Parameterization is one of the key problems in the construction of a curve to interpolate a set of ordered points. We propose a new local parameterization method based on the curvature model in this paper. The new met...Parameterization is one of the key problems in the construction of a curve to interpolate a set of ordered points. We propose a new local parameterization method based on the curvature model in this paper. The new method determines the knots by mi- nimizing the maximum curvature of quadratic curve. When the knots by the new method are used to construct interpolation curve, the constructed curve have good precision. We also give some comparisons of the new method with existing methods, and our method can perform better in interpolation error, and the interpolated curve is more fairing.展开更多
Information on the population distribution at the building scale can help governments make supplemental decisions to address complex urban management issues.However,the discontinuity and strong spatial heterogeneity o...Information on the population distribution at the building scale can help governments make supplemental decisions to address complex urban management issues.However,the discontinuity and strong spatial heterogeneity of research units at the building scale make it challenging to fuse multi-source geographic data,which causes significant errors in population estimation.To address this problem,this study proposes a method for population estimation at the building scale based on Dual-Environment Feature Fusion(DEFF).The dual environments of buildings were constructed by splitting the physical boundaries and extracting features suitable for the dual-environment scale from multi-source geographic data to describe the complex environmental features of buildings.Meanwhile,Data Quality Weighting based Technique for Order of Preference by Similarity to Ideal Solution(DQW-TOPSIS)method was proposed to assign appropriate weights to the features of the external environment for better feature fusion.Finally,a regression model was established using dual-environment features for building-scale population estimation.The experimental areas chosen for this study were Jianghan and Wuchang Districts,both located in Wuhan City,China.The estimated results of the DEFF were compared with those of the ablation experiments,as well as three publicly accessible population datasets,specifically LandScan,WorldPop,and GHS-POP,at the community scale.The evaluation results showed that DEFF had an R2 of approximately 0.8,Mean Absolute Error(MAE)of approximately 1200,Root Mean Square Error(RMSE)of approximately 1700,and both Mean Absolute Percentage Error(MAPE)and Symmetric Mean Absolute Percentage Error(SMAPE)of approximately 26%,indicating an improved performance and verifying the validity of the proposed method for fine-scale population estimation.展开更多
Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applicat...Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applications, Springer-Verlag, （2006） 83, pp. 25-33], the Pool-Adjazent-Violators algorithm （PAV） was generalized from completely to partially ordered data sets （posets）. The new algorithm, called CPAV, is characterized by the very low computational complexity, which is of second order in the number of observations. It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The CPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted CPAV solution is optimal. Furthermore, we present results of extensive numerical experiments, from which we draw conclusions about the most and the least preferable topological orders.展开更多
基金Supported by National Research Foundation for the Doctoral Program of Higher Education of China(20110131130004)Independent Innovation Foundation of Shandong University,IIFSDU(2012TB013)
文摘Parameterization is one of the key problems in the construction of a curve to interpolate a set of ordered points. We propose a new local parameterization method based on the curvature model in this paper. The new method determines the knots by mi- nimizing the maximum curvature of quadratic curve. When the knots by the new method are used to construct interpolation curve, the constructed curve have good precision. We also give some comparisons of the new method with existing methods, and our method can perform better in interpolation error, and the interpolated curve is more fairing.
基金supported by the National Natural Science Foundation of China[Grant numbers U20A2091,41930107]。
文摘Information on the population distribution at the building scale can help governments make supplemental decisions to address complex urban management issues.However,the discontinuity and strong spatial heterogeneity of research units at the building scale make it challenging to fuse multi-source geographic data,which causes significant errors in population estimation.To address this problem,this study proposes a method for population estimation at the building scale based on Dual-Environment Feature Fusion(DEFF).The dual environments of buildings were constructed by splitting the physical boundaries and extracting features suitable for the dual-environment scale from multi-source geographic data to describe the complex environmental features of buildings.Meanwhile,Data Quality Weighting based Technique for Order of Preference by Similarity to Ideal Solution(DQW-TOPSIS)method was proposed to assign appropriate weights to the features of the external environment for better feature fusion.Finally,a regression model was established using dual-environment features for building-scale population estimation.The experimental areas chosen for this study were Jianghan and Wuchang Districts,both located in Wuhan City,China.The estimated results of the DEFF were compared with those of the ablation experiments,as well as three publicly accessible population datasets,specifically LandScan,WorldPop,and GHS-POP,at the community scale.The evaluation results showed that DEFF had an R2 of approximately 0.8,Mean Absolute Error(MAE)of approximately 1200,Root Mean Square Error(RMSE)of approximately 1700,and both Mean Absolute Percentage Error(MAPE)and Symmetric Mean Absolute Percentage Error(SMAPE)of approximately 26%,indicating an improved performance and verifying the validity of the proposed method for fine-scale population estimation.
文摘Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applications, Springer-Verlag, （2006） 83, pp. 25-33], the Pool-Adjazent-Violators algorithm （PAV） was generalized from completely to partially ordered data sets （posets）. The new algorithm, called CPAV, is characterized by the very low computational complexity, which is of second order in the number of observations. It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The CPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted CPAV solution is optimal. Furthermore, we present results of extensive numerical experiments, from which we draw conclusions about the most and the least preferable topological orders.
