When the coordinates of a set of points are known, the pairwise Euclidean distances among the points can be easily computed. Conversely, if the Euclidean distance matrix is given, a set of coordinates for those points...When the coordinates of a set of points are known, the pairwise Euclidean distances among the points can be easily computed. Conversely, if the Euclidean distance matrix is given, a set of coordinates for those points can be computed through the well known classical Multi-Dimensional Scaling （MDS）. In this paper, we consider the case where some of the distances are far from being accurate （containing large noises or even missing）. In such a situation, the order of the known distances （i.e., some distances are larger than others） is valuable information that often yields far more accurate construction of the points than just using the magnitude of the known distances. The methods making use of the order information is collectively known as nonmetric MDS. A challenging computational issue among all existing nonmetric MDS methods is that there are often a large number of ordinal constraints. In this paper, we cast this problem as a matrix optimization problem with ordinal constraints. We then adapt an existing smoothing Newton method to our matrix problem. Extensive numerical results demonstrate the efficiency of the algorithm, which can potentially handle a very large number of ordinal constraints.展开更多
Robust PCA has found important applications in many areas,such as video surveillance,face recognition,latent semantic indexing and so on.In this paper,we study its application in ground moving target indication(GMTI)i...Robust PCA has found important applications in many areas,such as video surveillance,face recognition,latent semantic indexing and so on.In this paper,we study its application in ground moving target indication(GMTI)in wide-area surveillance radar system.MTI is the key task in wide-area surveillance radar system.Due to its great importance in future reconnaissance systems,it attracts great interest from scientists.In(Yan et al.in IEEE Geosci.Remote Sens.Lett.,10:617–621,2013),the authors first introduced robust PCA to model the GMTI problem,and demonstrate promising simulation results to verify the advantages over other models.However,the robust PCA model can not fully describe the problem.As pointed out in(Yan et al.in IEEE Geosci.Remote Sens.Lett.,10:617–621,2013),due to the special structure of the sparse matrix(which includes the moving target information),there will be difficulties for the exact extraction of moving targets.This motivates our work in this paper where we will detail the GMTI problem,explore the mathematical properties and discuss how to set up better models to solve the problem.We propose two models,the structured RPCA model and the row-modulus RPCA model,both of which will better fit the problem and take more use of the special structure of the sparse matrix.Simulation results confirm the improvement of the proposed models over the one in(Yan et al.in IEEE Geosci.Remote Sens.Lett.,10:617–621,2013).展开更多
文摘When the coordinates of a set of points are known, the pairwise Euclidean distances among the points can be easily computed. Conversely, if the Euclidean distance matrix is given, a set of coordinates for those points can be computed through the well known classical Multi-Dimensional Scaling （MDS）. In this paper, we consider the case where some of the distances are far from being accurate （containing large noises or even missing）. In such a situation, the order of the known distances （i.e., some distances are larger than others） is valuable information that often yields far more accurate construction of the points than just using the magnitude of the known distances. The methods making use of the order information is collectively known as nonmetric MDS. A challenging computational issue among all existing nonmetric MDS methods is that there are often a large number of ordinal constraints. In this paper, we cast this problem as a matrix optimization problem with ordinal constraints. We then adapt an existing smoothing Newton method to our matrix problem. Extensive numerical results demonstrate the efficiency of the algorithm, which can potentially handle a very large number of ordinal constraints.
基金supported by the National Science Foundation of China(No.11101410)China Postdoctoral Science Foundation(No.2011M500416).
文摘Robust PCA has found important applications in many areas,such as video surveillance,face recognition,latent semantic indexing and so on.In this paper,we study its application in ground moving target indication(GMTI)in wide-area surveillance radar system.MTI is the key task in wide-area surveillance radar system.Due to its great importance in future reconnaissance systems,it attracts great interest from scientists.In(Yan et al.in IEEE Geosci.Remote Sens.Lett.,10:617–621,2013),the authors first introduced robust PCA to model the GMTI problem,and demonstrate promising simulation results to verify the advantages over other models.However,the robust PCA model can not fully describe the problem.As pointed out in(Yan et al.in IEEE Geosci.Remote Sens.Lett.,10:617–621,2013),due to the special structure of the sparse matrix(which includes the moving target information),there will be difficulties for the exact extraction of moving targets.This motivates our work in this paper where we will detail the GMTI problem,explore the mathematical properties and discuss how to set up better models to solve the problem.We propose two models,the structured RPCA model and the row-modulus RPCA model,both of which will better fit the problem and take more use of the special structure of the sparse matrix.Simulation results confirm the improvement of the proposed models over the one in(Yan et al.in IEEE Geosci.Remote Sens.Lett.,10:617–621,2013).
