Projection Function

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Yujun Zhao - One of the best experts on this subject based on the ideXlab platform.

  • an intrinsic representation of atomic structure from clusters to periodic systems
    Journal of Chemical Physics, 2017
    Co-Authors: Xiaotian Li, Xiaobao Yang, Shaogang Xu, Yujun Zhao
    Abstract:

    We have improved our distance matrix and eigen-subspace Projection Function (EPF) [X.-T. Li et al., J. Chem. Phys. 146, 154108 (2017)] to describe the atomic structure for periodic systems. Depicting the local structure of an atom, the EPF turns out to be invariant with respect to the choices of the unit cell and coordinate frame, leading to an intrinsic representation of the crystal with a set of EPFs of the nontrivial atoms. The difference of EPFs reveals the difference of atoms in local structure, while the accumulated difference between two sets of EPFs can be taken as the distance between configurations. Exemplified with the cases of carbon allotropes and boron sheets, our EPF approach shows exceptional rationality and efficiency to distinguish the atomic structures, which is crucial in structure recognition, comparison, and analysis.

  • geometrical eigen subspace framework based molecular conformation representation for efficient structure recognition and comparison
    Journal of Chemical Physics, 2017
    Co-Authors: Xiaobao Yang, Yujun Zhao
    Abstract:

    We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace Projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace Projection Function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.

  • geometrical eigen subspace framework based molecular conformation representation for efficient structure recognition and comparison
    arXiv: Materials Science, 2017
    Co-Authors: Xiaobao Yang, Yujun Zhao
    Abstract:

    We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace Projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace Projection Function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance in the eigen-space can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.

Xiaobao Yang - One of the best experts on this subject based on the ideXlab platform.

  • an intrinsic representation of atomic structure from clusters to periodic systems
    Journal of Chemical Physics, 2017
    Co-Authors: Xiaotian Li, Xiaobao Yang, Shaogang Xu, Yujun Zhao
    Abstract:

    We have improved our distance matrix and eigen-subspace Projection Function (EPF) [X.-T. Li et al., J. Chem. Phys. 146, 154108 (2017)] to describe the atomic structure for periodic systems. Depicting the local structure of an atom, the EPF turns out to be invariant with respect to the choices of the unit cell and coordinate frame, leading to an intrinsic representation of the crystal with a set of EPFs of the nontrivial atoms. The difference of EPFs reveals the difference of atoms in local structure, while the accumulated difference between two sets of EPFs can be taken as the distance between configurations. Exemplified with the cases of carbon allotropes and boron sheets, our EPF approach shows exceptional rationality and efficiency to distinguish the atomic structures, which is crucial in structure recognition, comparison, and analysis.

  • geometrical eigen subspace framework based molecular conformation representation for efficient structure recognition and comparison
    Journal of Chemical Physics, 2017
    Co-Authors: Xiaobao Yang, Yujun Zhao
    Abstract:

    We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace Projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace Projection Function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.

  • geometrical eigen subspace framework based molecular conformation representation for efficient structure recognition and comparison
    arXiv: Materials Science, 2017
    Co-Authors: Xiaobao Yang, Yujun Zhao
    Abstract:

    We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace Projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace Projection Function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance in the eigen-space can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.

Soushi Suzuki - One of the best experts on this subject based on the ideXlab platform.

  • regional efficiency improvement by means of data envelopment analysis through euclidean distance minimization including fixed input factors an application to tourist regions in italy
    2011
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld
    Abstract:

    Standard Data Envelopment Analysis (DEA) is characterized by uniform proportional input reduction or output augmentation in calculating improvement Projections. This paper develops a new Euclidean Distance Minimization model in the context of DEA in order to derive a more appropriate efficiency-improving Projection model by means of a weighted Projection Function. The model is extended to the situation where some factor inputs are fixed, for instance, due to lumpiness or natural constraints. The extended DEA model is illustrated in the context of regional planning by using a data set on Italian tourist destination regions.

  • regional efficiency improvement by means of data envelopment analysis through euclidean distance minimization including fixed input factors an application to tourist regions in italy
    2011
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld
    Abstract:

    See also the article in Papers in Regional Science (2011). Volume 90, issue 1, pages 67-90. Standard Data Envelopment Analysis (DEA) is characterized by uniform proportional input reduction or output augmentation in calculating improvement Projections. This paper develops a new Euclidean Distance Minimization model in the context of DEA in order to derive a more appropriate efficiency-improving Projection model by means of a weighted Projection Function. The model is extended to the situation where some factor inputs are fixed, for instance, due to lumpiness or natural constraints. The extended DEA model is illustrated in the context of regional planning by using a data set on Italian tourist destination regions.

  • regional efficiency improvement by means of data envelopment analysis through euclidean distance minimization including fixed input factors an application to tourist regions in italy
    Papers in Regional Science, 2011
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld
    Abstract:

    Standard Data Envelopment Analysis (DEA) is characterized by uniform proportional input reduction or output augmentation in calculating improvement Projections. This paper develops a new Euclidean Distance Minimization model in the context of DEA in order to derive a more appropriate efficiency-improving Projection model by means of a weighted Projection Function. The model is extended to the situation where some factor inputs are fixed, for instance, due to lumpiness or natural constraints. The extended DEA model is illustrated in the context of regional planning by using a data set on Italian tourist destination regions. Resumen El analisis envolvente de datos (DEA en ingles) estandar se caracteriza por la reduccion de insumos o el aumento de productos de manera proporcional y uniforme a la hora de calcular proyecciones sobre mejoras. Este articulo desarrolla un nuevo modelo de Minimizacion de la Distancia Euclidiana en el contexto de DEA para inferir un modelo de proyeccion de eficacia-mejora mas apropiado por medio de una funcion de proyeccion ponderada. El modelo se amplio a una situacion en la que varios factores insumos son fijos, por ejemplo debido al apelmazamiento o restricciones naturales. El modelo DEA ampliado se ilustra dentro del contexto de la planificacion regional, utilizando un conjunto de datos sobre regiones italianas que son destinos turisticos.

  • a distance friction minimization approach in data envelopment analysis a comparative study on airport efficiency
    European Journal of Operational Research, 2010
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld, Eric Pels
    Abstract:

    This paper aims to present a newly developed distance friction minimization (DFM) method in the context of data envelopment analysis (DEA) in order to generate an appropriate (non-radial) efficiency-improving Projection model, for both input reduction and output increase. In this approach, a generalized distance Function, based on a Euclidean distance metric in weighted spaces, is proposed to assist a decision making unit (DMU) to improve its performance by an appropriate movement towards the efficiency frontier surface. A suitable form of multidimensional Projection Function for efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model. The paper describes the various steps involved in a systematic manner. The above-mentioned DFM model is illustrated empirically by using a data set on 30 European airports, where the aim is to present a comparative analysis of the efficiency of operational management in these airports. In addition, the comparative analysis of these airports is able to assess both input slacks and output slacks (or a combination of input reduction and output rise).

Piet Rietveld - One of the best experts on this subject based on the ideXlab platform.

  • regional efficiency improvement by means of data envelopment analysis through euclidean distance minimization including fixed input factors an application to tourist regions in italy
    2011
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld
    Abstract:

    Standard Data Envelopment Analysis (DEA) is characterized by uniform proportional input reduction or output augmentation in calculating improvement Projections. This paper develops a new Euclidean Distance Minimization model in the context of DEA in order to derive a more appropriate efficiency-improving Projection model by means of a weighted Projection Function. The model is extended to the situation where some factor inputs are fixed, for instance, due to lumpiness or natural constraints. The extended DEA model is illustrated in the context of regional planning by using a data set on Italian tourist destination regions.

  • regional efficiency improvement by means of data envelopment analysis through euclidean distance minimization including fixed input factors an application to tourist regions in italy
    2011
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld
    Abstract:

    See also the article in Papers in Regional Science (2011). Volume 90, issue 1, pages 67-90. Standard Data Envelopment Analysis (DEA) is characterized by uniform proportional input reduction or output augmentation in calculating improvement Projections. This paper develops a new Euclidean Distance Minimization model in the context of DEA in order to derive a more appropriate efficiency-improving Projection model by means of a weighted Projection Function. The model is extended to the situation where some factor inputs are fixed, for instance, due to lumpiness or natural constraints. The extended DEA model is illustrated in the context of regional planning by using a data set on Italian tourist destination regions.

  • regional efficiency improvement by means of data envelopment analysis through euclidean distance minimization including fixed input factors an application to tourist regions in italy
    Papers in Regional Science, 2011
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld
    Abstract:

    Standard Data Envelopment Analysis (DEA) is characterized by uniform proportional input reduction or output augmentation in calculating improvement Projections. This paper develops a new Euclidean Distance Minimization model in the context of DEA in order to derive a more appropriate efficiency-improving Projection model by means of a weighted Projection Function. The model is extended to the situation where some factor inputs are fixed, for instance, due to lumpiness or natural constraints. The extended DEA model is illustrated in the context of regional planning by using a data set on Italian tourist destination regions. Resumen El analisis envolvente de datos (DEA en ingles) estandar se caracteriza por la reduccion de insumos o el aumento de productos de manera proporcional y uniforme a la hora de calcular proyecciones sobre mejoras. Este articulo desarrolla un nuevo modelo de Minimizacion de la Distancia Euclidiana en el contexto de DEA para inferir un modelo de proyeccion de eficacia-mejora mas apropiado por medio de una funcion de proyeccion ponderada. El modelo se amplio a una situacion en la que varios factores insumos son fijos, por ejemplo debido al apelmazamiento o restricciones naturales. El modelo DEA ampliado se ilustra dentro del contexto de la planificacion regional, utilizando un conjunto de datos sobre regiones italianas que son destinos turisticos.

  • a distance friction minimization approach in data envelopment analysis a comparative study on airport efficiency
    European Journal of Operational Research, 2010
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld, Eric Pels
    Abstract:

    This paper aims to present a newly developed distance friction minimization (DFM) method in the context of data envelopment analysis (DEA) in order to generate an appropriate (non-radial) efficiency-improving Projection model, for both input reduction and output increase. In this approach, a generalized distance Function, based on a Euclidean distance metric in weighted spaces, is proposed to assist a decision making unit (DMU) to improve its performance by an appropriate movement towards the efficiency frontier surface. A suitable form of multidimensional Projection Function for efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model. The paper describes the various steps involved in a systematic manner. The above-mentioned DFM model is illustrated empirically by using a data set on 30 European airports, where the aim is to present a comparative analysis of the efficiency of operational management in these airports. In addition, the comparative analysis of these airports is able to assess both input slacks and output slacks (or a combination of input reduction and output rise).

Eric Pels - One of the best experts on this subject based on the ideXlab platform.

  • a distance friction minimization approach in data envelopment analysis a comparative study on airport efficiency
    European Journal of Operational Research, 2010
    Co-Authors: Soushi Suzuki, Peter Nijkamp, Piet Rietveld, Eric Pels
    Abstract:

    This paper aims to present a newly developed distance friction minimization (DFM) method in the context of data envelopment analysis (DEA) in order to generate an appropriate (non-radial) efficiency-improving Projection model, for both input reduction and output increase. In this approach, a generalized distance Function, based on a Euclidean distance metric in weighted spaces, is proposed to assist a decision making unit (DMU) to improve its performance by an appropriate movement towards the efficiency frontier surface. A suitable form of multidimensional Projection Function for efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model. The paper describes the various steps involved in a systematic manner. The above-mentioned DFM model is illustrated empirically by using a data set on 30 European airports, where the aim is to present a comparative analysis of the efficiency of operational management in these airports. In addition, the comparative analysis of these airports is able to assess both input slacks and output slacks (or a combination of input reduction and output rise).