The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform

Gert R. G. Lanckriet - One of the best experts on this subject based on the ideXlab platform.

  • A Direct Formulation for Sparse PCA Using Semidefinite Programming
    SIAM Review, 2007
    Co-Authors: Alexandre D'aspremont, Laurent El Ghaoui, Michael I. Jordan, Gert R. G. Lanckriet
    Abstract:

    Given a covariance matrix, we consider the problem of maximizing the variance explained by a particular linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This problem arises in the decomposition of a covariance matrix into sparse factors or sparse principal component analysis (PCA), and has wide applications ranging from biology to finance. We use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming-based relaxation for our problem. We also discuss Nesterov's smooth minimization technique applied to the semidefinite program arising in the semidefinite relaxation of the sparse PCA problem. The method has complexity $O(n^4 \sqrt{\log(n)}/\epsilon)$, where $n$ is the size of the underlying covariance matrix and $\epsilon$ is the desired absolute accuracy on the optimal value of the problem.

  • a Direct Formulation for sparse pca using semidefinite programming
    Neural Information Processing Systems, 2004
    Co-Authors: Alexandre Daspremont, Laurent El Ghaoui, Michael I. Jordan, Gert R. G. Lanckriet
    Abstract:

    We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming based relaxation for our problem.

  • NIPS - A Direct Formulation for Sparse PCA Using Semidefinite Programming
    2004
    Co-Authors: Alexandre D'aspremont, Laurent El Ghaoui, Michael I. Jordan, Gert R. G. Lanckriet
    Abstract:

    We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming based relaxation for our problem.

  • A Direct Formulation for Sparse Pca Using Semidefinite Programming
    SSRN Electronic Journal, 2004
    Co-Authors: Alexandre D'aspremont, Laurent El Ghaoui, Michael I. Jordan, Gert R. G. Lanckriet
    Abstract:

    We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming based relaxation for our problem. We also discuss Nesterov's smooth minimization technique applied to the SDP arising in the Direct sparse PCA method.

Fulin Tang - One of the best experts on this subject based on the ideXlab platform.

  • fmd stereo slam fusing mvg and Direct Formulation towards accurate and fast stereo slam
    International Conference on Robotics and Automation, 2019
    Co-Authors: Fulin Tang
    Abstract:

    We propose a novel stereo visual SLAM framework considering both accuracy and speed at the same time. The framework makes full use of the advantages of key-feature-based multiple view geometry (MVG) and Direct-based Formulation. At the front-end, our system performs Direct Formulation and constant motion model to predict a robust initial pose, reprojects local map to find 3D-2D correspondence and finally refines pose by the reprojection error minimization. This frontend process makes our system faster. At the back-end, MVG is used to estimate 3D structure. When a new keyframe is inserted, new mappoints are generated by triangulating. In order to improve the accuracy of the proposed system, bad mappoints are removed and a global map is kept by bundle adjustment. Especially, the stereo constraint is performed to optimize the map. This back-end process makes our system more accurate. Experimental evaluation on EuRoC dataset shows that the proposed algorithm can run at more than 100 frames per second on a consumer computer while achieving highly competitive accuracy.

  • ICRA - FMD Stereo SLAM: Fusing MVG and Direct Formulation Towards Accurate and Fast Stereo SLAM
    2019 International Conference on Robotics and Automation (ICRA), 2019
    Co-Authors: Fulin Tang
    Abstract:

    We propose a novel stereo visual SLAM framework considering both accuracy and speed at the same time. The framework makes full use of the advantages of key-feature-based multiple view geometry (MVG) and Direct-based Formulation. At the front-end, our system performs Direct Formulation and constant motion model to predict a robust initial pose, reprojects local map to find 3D-2D correspondence and finally refines pose by the reprojection error minimization. This frontend process makes our system faster. At the back-end, MVG is used to estimate 3D structure. When a new keyframe is inserted, new mappoints are generated by triangulating. In order to improve the accuracy of the proposed system, bad mappoints are removed and a global map is kept by bundle adjustment. Especially, the stereo constraint is performed to optimize the map. This back-end process makes our system more accurate. Experimental evaluation on EuRoC dataset shows that the proposed algorithm can run at more than 100 frames per second on a consumer computer while achieving highly competitive accuracy.

Teddy M. Keller - One of the best experts on this subject based on the ideXlab platform.

  • Direct Formulation of nanocrystalline silicon carbide/nitride solid ceramics
    Journal of Materials Science, 2017
    Co-Authors: Teddy M. Keller, Andrew P. Saab, Matthew Laskoski, Boris Dyatkin, Syed B. Qadri, Manoj Kolel-veetil
    Abstract:

    We developed a new in situ reaction method to synthesize SiC and Si_3N_4 ceramic solids from meltable precursor compositions into shaped ceramic composites with nanocrystalline grains. The process uses Si powder and 1,2,4,5-tetrakis(phenylethynyl)benzene, which readily react above 1400 °C to form the SiC and Si_3N_4 crystallites in the presence of argon and nitrogen, respectively. X-ray diffraction analysis, Raman spectroscopy and density measurements indicated the formation of near stoichiometric SiC and Si_3N_4 within the shaped solid. Further characterization of electrical conductivity and oxidative stability of the prepared ceramics analyzed the influence of nanoscale features on intrinsic properties of resulting composites. The hardness and elastic modulus values for the synthesized SiC determined by nanoindentation varied in the range of 25–46 GPa and 300–440 GPa.Graphical Abstract

  • Direct Formulation of nanocrystalline silicon carbide nitride solid ceramics
    Journal of Materials Science, 2017
    Co-Authors: Teddy M. Keller, Andrew P. Saab, Matthew Laskoski, Boris Dyatkin, Syed B. Qadri, Manoj K Kolelveetil
    Abstract:

    We developed a new in situ reaction method to synthesize SiC and Si3N4 ceramic solids from meltable precursor compositions into shaped ceramic composites with nanocrystalline grains. The process uses Si powder and 1,2,4,5-tetrakis(phenylethynyl)benzene, which readily react above 1400 °C to form the SiC and Si3N4 crystallites in the presence of argon and nitrogen, respectively. X-ray diffraction analysis, Raman spectroscopy and density measurements indicated the formation of near stoichiometric SiC and Si3N4 within the shaped solid. Further characterization of electrical conductivity and oxidative stability of the prepared ceramics analyzed the influence of nanoscale features on intrinsic properties of resulting composites. The hardness and elastic modulus values for the synthesized SiC determined by nanoindentation varied in the range of 25–46 GPa and 300–440 GPa.

Manoj Kolel-veetil - One of the best experts on this subject based on the ideXlab platform.

  • Direct Formulation of nanocrystalline silicon carbide/nitride solid ceramics
    Journal of Materials Science, 2017
    Co-Authors: Teddy M. Keller, Andrew P. Saab, Matthew Laskoski, Boris Dyatkin, Syed B. Qadri, Manoj Kolel-veetil
    Abstract:

    We developed a new in situ reaction method to synthesize SiC and Si_3N_4 ceramic solids from meltable precursor compositions into shaped ceramic composites with nanocrystalline grains. The process uses Si powder and 1,2,4,5-tetrakis(phenylethynyl)benzene, which readily react above 1400 °C to form the SiC and Si_3N_4 crystallites in the presence of argon and nitrogen, respectively. X-ray diffraction analysis, Raman spectroscopy and density measurements indicated the formation of near stoichiometric SiC and Si_3N_4 within the shaped solid. Further characterization of electrical conductivity and oxidative stability of the prepared ceramics analyzed the influence of nanoscale features on intrinsic properties of resulting composites. The hardness and elastic modulus values for the synthesized SiC determined by nanoindentation varied in the range of 25–46 GPa and 300–440 GPa.Graphical Abstract

Manoj K Kolelveetil - One of the best experts on this subject based on the ideXlab platform.

  • Direct Formulation of nanocrystalline silicon carbide nitride solid ceramics
    Journal of Materials Science, 2017
    Co-Authors: Teddy M. Keller, Andrew P. Saab, Matthew Laskoski, Boris Dyatkin, Syed B. Qadri, Manoj K Kolelveetil
    Abstract:

    We developed a new in situ reaction method to synthesize SiC and Si3N4 ceramic solids from meltable precursor compositions into shaped ceramic composites with nanocrystalline grains. The process uses Si powder and 1,2,4,5-tetrakis(phenylethynyl)benzene, which readily react above 1400 °C to form the SiC and Si3N4 crystallites in the presence of argon and nitrogen, respectively. X-ray diffraction analysis, Raman spectroscopy and density measurements indicated the formation of near stoichiometric SiC and Si3N4 within the shaped solid. Further characterization of electrical conductivity and oxidative stability of the prepared ceramics analyzed the influence of nanoscale features on intrinsic properties of resulting composites. The hardness and elastic modulus values for the synthesized SiC determined by nanoindentation varied in the range of 25–46 GPa and 300–440 GPa.