ABSTRACT
This chapter explores techniques in unsupervised learning, where there is no response variable y. A tree-sometimes called a dendrogram-is an attractive organizing structure for relationships. The tree may or may not reflect some deeper relationship among the objects, but it often provides a simple way to visualize relationships. Cities can be different and similar in many ways: population, age structure, public transportation and roads, building space per person, etc. The choice of features depends on the purpose you have for making the grouping. It is usually helpful to remove irrelevant or redundant variables so that they-and the noise they carry-don't obscure the patterns that machine learning algorithms could identify. In fact, there is a mathematical approach to finding the best approximation to the ballot-voter matrix using simple matrices, called singular value decomposition.
