. 2010

Proceedings of 2010 IEEE International Symposium on Circuits and Systems

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Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. One of attractive features of the proposed algorithm is that the BD can be achieved by calculating the eigenvectors of a matrix relevant to it. However, the performance accuracy of the EVM depends highly on computational results of the eigenvectors. In this paper, by modifying the EVM, we propose an algorithm which can achieve the BD without calculating the eigenvectors. Then the pseudo-inverse which is needed to carry out the BD is calculated by our proposed matrix pseudo-inversion lemma. Moreover, using a combination of the conventional EVM and the modified EVM, we will show its performances comparing with each EVM. Simulation results will be presented for showing the effectiveness of the proposed methods.

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Computational Experience with Pseudoinversion-Based Training of Neural Networks Using Random Projection Matrices

Rubini¹,

Cancelliere²,

Gallinari³

et al. 2014

Artificial Intelligence: Methodology, Systems, and Applications

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Recently some novel strategies have been proposed for neural network training that set randomly the weights from input to hidden layer, while weights from hidden to output layer are analytically determined by Moore-Penrose generalised inverse; such non-iterative strategies are appealing since they allow fast learning. Aim of this study is to investigate the performance variability when random projections are used for convenient setting of the input weights: we compare them with state of the art setting i.e. weights randomly chosen according to a continuous uniform distribution. We compare the solutions obtained by different methods testing this approach on some UCI datasets for both regression and classification tasks; this results in a significant performance improvement with respect to conventional method.

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A Matrix Pseudoinversion Lemma and Its Application to Block-Based Adaptive Blind Deconvolution for MIMO Systems

Cited by 13 publications

References 19 publications

Matrix Pseudoinversion for Image Neural Processing

Matrix Pseudoinversion for Image Neural Processing

A modified eigenvector method for blind deconvolution of MIMO systems using the matrix pseudo-inversion lemma

Computational Experience with Pseudoinversion-Based Training of Neural Networks Using Random Projection Matrices

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