ABSTRACT
This chapter provides a short review on relevant research in next section, including the coordinate minimization, the widely used semi-definite programming approach, and more recent Euclidean distance matrix (EDM) optimization. It discusses some essential mathematical background for EDM optimization with particular attention on why EDM optimization has no easy solution, by focusing on the notion of the EDM cone. The chapter reviews three main algorithms for EDM optimization: the method of alternating projections, Newton's method, and a penalty approach. It shows that each regularization can be easily incorporated into the penalty approach. Regularization in sensor network localization (SLN) seems to have been motivated by a similar strategy for dimension reduction in manifold learning, where data sitting on a manifold in a high-dimensional space are mapped to a low-dimensional Euclidean space. SNL has been extensively studied and has a capacity of modeling various practical problems.
