ABSTRACT
A dimensionality reduction technique that is closely related to spectral clustering is the Laplacian Eigenmap. The low dimensional representation created by this dimensionality reduction technique closely reflects the intrinsic geometric structure of the manifold and preserves the neighborhood properties by taking into consideration the structure of the underlying manifold. Laplacian Eigenmap uses Graph Laplacians to find the low dimensional embeddings. This chapter starts with a detailed explanation of this technique and how the Laplacian Eigenmap finds neighborhood preserving mapping of the data in low dimensional space. Further, the advantages and shortcomings of this algorithm are also discussed. Finally, the chapter ends with examples using datasets along with a tutorial to better understand the working of this dimensionality reduction technique.
