ABSTRACT
This chapter discusses the sensor localization problem using kernel Isomap. It describes problem statement and explores localization using Isomap and its limitations. The chapter explains kernel Isomap with several constant shifting methods and its generalization property. It discusses the performance evaluation of kernel Isomap is done using simulation results. Kernel-based localization algorithms possess the capability to localize these new arrivals efficiently, but the selection of a suitable kernel which satisfies the network conditions well is another challenge. Using the kernel trick, the position of a new point in kernel principal component analysis is computed as the projection of the centered data matrix onto the normalized eigenvectors of the respective covariance matrix. The generalization property of kernel Isomap utilizes the previously computed results to localize the new nodes, whereas Isomap repeats the whole centralized procedure whenever a new node arrives in the network, rejecting previous computations.
