Sensor Network Localization by Dual Embedding Spectral Regression
Abstract: We propose an algorithm for localizing nodes of sensor network given a subset of highly noised inter-sensor distances and a small subset of sensors’ true locations. The algorithm derives geometrically adaptive bases over the entire sensor network by multiscale Diffusion bases and an Isomap embedding of the Diffusion basis. By implementing dual embedding we discover a basis that better describes the geometrical data in a low dimensional representation. This basis is then utilized to formulate an L1 regression based extension of the anchor points coordinates to the entire network. The results is used as an initial prediction for a global computation of the objective function. Due to high noise levels some measured distances may not admit to the triangle inequality in small triangular 3-hop paths. Hence, we add a preprocessing step that resizes the given inter-sensor distances in the desired direction. Our algorithm is capable of localizing the sensors in two different models of implemented networks where the input distances may consist of either a small subset of fairly large neighborhood of each sensor, or a model describing a small radius disc graph. We experimentally show that results obtained under high levels of noise are state-of-the-art.