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Alfred O. Hero - One of the best experts on this subject based on the ideXlab platform.

  • kronecker sum decompositions of space time data
    IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2013
    Co-Authors: Kristjan Greenewald, Theodoros Tsiligkaridis, Alfred O. Hero
    Abstract:

    In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum-of-kronecker products representation in [1].We derive an asymptotic Cramer-Rao bound (CRB) on the minimum attainable mean squared Predictor Coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to the prediction of human activity video.

  • kronecker sum decompositions of space time data
    arXiv: Methodology, 2013
    Co-Authors: Kristjan Greenewald, Theodoros Tsiligkaridis, Alfred O. Hero
    Abstract:

    In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum of kronecker products representation [1]. We derive a Cramer-Rao bound (CRB) on the minimum attainable mean squared Predictor Coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to video data of human activity.

Kristjan Greenewald - One of the best experts on this subject based on the ideXlab platform.

  • kronecker sum decompositions of space time data
    IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2013
    Co-Authors: Kristjan Greenewald, Theodoros Tsiligkaridis, Alfred O. Hero
    Abstract:

    In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum-of-kronecker products representation in [1].We derive an asymptotic Cramer-Rao bound (CRB) on the minimum attainable mean squared Predictor Coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to the prediction of human activity video.

  • kronecker sum decompositions of space time data
    arXiv: Methodology, 2013
    Co-Authors: Kristjan Greenewald, Theodoros Tsiligkaridis, Alfred O. Hero
    Abstract:

    In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum of kronecker products representation [1]. We derive a Cramer-Rao bound (CRB) on the minimum attainable mean squared Predictor Coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to video data of human activity.

Theodoros Tsiligkaridis - One of the best experts on this subject based on the ideXlab platform.

  • kronecker sum decompositions of space time data
    IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2013
    Co-Authors: Kristjan Greenewald, Theodoros Tsiligkaridis, Alfred O. Hero
    Abstract:

    In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum-of-kronecker products representation in [1].We derive an asymptotic Cramer-Rao bound (CRB) on the minimum attainable mean squared Predictor Coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to the prediction of human activity video.

  • kronecker sum decompositions of space time data
    arXiv: Methodology, 2013
    Co-Authors: Kristjan Greenewald, Theodoros Tsiligkaridis, Alfred O. Hero
    Abstract:

    In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum of kronecker products representation [1]. We derive a Cramer-Rao bound (CRB) on the minimum attainable mean squared Predictor Coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to video data of human activity.

Cristina E Davis - One of the best experts on this subject based on the ideXlab platform.

  • autoregressive modeling of analytical sensor data can yield classifiers in the Predictor Coefficient parameter space
    Bioinformatics, 2005
    Co-Authors: Melissa D Krebs, Robert D Tingley, Julie E Zeskind, Joungmo Kang, Maria E Holmboe, Cristina E Davis
    Abstract:

    Summary: The analysis of chromatographic data resulting from complex chemical mixtures is challenging. Components may co-elute, causing their signals to overlap. An algorithm that will increase the signal-to-noise ratio so compounds present in low abundance can be better distinguished from noise is useful in this type of analysis. The autoregressive (AR) filter offers the advantage of smoothing chromatograms to increase this ratio, while also offering data compression and increased resolution. Furthermore, this filter can be useful for classification, as the roots of the Predictor Coefficient vectors represent features present in the data and can therefore be used for pattern recognition. In this paper, we present a novel method for applying AR filtering to chromatogram data. We show that the AR filter outperforms the Savitzky--Golay filter for smoothing noise while retaining important information within chromatograms, and also that AR correlation Coefficients have the potential to be used to classify chromatogram data into groups. Contact: cdavis@draper.com

Melissa D Krebs - One of the best experts on this subject based on the ideXlab platform.

  • autoregressive modeling of analytical sensor data can yield classifiers in the Predictor Coefficient parameter space
    Bioinformatics, 2005
    Co-Authors: Melissa D Krebs, Robert D Tingley, Julie E Zeskind, Joungmo Kang, Maria E Holmboe, Cristina E Davis
    Abstract:

    Summary: The analysis of chromatographic data resulting from complex chemical mixtures is challenging. Components may co-elute, causing their signals to overlap. An algorithm that will increase the signal-to-noise ratio so compounds present in low abundance can be better distinguished from noise is useful in this type of analysis. The autoregressive (AR) filter offers the advantage of smoothing chromatograms to increase this ratio, while also offering data compression and increased resolution. Furthermore, this filter can be useful for classification, as the roots of the Predictor Coefficient vectors represent features present in the data and can therefore be used for pattern recognition. In this paper, we present a novel method for applying AR filtering to chromatogram data. We show that the AR filter outperforms the Savitzky--Golay filter for smoothing noise while retaining important information within chromatograms, and also that AR correlation Coefficients have the potential to be used to classify chromatogram data into groups. Contact: cdavis@draper.com