The Experts below are selected from a list of 38880 Experts worldwide ranked by ideXlab platform
Vladimir Spokoiny - One of the best experts on this subject based on the ideXlab platform.
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Sparse non Gaussian Component analysis by semidefinite programming
Machine Learning, 2013Co-Authors: Elmar Diederichs, Anatoli Juditsky, Arkadi Nemirovski, Vladimir SpokoinyAbstract:Sparse non-Gaussian Component analysis is an unsupervised linear method of extracting any structure from high-dimensional distributed data based on estimating a low-dimensional non-Gaussian data Component. In this paper we discuss a new approach with known apriori reduced dimension to direct estimation of the projector on the target space using semidefinite programming. The new approach avoids the estimation of the data covariance matrix and overcomes the traditional separation of element estimation of the target space and target space reconstruction. This allows to reduced the sampling size while improving the sensitivity to a broad variety of deviations from normality. Moreover the complexity of the new approach is limited to O ( d log d ). We also discuss the procedures which allows to recover the structure when its effective dimension is unknown.
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sparse non Gaussian Component analysis by semidefinite programming
Research Papers in Economics, 2011Co-Authors: Elmar Diederichs, Anatoli Juditsky, Arkadi Nemirovski, Vladimir SpokoinyAbstract:Sparse non-Gaussian Component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data Component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinite programming which improves the method sensitivity to a broad variety of deviations from normality. We also discuss the procedures which allows to recover the structure when its e ective dimension is unknown.
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sparse non Gaussian Component analysis
IEEE Transactions on Information Theory, 2010Co-Authors: Elmar Diederichs, Vladimir Spokoiny, Anatoli Juditsky, Christof SchutteAbstract:Non-Gaussian Component analysis (NGCA) introduced in offered a method for high-dimensional data analysis allowing for identifying a low-dimensional non-Gaussian Component of the whole distribution in an iterative and structure adaptive way. An important step of the NGCA procedure is identification of the non-Gaussian subspace using principle Component analysis (PCA) method. This article proposes a new approach to NGCA called sparse NGCA which replaces the PCA-based procedure with a new the algorithm we refer to as convex projection.
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in search of non Gaussian Components of a high dimensional distribution
Journal of Machine Learning Research, 2006Co-Authors: Gilles Blanchard, Motoaki Kawanabe, Masashi Sugiyama, Vladimir Spokoiny, Klausrobert MullerAbstract:Finding non-Gaussian Components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the "non-Gaussian subspace" within a very general semi-parametric framework. Our proposed method, called NGCA (non-Gaussian Component analysis), is based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector belonging to the low dimensional non-Gaussian target subspace, up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.
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non Gaussian Component analysis a semi parametric framework for linear dimension reduction
Neural Information Processing Systems, 2005Co-Authors: Gilles Blanchard, Motoaki Kawanabe, Masashi Sugiyama, Vladimir Spokoiny, Klausrobert MullerAbstract:We propose a new linear method for dimension reduction to identify non-Gaussian Components in high dimensional data. Our method, NGCA (non-Gaussian Component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (Gaussian): by projecting out uninterestingness, we can estimate the relevant non-Gaussian subspace. We show that the estimation error of finding the non-Gaussian Components tends to zero at a parametric rate. Once NGCA Components are identified and extracted, various tasks can be applied in the data analysis process, like data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.
Dan Ruan - One of the best experts on this subject based on the ideXlab platform.
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Dose impact in radiographic lung injury following lung SBRT: Statistical analysis and geometric interpretation
Medical physics, 2014Co-Authors: Amar U. Kishan, Minsong Cao, Daniel A. Low, Percy Lee, Dan RuanAbstract:Purpose: To demonstrate a new method of evaluating dose response of treatment-induced lung radiographic injury post-SBRT (stereotactic body radiotherapy) treatment and the discovery of bimodal dose behavior within clinically identified injury volumes. Methods: Follow-up CT scans at 3, 6, and 12 months were acquired from 24 patients treated with SBRT for stage-1 primary lung cancers or oligometastic lesions. Injury regions in these scans were propagated to the planning CT coordinates by performing deformable registration of the follow-ups to the planning CTs. A bimodal behavior was repeatedly observed from the probability distribution for dose values within the deformed injury regions. Based on a mixture-Gaussian assumption, an Expectation-Maximization (EM) algorithm was used to obtain characteristic parameters for such distribution. Geometric analysis was performed to interpret such parameters and infer the critical dose level that is potentially inductive of post-SBRT lung injury. Results: The Gaussian mixture obtained from the EM algorithm closely approximates the empirical dose histogram within the injury volume with good consistency. The average Kullback-Leibler divergence values between the empirical differential dose volume histogram and the EM-obtained Gaussian mixture distribution were calculated to be 0.069, 0.063, and 0.092 for the 3, 6, and 12 month follow-up groups, respectively. The lower Gaussian Component was located at approximately 70% prescription dose (35 Gy) for all three follow-up time points. The higher Gaussian Component, contributed by the dose received by planning target volume, was located at around 107% of the prescription dose. Geometrical analysis suggests the mean of the lower Gaussian Component, located at 35 Gy, as a possible indicator for a critical dose that induces lung injury after SBRT. Conclusions: An innovative and improved method for analyzing the correspondence between lung radiographic injury and SBRT treatment dose has been demonstrated. Bimodal behavior was observed in the dose distribution of lung injury after SBRT. Novel statistical and geometrical analysis has shown that the systematically quantified low-dose peak at approximately 35 Gy, or 70% prescription dose, is a good indication of a critical dose for injury. The determined critical dose of 35 Gy resembles the critical dose volume limit of 30 Gy for ipsilateral bronchus in RTOG 0618 and results from previous studies. The authors seek to further extend this improved analysis method to a larger cohort to better understand the interpatient variation in radiographic lung injury dose response post-SBRT.
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su c 141 01 dose impact in lung fibrosis following lung sbrt statistical analysis and geometric interpretation
Medical Physics, 2013Co-Authors: Amar U. Kishan, Percy Lee, D Low, Dan RuanAbstract:Purpose: To test the hypothesis that certain dosimetric parameters prognosticate treatment-induced lung fibrosis. To obtain estimates for most prognostic dose values and to utilize them in developing new planning strategies to reduce injury in future SBRT. Methods: Follow-up CT scans at 6 and 12 months were acquired from patients treated with SBRT (18Gy/Fx*3Fx or 12.5Gy/Fx*4Fx) for stage-1 primary lung cancers or oligometastic lesions. Fibrosis regions were identified in these scans and propagated to the planning CT coordinates by rigidly registering the follow-up and the planning CTs. Among a cohort of 8 properly registered cases, a bimodal behavior was repeatedly observed from the probability distribution for dose values within fibrosis regions. Based on a mixture-Gaussian assumption, an Expectation-Maximization (EM) algorithm was used to obtain characteristic parameters for such distribution. Geometric analysis was performed to interpret such parameters and infer the dose level that is potentially inductive of post-SBRT fibrosis. Results: The Gaussian mixture obtained from the EM algorithm closely approximates the empirical dose histogram within the fibrosis volume with good consistency. The Kolmogorov-Smirnov test yields a goodness of fit value 0.039. The higher Gaussian Component, contributed by the dose received by PTV, was located around the prescription dose (50 or 54 Gy), as expected. Geometrical analysis suggests the mean of the lower Gaussian Component as a possible indicator for a threshold dose that induces fibrosis after SBRT. Conclusion: Bimodal behavior was observed in the dose distribution of lung fibrosis volumes after SBRT. Novel statistical and geometrical analysis has shown that the systematically quantified low-dose peak is a good indication of a threshold dose for injury. We seek to further improve the quality of registration to extend this analysis to a larger cohort for validation, and to explore planning strategies to reduce post-SBRT injury by controlling the exposure above the threshold value.
Klausrobert Muller - One of the best experts on this subject based on the ideXlab platform.
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A new algorithm of non-Gaussian Component analysis with radial kernel functions
Annals of the Institute of Statistical Mathematics, 2007Co-Authors: Motoaki Kawanabe, Gilles Blanchard, Masashi Sugiyama, Klausrobert MullerAbstract:We consider high-dimensional data which contains a linear low-dimensional non-Gaussian structure contaminated with Gaussian noise, and discuss a method to identify this non-Gaussian subspace. For this problem, we provided in our previous work a very general semi-parametric framework called non-Gaussian Component analysis (NGCA). NGCA has a uniform probabilistic bound on the error of finding the non-Gaussian Components and within this framework, we presented an efficient NGCA algorithm called Multi-index Projection Pursuit . The algorithm is justified as an extension of the ordinary projection pursuit (PP) methods and is shown to outperform PP particularly when the data has complicated non-Gaussian structure. However, it turns out that multi-index PP is not optimal in the context of NGCA. In this article, we therefore develop an alternative algorithm called iterative metric adaptation for radial kernel functions ( IMAK ), which is theoretically better justifiable within the NGCA framework. We demonstrate that the new algorithm tends to outperform existing methods through numerical examples.
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in search of non Gaussian Components of a high dimensional distribution
Journal of Machine Learning Research, 2006Co-Authors: Gilles Blanchard, Motoaki Kawanabe, Masashi Sugiyama, Vladimir Spokoiny, Klausrobert MullerAbstract:Finding non-Gaussian Components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the "non-Gaussian subspace" within a very general semi-parametric framework. Our proposed method, called NGCA (non-Gaussian Component analysis), is based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector belonging to the low dimensional non-Gaussian target subspace, up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.
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obtaining the best linear unbiased estimator of noisy signals by non Gaussian Component analysis
International Conference on Acoustics Speech and Signal Processing, 2006Co-Authors: Masashi Sugiyama, Gilles Blanchard, Motoaki Kawanabe, Klausrobert Muller, V SpokinyAbstract:Obtaining the best linear unbiased estimator (BLUE) of noisy signals is a traditional but powerful approach to noise reduction Explicitly computing BLUE usually requires the prior knowledge of the subspace to which the true signal belongs and the noise covariance matrix. However, such prior knowledge is often unavailable in reality, which prevents us from applying BLUE to real-world problems. In this paper, we therefore give a method for obtaining BLUE without such prior knowledge. Our additional assumption is that the true signal follows a non-Gaussian distribution while the noise is Gaussian.
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non Gaussian Component analysis a semi parametric framework for linear dimension reduction
Neural Information Processing Systems, 2005Co-Authors: Gilles Blanchard, Motoaki Kawanabe, Masashi Sugiyama, Vladimir Spokoiny, Klausrobert MullerAbstract:We propose a new linear method for dimension reduction to identify non-Gaussian Components in high dimensional data. Our method, NGCA (non-Gaussian Component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (Gaussian): by projecting out uninterestingness, we can estimate the relevant non-Gaussian subspace. We show that the estimation error of finding the non-Gaussian Components tends to zero at a parametric rate. Once NGCA Components are identified and extracted, various tasks can be applied in the data analysis process, like data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.
Elmar Diederichs - One of the best experts on this subject based on the ideXlab platform.
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Sparse non Gaussian Component analysis by semidefinite programming
Machine Learning, 2013Co-Authors: Elmar Diederichs, Anatoli Juditsky, Arkadi Nemirovski, Vladimir SpokoinyAbstract:Sparse non-Gaussian Component analysis is an unsupervised linear method of extracting any structure from high-dimensional distributed data based on estimating a low-dimensional non-Gaussian data Component. In this paper we discuss a new approach with known apriori reduced dimension to direct estimation of the projector on the target space using semidefinite programming. The new approach avoids the estimation of the data covariance matrix and overcomes the traditional separation of element estimation of the target space and target space reconstruction. This allows to reduced the sampling size while improving the sensitivity to a broad variety of deviations from normality. Moreover the complexity of the new approach is limited to O ( d log d ). We also discuss the procedures which allows to recover the structure when its effective dimension is unknown.
-
sparse non Gaussian Component analysis by semidefinite programming
Research Papers in Economics, 2011Co-Authors: Elmar Diederichs, Anatoli Juditsky, Arkadi Nemirovski, Vladimir SpokoinyAbstract:Sparse non-Gaussian Component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data Component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinite programming which improves the method sensitivity to a broad variety of deviations from normality. We also discuss the procedures which allows to recover the structure when its e ective dimension is unknown.
-
sparse non Gaussian Component analysis
IEEE Transactions on Information Theory, 2010Co-Authors: Elmar Diederichs, Vladimir Spokoiny, Anatoli Juditsky, Christof SchutteAbstract:Non-Gaussian Component analysis (NGCA) introduced in offered a method for high-dimensional data analysis allowing for identifying a low-dimensional non-Gaussian Component of the whole distribution in an iterative and structure adaptive way. An important step of the NGCA procedure is identification of the non-Gaussian subspace using principle Component analysis (PCA) method. This article proposes a new approach to NGCA called sparse NGCA which replaces the PCA-based procedure with a new the algorithm we refer to as convex projection.
Amar U. Kishan - One of the best experts on this subject based on the ideXlab platform.
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Dose impact in radiographic lung injury following lung SBRT: Statistical analysis and geometric interpretation
Medical physics, 2014Co-Authors: Amar U. Kishan, Minsong Cao, Daniel A. Low, Percy Lee, Dan RuanAbstract:Purpose: To demonstrate a new method of evaluating dose response of treatment-induced lung radiographic injury post-SBRT (stereotactic body radiotherapy) treatment and the discovery of bimodal dose behavior within clinically identified injury volumes. Methods: Follow-up CT scans at 3, 6, and 12 months were acquired from 24 patients treated with SBRT for stage-1 primary lung cancers or oligometastic lesions. Injury regions in these scans were propagated to the planning CT coordinates by performing deformable registration of the follow-ups to the planning CTs. A bimodal behavior was repeatedly observed from the probability distribution for dose values within the deformed injury regions. Based on a mixture-Gaussian assumption, an Expectation-Maximization (EM) algorithm was used to obtain characteristic parameters for such distribution. Geometric analysis was performed to interpret such parameters and infer the critical dose level that is potentially inductive of post-SBRT lung injury. Results: The Gaussian mixture obtained from the EM algorithm closely approximates the empirical dose histogram within the injury volume with good consistency. The average Kullback-Leibler divergence values between the empirical differential dose volume histogram and the EM-obtained Gaussian mixture distribution were calculated to be 0.069, 0.063, and 0.092 for the 3, 6, and 12 month follow-up groups, respectively. The lower Gaussian Component was located at approximately 70% prescription dose (35 Gy) for all three follow-up time points. The higher Gaussian Component, contributed by the dose received by planning target volume, was located at around 107% of the prescription dose. Geometrical analysis suggests the mean of the lower Gaussian Component, located at 35 Gy, as a possible indicator for a critical dose that induces lung injury after SBRT. Conclusions: An innovative and improved method for analyzing the correspondence between lung radiographic injury and SBRT treatment dose has been demonstrated. Bimodal behavior was observed in the dose distribution of lung injury after SBRT. Novel statistical and geometrical analysis has shown that the systematically quantified low-dose peak at approximately 35 Gy, or 70% prescription dose, is a good indication of a critical dose for injury. The determined critical dose of 35 Gy resembles the critical dose volume limit of 30 Gy for ipsilateral bronchus in RTOG 0618 and results from previous studies. The authors seek to further extend this improved analysis method to a larger cohort to better understand the interpatient variation in radiographic lung injury dose response post-SBRT.
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su c 141 01 dose impact in lung fibrosis following lung sbrt statistical analysis and geometric interpretation
Medical Physics, 2013Co-Authors: Amar U. Kishan, Percy Lee, D Low, Dan RuanAbstract:Purpose: To test the hypothesis that certain dosimetric parameters prognosticate treatment-induced lung fibrosis. To obtain estimates for most prognostic dose values and to utilize them in developing new planning strategies to reduce injury in future SBRT. Methods: Follow-up CT scans at 6 and 12 months were acquired from patients treated with SBRT (18Gy/Fx*3Fx or 12.5Gy/Fx*4Fx) for stage-1 primary lung cancers or oligometastic lesions. Fibrosis regions were identified in these scans and propagated to the planning CT coordinates by rigidly registering the follow-up and the planning CTs. Among a cohort of 8 properly registered cases, a bimodal behavior was repeatedly observed from the probability distribution for dose values within fibrosis regions. Based on a mixture-Gaussian assumption, an Expectation-Maximization (EM) algorithm was used to obtain characteristic parameters for such distribution. Geometric analysis was performed to interpret such parameters and infer the dose level that is potentially inductive of post-SBRT fibrosis. Results: The Gaussian mixture obtained from the EM algorithm closely approximates the empirical dose histogram within the fibrosis volume with good consistency. The Kolmogorov-Smirnov test yields a goodness of fit value 0.039. The higher Gaussian Component, contributed by the dose received by PTV, was located around the prescription dose (50 or 54 Gy), as expected. Geometrical analysis suggests the mean of the lower Gaussian Component as a possible indicator for a threshold dose that induces fibrosis after SBRT. Conclusion: Bimodal behavior was observed in the dose distribution of lung fibrosis volumes after SBRT. Novel statistical and geometrical analysis has shown that the systematically quantified low-dose peak is a good indication of a threshold dose for injury. We seek to further improve the quality of registration to extend this analysis to a larger cohort for validation, and to explore planning strategies to reduce post-SBRT injury by controlling the exposure above the threshold value.