The Experts below are selected from a list of 19941 Experts worldwide ranked by ideXlab platform
Dobigeon Nicolas - One of the best experts on this subject based on the ideXlab platform.
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Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures
'Institute of Electrical and Electronics Engineers (IEEE)', 2021Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:International audienceIn this work, we tackle the problem of hyperspectral unmixing by departing from the Usual Linear Model and focusing on a Linear-quadratic (LQ) one. The algorithm we propose, coined Successive Nonnegative Projection Algorithm for Linear Quadratic mixtures (SNPALQ), extends the Successive Nonnegative Projection Algorithm (SNPA), specifically designed to address the unmixing problem under a Linear non-negative Model and the pure-pixel assumption (a.k.a. near-separable assumption). By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. The approach is shown to be relevant in realistic numerical experiments, which further highlight that SNPALQ is robust to noise
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Provably robust blind source separation of Linear-quadratic near-separable mixtures
'The Japan Society for Industrial and Applied Mathematics', 2021Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:International audienceIn this work, we consider the problem of blind source separation (BSS) by departing from the Usual Linear Model and focusing on the Linear-quadratic (LQ) Model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for Linear BSS, and is referred to as SNPALQ. By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments
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Provably robust blind source separation of Linear-quadratic near-separable mixtures
2020Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:In this work, we consider the problem of blind source separation (BSS) by departing from the Usual Linear Model and focusing on the Linear-quadratic (LQ) Model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for Linear BSS, and is referred to as SNPALQ. By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments.Comment: 23 pages + 24 pages of Appendix containing the proof
Kervazo Christophe - One of the best experts on this subject based on the ideXlab platform.
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Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures
'Institute of Electrical and Electronics Engineers (IEEE)', 2021Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:International audienceIn this work, we tackle the problem of hyperspectral unmixing by departing from the Usual Linear Model and focusing on a Linear-quadratic (LQ) one. The algorithm we propose, coined Successive Nonnegative Projection Algorithm for Linear Quadratic mixtures (SNPALQ), extends the Successive Nonnegative Projection Algorithm (SNPA), specifically designed to address the unmixing problem under a Linear non-negative Model and the pure-pixel assumption (a.k.a. near-separable assumption). By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. The approach is shown to be relevant in realistic numerical experiments, which further highlight that SNPALQ is robust to noise
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Provably robust blind source separation of Linear-quadratic near-separable mixtures
'The Japan Society for Industrial and Applied Mathematics', 2021Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:International audienceIn this work, we consider the problem of blind source separation (BSS) by departing from the Usual Linear Model and focusing on the Linear-quadratic (LQ) Model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for Linear BSS, and is referred to as SNPALQ. By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments
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Provably robust blind source separation of Linear-quadratic near-separable mixtures
2020Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:In this work, we consider the problem of blind source separation (BSS) by departing from the Usual Linear Model and focusing on the Linear-quadratic (LQ) Model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for Linear BSS, and is referred to as SNPALQ. By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments.Comment: 23 pages + 24 pages of Appendix containing the proof
Gillis Nicolas - One of the best experts on this subject based on the ideXlab platform.
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Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures
'Institute of Electrical and Electronics Engineers (IEEE)', 2021Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:International audienceIn this work, we tackle the problem of hyperspectral unmixing by departing from the Usual Linear Model and focusing on a Linear-quadratic (LQ) one. The algorithm we propose, coined Successive Nonnegative Projection Algorithm for Linear Quadratic mixtures (SNPALQ), extends the Successive Nonnegative Projection Algorithm (SNPA), specifically designed to address the unmixing problem under a Linear non-negative Model and the pure-pixel assumption (a.k.a. near-separable assumption). By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. The approach is shown to be relevant in realistic numerical experiments, which further highlight that SNPALQ is robust to noise
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Provably robust blind source separation of Linear-quadratic near-separable mixtures
'The Japan Society for Industrial and Applied Mathematics', 2021Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:International audienceIn this work, we consider the problem of blind source separation (BSS) by departing from the Usual Linear Model and focusing on the Linear-quadratic (LQ) Model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for Linear BSS, and is referred to as SNPALQ. By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments
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Provably robust blind source separation of Linear-quadratic near-separable mixtures
2020Co-Authors: Kervazo Christophe, Gillis Nicolas, Dobigeon NicolasAbstract:In this work, we consider the problem of blind source separation (BSS) by departing from the Usual Linear Model and focusing on the Linear-quadratic (LQ) Model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for Linear BSS, and is referred to as SNPALQ. By explicitly Modeling the product terms inherent to the LQ Model along the iterations of the SNPA scheme, the nonLinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments.Comment: 23 pages + 24 pages of Appendix containing the proof
Yasushi Kondo - One of the best experts on this subject based on the ideXlab platform.
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hedonic price index estimation under mean independence of time dummies from quality characteristics
Social Science Research Network, 2003Co-Authors: Yasushi Kondo, Myoungjae LeeAbstract:We estimate hedonic price indices (HPI) for rental offices in Tokyo for the period 1985-1991. We take a partially Linear regression (PLR) Model, Linear in x (year dummies) and nonparametric in z (office quality characteristics), as our main Model; the Usual Linear Model is used as well. Since x consists of year dummies, the Linearity in x is not a restriction in the PLR Model; the only restriction is that of no interaction between x and z. For the PLR Model, the HPI are estimated pN-consistently with a two-stage procedure. For our data, x turns out to be (almost) mean-independent of z. This implies that least squares estimation (LSE) for Models with a misspecified function for z is still consistent. The meanindependence also leads to an efficiency result that, under heteroskedasticity of unknown form, the two-stage PLR Model estimator is at least as efficient as any LSE for Models specifying (rightly or wrongly) the part for z. In addition to these, several interesting practical lessons are noted in doing the two-stage PLR Model estimation. First, the cross validation (CV) used in the PLR Model literature can fail if the mean-independence is ignored. Second, high order kernels can make the CV criterion function ill behaved. Third, product kernels work as well as spherically symmetric kernels. Fourth, nonparametric specification tests may work poorly due to a sample splitting problem with outliers in the data or due to choosing more than one bandwidth; in this regard, a test suggested by Stute (1997) and Stute et al. (1998) is recommended.
Myoungjae Lee - One of the best experts on this subject based on the ideXlab platform.
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hedonic price index estimation under mean independence of time dummies from quality characteristics
Social Science Research Network, 2003Co-Authors: Yasushi Kondo, Myoungjae LeeAbstract:We estimate hedonic price indices (HPI) for rental offices in Tokyo for the period 1985-1991. We take a partially Linear regression (PLR) Model, Linear in x (year dummies) and nonparametric in z (office quality characteristics), as our main Model; the Usual Linear Model is used as well. Since x consists of year dummies, the Linearity in x is not a restriction in the PLR Model; the only restriction is that of no interaction between x and z. For the PLR Model, the HPI are estimated pN-consistently with a two-stage procedure. For our data, x turns out to be (almost) mean-independent of z. This implies that least squares estimation (LSE) for Models with a misspecified function for z is still consistent. The meanindependence also leads to an efficiency result that, under heteroskedasticity of unknown form, the two-stage PLR Model estimator is at least as efficient as any LSE for Models specifying (rightly or wrongly) the part for z. In addition to these, several interesting practical lessons are noted in doing the two-stage PLR Model estimation. First, the cross validation (CV) used in the PLR Model literature can fail if the mean-independence is ignored. Second, high order kernels can make the CV criterion function ill behaved. Third, product kernels work as well as spherically symmetric kernels. Fourth, nonparametric specification tests may work poorly due to a sample splitting problem with outliers in the data or due to choosing more than one bandwidth; in this regard, a test suggested by Stute (1997) and Stute et al. (1998) is recommended.
