ABSTRACT
Multidimensional Scaling tries to maintain the Euclidean distance in the lower dimension. However, sometimes preserving Euclidean distance in the lower dimension while carrying out dimensionality reduction might not give us the desired result. The Euclidean metric for distance works only if the neighborhood structure can be approximated as a linear structure in nonlinear manifolds. In this chapter we discuss yet another algorithm called Isomap. It is another distance-preserving nonlinear dimensionality reduction technique that is based on spectral theory. Here, the concept of geodesic distance is used to solve for the problem of dimensionality reduction. Further, the advantages and limitations, and the practical use cases of Isomaps are discussed along with some examples and tutorials for better understanding.
