  Many problems in machine learning can be expressed by means of a graph with
nodes representing training samples and edges representing the relationship
between samples in terms of similarity, temporal proximity, or label
information. Graphs can in turn be represented by matrices. A special example
is the Laplacian matrix, which allows us to assign each node a value that
varies only little between strongly connected nodes and more between distant
nodes. Such an assignment can be used to extract a useful feature
representation, find a good embedding of data in a low dimensional space, or
perform clustering on the original samples. In these lecture notes we first
introduce the Laplacian matrix and then present a small number of algorithms
designed around it.
