Spatially-correlated sensor discriminant analysis

A study of generalization error in signal detection by multiple spatially-distributed and -correlated sensors is provided when the detection rule is learned from a finite number of training samples via the classical linear discriminant analysis formulation. Spatial correlation among sensors is modeled by a Gauss-Markov random field defined on a nearest neighbor graph according to inter-sensor spatial distance, where sensors are placed randomly on a growing bounded region of the plane. A fairly simple approximate expression for generalization error is derived involving few parameters. It is shown that generalization error is minimized not when there are an infinite number of sensors, but a number of sensors equal to half the number of samples in the training set. The minimum generalization error is related to a single parameter of the sensor spatial location distribution, derived based on weak laws of large numbers in geometric probability. The finite number of training samples acts like a budgeting variable, similar to a total communication power constraint.