Effect of Objective Function on Data-Driven Greedy Sparse Sensor Optimization

The selection problem of an optimal set sensors estimating the snapshot high-dimensional data is considered. objective functions based on various criteria design are adopted to greedy method: D-optimality, A-optimality, and E-optimality, which maximizes determinant, minimize trace inverse, maximize minimum eigenvalue Fisher information matrix, respectively. First, matrix derived depending numbers latent state variables sensors. Then, unified formulation function A-optimality introduced proved be submodular, provides lower bound performance method. Next, methods D-, A-, E-optimality applied randomly generated systems a practical global climates. selected by D-optimality works better than those A- with regard reconstruction error, while best eigenvalue. On other hand, worse for all indices error. This might because lack submodularity as in paper. results indicate that method most suitable high accurate low computational cost.