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Feng Ding - One of the best experts on this subject based on the ideXlab platform.

Geert Leus - One of the best experts on this subject based on the ideXlab platform.

  • filter design for Autoregressive Moving Average graph filters
    IEEE Transactions on Signal and Information Processing over Networks, 2019
    Co-Authors: Jiani Liu, Elvin Isufi, Geert Leus
    Abstract:

    In the field of signal processing on graphs, graph filters play a crucial role in processing the spectrum of graph signals. This paper proposes two different strategies for designing Autoregressive Moving Average (ARMA) graph filters on both directed and undirected graphs. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second technique is based on an iterative approach, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed algorithms is evaluated and compared with finite impulse response (FIR) graph filters, on both synthetic and real data. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy and they are suitable for graph signal interpolation, compression, and prediction.

  • Autoregressive Moving Average graph filters a stable distributed implementation
    2017 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2017
    Co-Authors: Elvin Isufi, Andreas Loukas, Geert Leus
    Abstract:

    We present a novel implementation strategy for distributed Autoregressive Moving Average (ARMA) graph filters. Differently from the state of the art implementation, the proposed approach has the following benefits: (i) the designed filter coefficients come with stability guarantees, (ii) the linear convergence time can now be controlled by the filter coefficients, and (iii) the stable filter coefficients that approximate a desired frequency response are optimal in a least squares sense. Numerical results show that the proposed implementation outperforms the state of the art distributed infinite impulse response (IIR) graph filters. Further, even at fixed distributed costs, compared with the popular finite impulse response (FIR) filters, at high orders our method achieves tighter low-pass responses, suggesting that it should be preferable in accuracy-demanding applications.

  • Autoregressive Moving Average graph filter design
    2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2017
    Co-Authors: Elvin Isufi, Geert Leus
    Abstract:

    In graph signal processing, signals are processed by explicitly taking into account their underlying structure, which is generally characterized by a graph. In this field, graph filters play a major role to process such signals in the so-called graph frequency domain. In this paper, we focus on the design of Autoregressive Moving Average (ARMA) graph filters and basically present two design approaches. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second approach is based on an iterative method, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed design algorithms is evaluated and compared with finite impulse response (FIR) graph filters. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy even for the same computational cost.

  • Autoregressive Moving Average Graph Filtering
    IEEE Transactions on Signal Processing, 2017
    Co-Authors: Elvin Isufi, Andreas Loukas, Andrea Simonetto, Geert Leus
    Abstract:

    One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogs of classical filters, but intended for signals defined on graphs. This paper brings forth new insights on the distributed graph filtering problem. We design a family of Autoregressive Moving Average (ARMA) recursions, which are able to approximate any desired graph frequency response, and give exact solutions for specific graph signal denoising and interpolation problems. The philosophy to design the ARMA coefficients independently from the underlying graph renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph topology are changing over time. We show that in case of a time-varying graph signal, our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domain. We also derive the graph filter behavior, as well as sufficient conditions for filter stability when the graph and signal are time varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.

  • Separable Autoregressive Moving Average graph-temporal filters
    2016 24th European Signal Processing Conference (EUSIPCO), 2016
    Co-Authors: Elvin Isufi, Andreas Loukas, Andrea Simonetto, Geert Leus
    Abstract:

    Despite their widespread use for the analysis of graph data, current graph filters are designed for graph signals that do not change over time, and thus they cannot simultaneously process time and graph frequency content in an adequate manner. This work presents ARMA2D, an Autoregressive Moving Average graph-temporal filter that captures jointly the signal variations over the graph and time. By its unique nature, this filter is able to achieve a separable 2-dimensional frequency response, making it possible to approximate the filtering specifications along both the graph and temporal frequency domains. Numerical results show that the proposed solution outperforms the state of the art graph filters when the graph signal is time-varying.

Wai Keung Li - One of the best experts on this subject based on the ideXlab platform.

  • least absolute deviation estimation for fractionally integrated Autoregressive Moving Average time series models with conditional heteroscedasticity
    Biometrika, 2008
    Co-Authors: Guodong Li, Wai Keung Li
    Abstract:

    We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated Autoregressive Moving Average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau tests, is designed to check whether or not the estimated models are adequate. The simulation experiments give further support to our model and the results for the absolute returns of the Dow Jones Industrial Average Index daily closing price demonstrate their usefulness in modelling time series exhibiting the features of long memory, conditional heteroscedasticity and heavy tails. Copyright 2008, Oxford University Press.

  • limiting distributions of maximum likelihood estimators for unstable Autoregressive Moving Average time series with general Autoregressive heteroscedastic errors
    Annals of Statistics, 1998
    Co-Authors: Shiqing Ling, Wai Keung Li
    Abstract:

    This paper investigates the maximum likelihood estimator (MLE) for unstable Autoregressive Moving-Average (ARMA) time series with the noise sequence satisfying a general Autoregressive heteroscedastic (GARCH) process. Under some mild conditions, it is shown that the MLE satisfying the likelihood equation exists and is consistent. The limiting distribution of the MLE is derived in a unified manner for all types of characteristic roots on or outside the unit circle and is expressed as a functional of stochastic integrals in terms of Brownian motions. For various types of unit roots, the limiting distribution of the MLE does not depend on the parameters in the Moving-Average component and hence, when the GARCH innovations reduce to usual white noises with a constant conditional variance, they are the same as those for the least squares estimators (LSE) for unstable Autoregressive models given by Chan and Wei (1988). In the presence of the GARCH innovations, the limiting distribution will involve a sequence of independent bivariate Brownian motions with correlated components. These results are different from those already known in the literature and, in this case, the MLE of unit roots will be much more efficient than the ordinary least squares estimation.

  • on fractionally integrated Autoregressive Moving Average time series models with conditional heteroscedasticity
    Journal of the American Statistical Association, 1997
    Co-Authors: Shiqing Ling, Wai Keung Li
    Abstract:

    Abstract This article considers fractionally integrated Autoregressive Moving-Average time series models with conditional heteroscedasticity, which combines the popular generalized Autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration,...

Tasawar Hayat - One of the best experts on this subject based on the ideXlab platform.

Elvin Isufi - One of the best experts on this subject based on the ideXlab platform.

  • filter design for Autoregressive Moving Average graph filters
    IEEE Transactions on Signal and Information Processing over Networks, 2019
    Co-Authors: Jiani Liu, Elvin Isufi, Geert Leus
    Abstract:

    In the field of signal processing on graphs, graph filters play a crucial role in processing the spectrum of graph signals. This paper proposes two different strategies for designing Autoregressive Moving Average (ARMA) graph filters on both directed and undirected graphs. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second technique is based on an iterative approach, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed algorithms is evaluated and compared with finite impulse response (FIR) graph filters, on both synthetic and real data. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy and they are suitable for graph signal interpolation, compression, and prediction.

  • Autoregressive Moving Average graph filters a stable distributed implementation
    2017 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2017
    Co-Authors: Elvin Isufi, Andreas Loukas, Geert Leus
    Abstract:

    We present a novel implementation strategy for distributed Autoregressive Moving Average (ARMA) graph filters. Differently from the state of the art implementation, the proposed approach has the following benefits: (i) the designed filter coefficients come with stability guarantees, (ii) the linear convergence time can now be controlled by the filter coefficients, and (iii) the stable filter coefficients that approximate a desired frequency response are optimal in a least squares sense. Numerical results show that the proposed implementation outperforms the state of the art distributed infinite impulse response (IIR) graph filters. Further, even at fixed distributed costs, compared with the popular finite impulse response (FIR) filters, at high orders our method achieves tighter low-pass responses, suggesting that it should be preferable in accuracy-demanding applications.

  • Autoregressive Moving Average Graph Filtering
    IEEE Transactions on Signal Processing, 2017
    Co-Authors: Elvin Isufi, Andreas Loukas, Andrea Simonetto, Geert Leus
    Abstract:

    One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogs of classical filters, but intended for signals defined on graphs. This paper brings forth new insights on the distributed graph filtering problem. We design a family of Autoregressive Moving Average (ARMA) recursions, which are able to approximate any desired graph frequency response, and give exact solutions for specific graph signal denoising and interpolation problems. The philosophy to design the ARMA coefficients independently from the underlying graph renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph topology are changing over time. We show that in case of a time-varying graph signal, our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domain. We also derive the graph filter behavior, as well as sufficient conditions for filter stability when the graph and signal are time varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.

  • Autoregressive Moving Average graph filter design
    2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2017
    Co-Authors: Elvin Isufi, Geert Leus
    Abstract:

    In graph signal processing, signals are processed by explicitly taking into account their underlying structure, which is generally characterized by a graph. In this field, graph filters play a major role to process such signals in the so-called graph frequency domain. In this paper, we focus on the design of Autoregressive Moving Average (ARMA) graph filters and basically present two design approaches. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second approach is based on an iterative method, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed design algorithms is evaluated and compared with finite impulse response (FIR) graph filters. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy even for the same computational cost.

  • Separable Autoregressive Moving Average graph-temporal filters
    2016 24th European Signal Processing Conference (EUSIPCO), 2016
    Co-Authors: Elvin Isufi, Andreas Loukas, Andrea Simonetto, Geert Leus
    Abstract:

    Despite their widespread use for the analysis of graph data, current graph filters are designed for graph signals that do not change over time, and thus they cannot simultaneously process time and graph frequency content in an adequate manner. This work presents ARMA2D, an Autoregressive Moving Average graph-temporal filter that captures jointly the signal variations over the graph and time. By its unique nature, this filter is able to achieve a separable 2-dimensional frequency response, making it possible to approximate the filtering specifications along both the graph and temporal frequency domains. Numerical results show that the proposed solution outperforms the state of the art graph filters when the graph signal is time-varying.