In this chapter, we learn the concept, usefulness, and execution of

dimensionality reduction. This important topic has been exten-

sively studied in different disciplines. A large variety of techniques

have been developed and there have been numerous articles in the

literature including several accessible surveys [BDR+06, HLMS04]

and even books [CC94, STC04]. Here we shall present and discuss

only a sampler of techniques and illuminate them using visually

intuitive examples.