I. Yamada

Tokyo Institute of Technology, Tokyo, Tokyo-to, Japan

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Publications (136)192.92 Total impact

  • Tuan Duong Nguyen, Isao Yamada
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    ABSTRACT: Recently, we presented a first deterministic discrete time (DDT) analysis of the normalized normalized projection approximation subspace tracking (Normalized PAST) algorithms, for estimating principal and minor components of an input signal. The analysis shows that the DDT systems of the Normalized PAST algorithms converge to the desired eigenvectors under certain sufficient conditions on the forgetting factor @b@?(0,1]. However, it has not yet been clarified whether the sufficient conditions can be relaxed or not for guaranteed convergence. In this paper, by characterizing the maximal ranges of the forgetting factor, we establish the necessary and sufficient conditions for convergence of the DDT systems of the Normalized PAST algorithms. The proposed maximal range of the forgetting factor, for the minor component estimation, is doubled from the range assumed in the first DDT analysis, while the proposed maximal range of the forgetting factor, for principal component estimation, achieves the full range (0, 1]. Numerical examples further confirm the results.
    Signal Processing. 01/2014; 94:288-299.
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    ABSTRACT: The contribution of this paper is three-fold: first, we propose a novel scheme for generalized minor subspace extraction by extending an idea of dimension reduction technique. The key of this scheme is the reduction of the problem for extracting the ith (i ≥ 2) minor generalized eigenvector of the original matrix pencil to that for extracting the first minor generalized eigenvector of a matrix pencil of lower dimensionality. The proposed scheme can employ any algorithm capable of estimating the first minor generalized eigenvector. Second, we propose a pair of such iterative algorithms and analyze their convergence properties in the general case where the generalized eigenvalues are not necessarily distinct. Third, by using these algorithms inductively, we present adaptive implementations of the proposed scheme for estimating an orthonormal basis of the generalized minor subspace. Numerical examples show that the proposed adaptive subspace extraction algorithms have better numerical stability than conventional algorithms.
    Multidimensional Systems and Signal Processing 09/2013; 24(3). · 0.86 Impact Factor
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    ABSTRACT: This letter establishes a novel analysis of the Adaptive Projected Subgradient Method (APSM) in the intersection of the stochastic and robust estimation paradigms. Utilizing classical worst-case bounds on the noise process, drawn from the robust estimation methodology, the present study demonstrates that the hyperslab-inspired version of the APSM generates a sequence of estimates which converges to a point located, with probability one, arbitrarily close to the estimand. Numerical tests and comparisons with classical time-adaptive algorithms corroborate the theoretical findings of the study.
    IEEE Signal Processing Letters 07/2013; 20(7):729-732. · 1.67 Impact Factor
  • Source
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    ABSTRACT: The articles in this special issue report on up-to-date advances in the broad area of information processing over graphs. Due to the highly cross-disciplinary nature of complex networks, the technical articles in this April 2013 issue of the IEEE Journal of Selected Topics in Signal Processing are coupled with valuable tutorial articles that appear in a second special issue, organized by the same Guest Editors, and which is published as the May 2013 issue of the IEEE Signal Processing Magazine. The survey articles in the magazine are meant to introduce readers to the main tools and concepts, while the more focused technical articles in J-STSP cover state-of-the-art results. Through this combination of tutorial and technical articles in both journals, readers will become better acquainted with the challenges and opportunities that the broader field of network science has to offer across the domains of information sciences, system science, computer science, social sciences,machine learning, and optimization theory. Complex networks represent a typical paradigm that helps demonstrate well how barriers among seemingly different disciplines are becoming more transparent.
    IEEE Journal of Selected Topics in Signal Processing 04/2013; 7(2):161-162. · 3.30 Impact Factor
  • Tuan Duong Nguyen, Isao Yamada
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    ABSTRACT: The main contributions of this paper are to propose and analyze fast and numerically stable adaptive algorithms for the generalized Hermitian eigenvalue problem (GHEP), which arises in many signal processing applications. First, for given explicit knowledge of a matrix pencil, we formulate two novel deterministic discrete-time (DDT) systems for estimating the generalized eigen-pair (eigenvector and eigenvalue) corresponding to the largest/smallest generalized eigenvalue. By characterizing a generalized eigen-pair as a stationary point of a certain function, the proposed DDT systems can be interpreted as natural combinations of the normalization and quasi-Newton steps for finding the solution. Second, we present adaptive algorithms corresponding to the proposed DDT systems. Moreover, we establish rigorous analysis showing that, for a step size within a certain range, the sequence generated by the DDT systems converges to the orthogonal projection of the initial estimate onto the generalized eigensubspace corresponding to the largest/smallest generalized eigenvalue. Numerical examples demonstrate the practical applicability and efficacy of the proposed adaptive algorithms.
    IEEE Transactions on Signal Processing 03/2013; 61(6):1404-1418. · 2.81 Impact Factor
  • Tomasz Piotrowski, Isao Yamada
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    ABSTRACT: The stochastic MV-PURE estimator has been developed to provide linear estimation robust to ill-conditioning, high noise levels, and imperfections in model knowledge. In this paper, we investigate the theoretical performance of the stochastic MV-PURE estimator under varying level of additive noise. More precisely, we prove that the mean-square-error (MSE) of this estimator in the low signal-to-noise (SNR) region is much smaller than that obtained with its full-rank version, the minimum-variance distortionless estimator, and that the gap in performance is the larger the higher the noise level. These results shed light on the excellent performance of the stochastic MV-PURE estimator in highly noisy settings obtained in simulations so far. We extend here previously conducted numerical simulations to demonstrate a new insight provided by results of this paper in practical applications.
    Journal of the Franklin Institute. 03/2013;
  • M. Yamagishi, I. Yamada
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    ABSTRACT: Observing that a typical primary path in Active Noise Control (ANC) system is sparse, i.e., having a few significant coefficients, we propose an adaptive learning which promotes the sparsity of the concatenation of the adaptive filter and the secondary path. More precisely, we propose to suppress a time-varying sum of the data-fidelity term and the weighted ℓ1 norm of the concatenation by the adaptive Douglas-Rachford splitting scheme. Numerical examples demonstrate that the proposed algorithm shows excellent performance of the ANC by exploiting the sparsity and has robustness against a violation of the sparsity assumption.
    Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2013 Asia-Pacific; 01/2013
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    ABSTRACT: We consider the problem of dipole source signals estimation in electroencephalography (EEG) using beamforming techniques in ill-conditioned settings. We take advantage of the link between the linearly constrained minimum-variance (LCMV) beamformer in sensor array processing and the best linear unbiased estimator (BLUE) in linear regression modeling. We show that the recently introduced reduced-rank extension of BLUE, named minimum-variance pseudo-unbiased reduced-rank estimator (MV-PURE), achieves much lower estimation error not only than LCMV beamformer, but also than the previously derived reduced-rank principal components (PC) and cross-spectral metrics (CSM) beamformers in ill-conditioned settings. The practical scenarios where the considered estimation model becomes ill-conditioned are discussed, then we show the applicability of MV-PURE dipole source estimator under those conditions through realistic simulations.
    Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on; 01/2013
  • Tuan Duong Nguyen, Isao Yamada
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    ABSTRACT: We present a unified convergence analysis, based on a deterministic discrete time (DDT) approach, of the normalized projection approximation subspace tracking (Normalized PAST) algorithms for estimating principal and minor components of an input signal. The proposed analysis shows that the DDT system of the Normalized PAST algorithm (for PCA/MCA), with any forgetting factor in a certain range, converges to a desired eigenvector. This eigenvector is completely characterized as the normalized version of the orthogonal projection of the initial estimate onto the eigensubspace corresponding to the largest/smallest eigenvalue of the autocorrelation matrix of the input signal. This characterization holds in general case where the eigenvalues are not necessarily distinct. Numerical examples show that the proposed analysis demonstrates very well the convergence behavior of the Normalized PAST algorithms which uses a rank-1 instantaneous approximation of the autocorrelation matrix.
    Signal Processing. 01/2013; 93(1):176–184.
  • Source
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    ABSTRACT: The topic of this special issue deals with a subject matter that has been receiving immense attention from various research communities, and not only within the signal processing community. Discusses research and development in the area of the adaption and learning over complex network systems. Extensive research efforts on information processing over graphs exist within other fields such as statistics, computer science, optimization, control, economics, machine learning, biological sciences, and social sciences. Different fields tend to emphasize different aspects and challenges; nevertheless, opportunities for mutual cooperation are abundantly clear, and the role that signal processing plays in this domain is of fundamental importance.
    IEEE Signal Processing Magazine 01/2013; 30(3):14-15. · 3.37 Impact Factor
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    ABSTRACT: In this paper, a novel regularization-parameter design for the adaptive proximal forward-backward splitting algorithm is proposed for sparse system identification. The regularization parameter is controlled adaptively based on sparsity of an estimated unknown system. The regularizer is designed by approximating an !p quasi-norm (0 < p < 1) linearly. Numerical examples show that the proposed algorithm is robust to the variation of the system sparsity.
    Wireless Communication Systems (ISWCS 2013), Proceedings of the Tenth International Symposium on; 01/2013
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    ABSTRACT: We propose a novel sparsity-aware adaptive filtering algorithm based on iterative use of weighted soft-thresholding. The weights are determined based on a rough local approximation of the ℓp norm (0
    Circuits and Systems (ISCAS), 2012 IEEE International Symposium on; 01/2012
  • T. Piotrowski, I. Yamada
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    ABSTRACT: The stochastic MV-PURE estimator is a linear estimator for stochastic linear model that is highly robust to mismatches in model knowledge and which is specially designed for efficient estimation in noisy and ill-conditioned cases. To date, its properties were analyzed in the theoretical settings of perfect model knowledge and thus could not explain clearly the reason behind its superior performance compared to the Wiener filter observed in simulations in practical cases of imperfect model knowledge. In this paper we derive closed form expressions of the mean-square-error (MSE) of both Wiener filter and the stochastic MV-PURE estimator for the case of perturbed singular values of a model matrix in the linear model considered. These expressions provide in particular conditions under which the stochastic MV-PURE estimator achieves smaller MSE not only than Wiener filter, but also than its full-rank version, the minimum-variance distortionless (MVDR) estimator in such settings. We provide numerical simulations confirming the main theoretical results presented.
    Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on; 01/2012
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    Tomasz Piotrowski, Isao Yamada
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    ABSTRACT: In this paper we consider the problem of efficient compu-tation of the stochastic MV-PURE estimator which is a reduced-rank estimator designed for robust linear estimation in ill-conditioned inverse problems. Our motivation for this result stems from the fact that the reduced-rank estimation by the stochastic MV-PURE estimator, while avoiding the problem of regularization parameter selection appearing in a common regularization technique used in inverse problems and machine learning, presents computational challenge due to nonconvexity induced by the rank constraint. To combat this problem, we propose a recursive scheme for computation of the general form of the stochastic MV-PURE estimator which does not require any matrix inversion and utilize the inherently parallel hybrid steepest descent method. We verify efficiency of the proposed scheme in numerical simulations.
    01/2012;
  • Masao Yamagishi, Isao Yamada
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    ABSTRACT: In this paper, we present an over-relaxed variant of the fast iterative shrinkage-thresholding algorithm (FISTA)/the monotone FISTA (MFISTA). FISTA and MFISTA are iterative first-order algorithms, whose convergence rates of the objective function are for an iteration counter k, for the minimization of the sum of a smooth and a nonsmooth convex function. FISTA and MFISTA are composed of the forward–backward splitting step together with a certain computationally efficient shifting step. The stepsize available in the forward–backward splitting step in these algorithms has been limited to a fixed value determined by the Lipschitz constant of the gradient of the smooth function. Examples of the proposed scheme admit variable stepsizes in broader ranges than FISTA/MFISTA, while keeping the same convergence rate . A numerical example in a well-conditioned case demonstrates the effect of the proposed relaxations by showing that the proposed scheme outperforms, in the speed of convergence, the original FISTA and MFISTA.
    Inverse Problems 09/2011; 27(10):105008. · 1.90 Impact Factor
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    ABSTRACT: We propose a non-hierarchical decentralized algorithm for the asymptotic minimization of possibly time-varying convex functions. In our method, each agent in a network has a private, local (possibly time-varying) cost function, and the objective is to minimize asymptotically the sum of these local functions in every agent (this problem appears in many different applications such as, among others, motion planning, acoustic source localization, and environmental modeling). The algorithm consists of two main steps. First, to improve the estimate of a minimizer, agents apply a particular version of the adaptive projected subgradient method to their local functions. Then the agents exchange and mix their estimates using a communication model based on recent results of consensus algorithms. We show formally the convergence of the resulting scheme, which reproduces as particular cases many existing methods such as gossip consensus algorithms and recent decentralized adaptive subgradient methods (which themselves include as particular cases many distributed adaptive filtering algorithms). To illustrate two possible applications, we consider the problems of acoustic source localization and environmental modeling via network gossiping with mobile agents.
    IEEE Journal of Selected Topics in Signal Processing 09/2011; · 3.30 Impact Factor
  • M. Yukawa, I. Yamada
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    ABSTRACT: We propose a novel adaptive beamforming algorithm based on the multi-domain adaptive filtering approach (Yukawa et al., 2009). The proposed algorithm exploits, as a soft constraint in a transform domain, the information that the array responses to the interference direction should be sufficiently low. Additional operations introduced are linear transformations and a metric projection onto a closed ball that bounds the energy of the transformed weight vector. The efficacy of the proposed algorithm is shown by simulations.
    Statistical Signal Processing Workshop (SSP), 2011 IEEE; 07/2011
  • M. Yamagishi, M. Yukawa, I. Yamada
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    ABSTRACT: In this paper, we propose an acceleration technique of the adaptive filtering scheme called adaptive proximal forward-backward splitting method. For accelerating the convergence rate, the proposed method includes a step to shift the current estimate in the direction of the difference between the current and previous estimates based on the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA). The computational complexity for this additional step is fairly low compared to the overall complexity of the algorithm. As an example of the proposed method, we derive an acceleration of the composition of the Adoptively Weighted Soft-Thresholding (AWST) operator and the exponentially weighted adaptive parallel projection. AWST shrinks the estimated filter coefficients to zero for exploiting the sparsity of the system to be estimated and the exponentially weighted adaptive parallel projection algorithm realizes high accuracy by utilizing all available information at each iteration. This accelerated method improves the steady-state mismatch drastically with its con vergence speed as fast as the proportionate affine projection algorithm.
    Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on; 06/2011
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    ABSTRACT: The first aim of this paper is to present a useful toolbox of quasi-nonexpansive mappings for convex optimization from the viewpoint of using their fixed point sets as constraints. Many convex optimization problems have been solved through elegant translations into fixed point problems. The underlying principle is to operate a certain quasi-nonexpansive mapping T iteratively and generate a convergent sequence to its fixed point. However, such a mapping often has infinitely many fixed points, meaning that a selection from the fixed point set Fix(T) should be of great importance. Nevertheless, most fixed point methods can only return an “unspecified” point from the fixed point set, which requires many iterations. Therefore, based on common sense, it seems unrealistic to wish for an “optimal” one from the fixed point set. Fortunately, considering the collection of quasi-nonexpansive mappings as a toolbox, we can accomplish this challenging mission simply by the hybrid steepest descent method, provided that the cost function is smooth and its derivative is Lipschitz continuous. A question arises: how can we deal with “nonsmooth” cost functions? The second aim is to propose a nontrivial integration of the ideas of the hybrid steepest descent method and the Moreau–Yosida regularization, yielding a useful approach to the challenging problem of nonsmooth convex optimization over Fix(T). The key is the use of smoothing of the original nonsmooth cost function by its Moreau–Yosida regularization whose the derivative is always Lipschitz continuous. The field of application of hybrid steepest descent method can be extended to the minimization of the ideal smooth approximation Fix(T). We present the mathematical ideas of the proposed approach together with its application to a combinatorial optimization problem: the minimal antenna-subset selection problem under a highly nonlinear capacity-constraint for efficient multiple input multiple output (MIMO) communication systems. KeywordsNonsmooth convex optimization-Moreau envelope-Hybrid steepest descent method
    05/2011: pages 345-390;
  • Masahiro Yukawa, Isao Yamada
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    ABSTRACT: In this article, we propose a fast and efficient algorithm named the adaptive parallel Krylov-metric projection algorithm. The proposed algorithm is derived from the variable-metric adaptive projected subgradient method, which has recently been presented as a unified analytic tool for various adaptive filtering algorithms. The proposed algorithm features parallel projection—in a variable-metric sense—onto multiple closed convex sets containing the optimal filter with high probability. The metric is designed based on (i) sparsification by means of a certain data-dependent Krylov subspace and (ii) maximal use of the obtained sparse structure for fast convergence. The numerical examples show the advantages of the proposed algorithm over the existing ones in stationary/nonstationary environments. Copyright © 2011 John Wiley & Sons, Ltd.
    International Journal of Adaptive Control and Signal Processing 03/2011; 25(8):707 - 722. · 1.22 Impact Factor

Publication Stats

920 Citations
192.92 Total Impact Points

Institutions

  • 1991–2013
    • Tokyo Institute of Technology
      • • Department of Communications and Integrated Sytems
      • • Electrical and Electronic Engineering Department
      Tokyo, Tokyo-to, Japan
  • 2011
    • Fraunhofer Heinrich-Hertz-Institute HHI
      Berlín, Berlin, Germany
  • 2007–2011
    • Athens State University
      Athens, Alabama, United States
  • 2008–2010
    • University of Peloponnese
      • Department of Telecommunications Science and Technology
      Trípolis, Peloponnisos, Greece
  • 2007–2010
    • RIKEN
      • Laboratory for Mathematical Neuroscience
      Wako, Saitama-ken, Japan
  • 2009
    • The University of Edinburgh
      • Institute for Digital Communications (IDCoM)
      Edinburgh, SCT, United Kingdom
  • 2006
    • Nagoya University
      • Department of Electrical Engineering and Computer Science
      Nagoya-shi, Aichi-ken, Japan