Fast Data-driven Greedy Sensor Selection for Ridge Regression

Abstract: We propose a data-driven sensor-selection algorithm for accurate estimation of the target variables from the selected measurements. The target variables are assumed to be estimated by a ridge-regression estimator which is trained based on the data. The proposed algorithm greedily selects sensors for minimizing the cost function of the estimator. Sensor selection which prevents overfitting of the resulting estimator can be realized by setting a positive regularization parameter. The greedy solution is computed in quite a short time by using some recurrent relations that we derive. The effectiveness of the proposed algorithm is verified for artificial datasets which are generated from linear systems and a real-wold dataset which are aimed for selection of pressure-sensor locations for estimating yaw angle of a ground vehicle. The demonstration for the datasets reveal that the proposed algorithm computes a sensor set resulting in more accurate estimation than existing data-drive selection algorithms in some conditions. Furthermore, it is confirmed that setting a positive regularization parameter in the proposed algorithm leads to accurate estimation when overfitting is problematic.