Which of the dimensionality reduction techniques described in this chapter is most appropriate in each of the following scenarios? Justify your answers. (a) We are granted license to place five gas...

Which of the dimensionality reduction techniques described in this chapter is most appropriate in each of the following scenarios? Justify your answers.

(a) We are granted license to place five gas stations in a new city, and we know the desired distances between them. We would like to determine how to place these stations in the city.

(b) We have 400 two-dimensional vectors that we would like to cluster using k-means. The data points are in the shape of closelyspaced zigzags.

(c) We are investigating the incidence of smoking among college students, and we have surveyed 500 college students on a range of topics, including whether they smoke or not.

(d) We have 75 graphs we want to cluster. The graphs represent molecular structures, and we have a symmetric function that estimates how much energy it would take to convert one molecule into another.