Stable label movement and smooth label trajectory are critical for effective information understanding.Sudden label changes cannot be avoided by whatever forced directed methods due to the unreliability of resultant f...Stable label movement and smooth label trajectory are critical for effective information understanding.Sudden label changes cannot be avoided by whatever forced directed methods due to the unreliability of resultant force or global optimization methods due to the complex trade-off on the different aspects.To solve this problem,we proposed a hybrid optimization method by taking advantages of the merits of both approaches.We first detect the spatial-temporal intersection regions from whole trajectories of the features,and initialize the layout by optimization in decreasing order by the number of the involved features.The label movements between the spatial-temporal intersection regions are determined by force directed methods.To cope with some features with high speed relative to neighbors,we introduced a force from future,called temporal force,so that the labels of related features can elude ahead of time and retain smooth movements.We also proposed a strategy by optimizing the label layout to predict the trajectories of features so that such global optimization method can be applied to streaming data.展开更多
This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabiliza...This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabilizability condition which is weaker than the controllability,normally imposed in the similar problem for ordinary differential systems.In dealing with the turnpike problem,a crucial issue is to determine the corresponding static optimization problem.Intuitively mimicking the deterministic situations,it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem.However,this would lead us to a wrong direction.It is found that the correct static problem should contain the diffusion as a part of the objective function,which reveals a deep feature of the stochastic turnpike problem.展开更多
基金supported by the National Key Technology R&D Program(Project No.2017YFB1002604)the National Natural Science Foundation of China(Project Nos.61772298 and 61832016)+1 种基金Research Grant of Beijing Higher Institution Engineering Research CenterTsinghua-Tencent Joint Laboratory for Internet Innovation Technology.
文摘Stable label movement and smooth label trajectory are critical for effective information understanding.Sudden label changes cannot be avoided by whatever forced directed methods due to the unreliability of resultant force or global optimization methods due to the complex trade-off on the different aspects.To solve this problem,we proposed a hybrid optimization method by taking advantages of the merits of both approaches.We first detect the spatial-temporal intersection regions from whole trajectories of the features,and initialize the layout by optimization in decreasing order by the number of the involved features.The label movements between the spatial-temporal intersection regions are determined by force directed methods.To cope with some features with high speed relative to neighbors,we introduced a force from future,called temporal force,so that the labels of related features can elude ahead of time and retain smooth movements.We also proposed a strategy by optimizing the label layout to predict the trajectories of features so that such global optimization method can be applied to streaming data.
基金supported by the National Natural Science Foundation of China(No.11901280,12271242,12201424)Guangdong Basic and Applied Basic Research Foundation(No.2021A1515010031)+1 种基金Shenzhen Fundamental Research General Program(No.JCYJ20220530112814032)NSF(No.DMS-1812921)。
文摘This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabilizability condition which is weaker than the controllability,normally imposed in the similar problem for ordinary differential systems.In dealing with the turnpike problem,a crucial issue is to determine the corresponding static optimization problem.Intuitively mimicking the deterministic situations,it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem.However,this would lead us to a wrong direction.It is found that the correct static problem should contain the diffusion as a part of the objective function,which reveals a deep feature of the stochastic turnpike problem.
