Relative Maximum

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Yanmin Niu - One of the best experts on this subject based on the ideXlab platform.

  • new one versus all ν svm solving intra inter class imbalance with extended manifold regularization and localized Relative Maximum margin
    Neurocomputing, 2013
    Co-Authors: Xuchu Wang, Yanmin Niu
    Abstract:

    Abstract The optimal separating hyperplane with Maximum margin plays a central role in the support vector machine (SVM) classifiers, but is exclusively determined by the support vectors that does not take any structure information into account, especially in the one-versus-all (OVA) SVM for the multi-class classification application where the positive samples and negative ones are usually unbalanced. To address this intra–inter class imbalance problem, a new OVA SVM method is proposed by extending manifold regularization and enhancing the Relative Maximum margin. It aims to minimize the scatter of nearby intra-class point pairs while penalize that of nearby inter-class point pairs not being arbitrarily large through the constraints of marginal separation and manifold regularization. This objective is transformed into a constrained optimization problem that overcomes both the classical SVM's weakness of ignoring the data underlying structure, and the Laplacian SVM's weakness of abandoning class label information and class separation of manifolds. It also takes the positive and negative samples into different consideration according to their unbalanced distribution. Additionally, risk bounds are derived for the proposed formulation based on the theory of Rademacher complexity and the improvement on the bounds of standard SVM is proven. The comparative experiments for multi-class classification, face recognition, and natural image segmentation on several synthetic and benchmark data sets validate the effectiveness of the proposed method and indicate the consideration of both preserving intrinsic within-class manifold structure and bounding the local Relative margin between class is helpful to improve the OVA SVM classification performance.

  • New one-versus-all ν-SVM solving intra–inter class imbalance with extended manifold regularization and localized Relative Maximum margin
    Neurocomputing, 2013
    Co-Authors: Xuchu Wang, Yanmin Niu
    Abstract:

    Abstract The optimal separating hyperplane with Maximum margin plays a central role in the support vector machine (SVM) classifiers, but is exclusively determined by the support vectors that does not take any structure information into account, especially in the one-versus-all (OVA) SVM for the multi-class classification application where the positive samples and negative ones are usually unbalanced. To address this intra–inter class imbalance problem, a new OVA SVM method is proposed by extending manifold regularization and enhancing the Relative Maximum margin. It aims to minimize the scatter of nearby intra-class point pairs while penalize that of nearby inter-class point pairs not being arbitrarily large through the constraints of marginal separation and manifold regularization. This objective is transformed into a constrained optimization problem that overcomes both the classical SVM's weakness of ignoring the data underlying structure, and the Laplacian SVM's weakness of abandoning class label information and class separation of manifolds. It also takes the positive and negative samples into different consideration according to their unbalanced distribution. Additionally, risk bounds are derived for the proposed formulation based on the theory of Rademacher complexity and the improvement on the bounds of standard SVM is proven. The comparative experiments for multi-class classification, face recognition, and natural image segmentation on several synthetic and benchmark data sets validate the effectiveness of the proposed method and indicate the consideration of both preserving intrinsic within-class manifold structure and bounding the local Relative margin between class is helpful to improve the OVA SVM classification performance.

Xuchu Wang - One of the best experts on this subject based on the ideXlab platform.

  • new one versus all ν svm solving intra inter class imbalance with extended manifold regularization and localized Relative Maximum margin
    Neurocomputing, 2013
    Co-Authors: Xuchu Wang, Yanmin Niu
    Abstract:

    Abstract The optimal separating hyperplane with Maximum margin plays a central role in the support vector machine (SVM) classifiers, but is exclusively determined by the support vectors that does not take any structure information into account, especially in the one-versus-all (OVA) SVM for the multi-class classification application where the positive samples and negative ones are usually unbalanced. To address this intra–inter class imbalance problem, a new OVA SVM method is proposed by extending manifold regularization and enhancing the Relative Maximum margin. It aims to minimize the scatter of nearby intra-class point pairs while penalize that of nearby inter-class point pairs not being arbitrarily large through the constraints of marginal separation and manifold regularization. This objective is transformed into a constrained optimization problem that overcomes both the classical SVM's weakness of ignoring the data underlying structure, and the Laplacian SVM's weakness of abandoning class label information and class separation of manifolds. It also takes the positive and negative samples into different consideration according to their unbalanced distribution. Additionally, risk bounds are derived for the proposed formulation based on the theory of Rademacher complexity and the improvement on the bounds of standard SVM is proven. The comparative experiments for multi-class classification, face recognition, and natural image segmentation on several synthetic and benchmark data sets validate the effectiveness of the proposed method and indicate the consideration of both preserving intrinsic within-class manifold structure and bounding the local Relative margin between class is helpful to improve the OVA SVM classification performance.

  • New one-versus-all ν-SVM solving intra–inter class imbalance with extended manifold regularization and localized Relative Maximum margin
    Neurocomputing, 2013
    Co-Authors: Xuchu Wang, Yanmin Niu
    Abstract:

    Abstract The optimal separating hyperplane with Maximum margin plays a central role in the support vector machine (SVM) classifiers, but is exclusively determined by the support vectors that does not take any structure information into account, especially in the one-versus-all (OVA) SVM for the multi-class classification application where the positive samples and negative ones are usually unbalanced. To address this intra–inter class imbalance problem, a new OVA SVM method is proposed by extending manifold regularization and enhancing the Relative Maximum margin. It aims to minimize the scatter of nearby intra-class point pairs while penalize that of nearby inter-class point pairs not being arbitrarily large through the constraints of marginal separation and manifold regularization. This objective is transformed into a constrained optimization problem that overcomes both the classical SVM's weakness of ignoring the data underlying structure, and the Laplacian SVM's weakness of abandoning class label information and class separation of manifolds. It also takes the positive and negative samples into different consideration according to their unbalanced distribution. Additionally, risk bounds are derived for the proposed formulation based on the theory of Rademacher complexity and the improvement on the bounds of standard SVM is proven. The comparative experiments for multi-class classification, face recognition, and natural image segmentation on several synthetic and benchmark data sets validate the effectiveness of the proposed method and indicate the consideration of both preserving intrinsic within-class manifold structure and bounding the local Relative margin between class is helpful to improve the OVA SVM classification performance.

Dieter Rosenbaum - One of the best experts on this subject based on the ideXlab platform.

  • development of healthy children s feet nine year results of a longitudinal investigation of plantar loading patterns
    Gait & Posture, 2010
    Co-Authors: Kerstin Bosch, Joachim Gers, Dieter Rosenbaum
    Abstract:

    Abstract The purpose of the present study was to provide normative data for foot loading patterns and foot form parameters in order to support decisions about the normal or abnormal development of the growing foot during childhood. In a longitudinal design, 36 healthy German children were followed over the course of nine years. The children had a mean age of 14.6 ± 1.8 months at the first appointment and 122.8 ± 2.0 months at the last appointment. The children participated in 17 measurement appointments every 3, 6 or 12 months. Dynamic foot loading was evaluated with plantar pressure measurements during walking and static footprints were taken to determine changes in foot form. During the investigation period an increase of peak pressures of the total foot by 190%, of the Relative Maximum force of the total foot by 20% and the foot length by 90% was observed. A decrease for the Relative Maximum force under the midfoot (63%) and for the arch index (49%) could also be demonstrated. Furthermore, body height showed a significant influence on foot length and midfoot width. Body weight had a significant influence on the static parameter midfoot width. Between genders, boys showed a significant wider midfoot and a smaller forefoot contact area as compared to girls. The established database can be used as comparative values for clinical decisions about the normal foot development.

  • Development of healthy children's feet—Nine-year results of a longitudinal investigation of plantar loading patterns
    Gait & posture, 2010
    Co-Authors: Kerstin Bosch, Joachim Gerß, Dieter Rosenbaum
    Abstract:

    The purpose of the present study was to provide normative data for foot loading patterns and foot form parameters in order to support decisions about the normal or abnormal development of the growing foot during childhood. In a longitudinal design, 36 healthy German children were followed over the course of nine years. The children had a mean age of 14.6 ± 1.8 months at the first appointment and 122.8 ± 2.0 months at the last appointment. The children participated in 17 measurement appointments every 3, 6 or 12 months. Dynamic foot loading was evaluated with plantar pressure measurements during walking and static footprints were taken to determine changes in foot form. During the investigation period an increase of peak pressures of the total foot by 190%, of the Relative Maximum force of the total foot by 20% and the foot length by 90% was observed. A decrease for the Relative Maximum force under the midfoot (63%) and for the arch index (49%) could also be demonstrated. Furthermore, body height showed a significant influence on foot length and midfoot width. Body weight had a significant influence on the static parameter midfoot width. Between genders, boys showed a significant wider midfoot and a smaller forefoot contact area as compared to girls. The established database can be used as comparative values for clinical decisions about the normal foot development.

Erkan Afacan - One of the best experts on this subject based on the ideXlab platform.

  • An Inequality for the Calculation of Relative Maximum Sideband Level in Time-Modulated Linear and Planar Arrays
    IEEE Transactions on Antennas and Propagation, 2014
    Co-Authors: Ertugrul Aksoy, Erkan Afacan
    Abstract:

    In this work, the Maximum point of Relative sideband level (SBL) with respect to Maximum level of main radiation (the radiation in carrier frequency) in time-modulated linear and planar arrays is examined. An inequality is derived which may be used for the determination and suppression of Maximum Relative sideband level. Performance analysis in terms of sideband level, harmonic power loss, directivity and feed network efficiency are conducted with state of the art methods to compare and to demonstrate the potential of the presented formulation for linear and planar cases.

Kerstin Bosch - One of the best experts on this subject based on the ideXlab platform.

  • development of healthy children s feet nine year results of a longitudinal investigation of plantar loading patterns
    Gait & Posture, 2010
    Co-Authors: Kerstin Bosch, Joachim Gers, Dieter Rosenbaum
    Abstract:

    Abstract The purpose of the present study was to provide normative data for foot loading patterns and foot form parameters in order to support decisions about the normal or abnormal development of the growing foot during childhood. In a longitudinal design, 36 healthy German children were followed over the course of nine years. The children had a mean age of 14.6 ± 1.8 months at the first appointment and 122.8 ± 2.0 months at the last appointment. The children participated in 17 measurement appointments every 3, 6 or 12 months. Dynamic foot loading was evaluated with plantar pressure measurements during walking and static footprints were taken to determine changes in foot form. During the investigation period an increase of peak pressures of the total foot by 190%, of the Relative Maximum force of the total foot by 20% and the foot length by 90% was observed. A decrease for the Relative Maximum force under the midfoot (63%) and for the arch index (49%) could also be demonstrated. Furthermore, body height showed a significant influence on foot length and midfoot width. Body weight had a significant influence on the static parameter midfoot width. Between genders, boys showed a significant wider midfoot and a smaller forefoot contact area as compared to girls. The established database can be used as comparative values for clinical decisions about the normal foot development.

  • Development of healthy children's feet—Nine-year results of a longitudinal investigation of plantar loading patterns
    Gait & posture, 2010
    Co-Authors: Kerstin Bosch, Joachim Gerß, Dieter Rosenbaum
    Abstract:

    The purpose of the present study was to provide normative data for foot loading patterns and foot form parameters in order to support decisions about the normal or abnormal development of the growing foot during childhood. In a longitudinal design, 36 healthy German children were followed over the course of nine years. The children had a mean age of 14.6 ± 1.8 months at the first appointment and 122.8 ± 2.0 months at the last appointment. The children participated in 17 measurement appointments every 3, 6 or 12 months. Dynamic foot loading was evaluated with plantar pressure measurements during walking and static footprints were taken to determine changes in foot form. During the investigation period an increase of peak pressures of the total foot by 190%, of the Relative Maximum force of the total foot by 20% and the foot length by 90% was observed. A decrease for the Relative Maximum force under the midfoot (63%) and for the arch index (49%) could also be demonstrated. Furthermore, body height showed a significant influence on foot length and midfoot width. Body weight had a significant influence on the static parameter midfoot width. Between genders, boys showed a significant wider midfoot and a smaller forefoot contact area as compared to girls. The established database can be used as comparative values for clinical decisions about the normal foot development.