The Novel Application of Dynamic Graphics to Unsupervised Learning, Graphs, and Cycle Clustering Table of Contents

Dynamic graphics are a collection of data visualization techniques that employ interaction and real-time updating to enhance graphical displays. Traditionally, dynamic graphics have been used to augment classic statistical plots, such as scatter plots. This thesis describes the novel application of dynamic graphics to explore several different areas: traditional unsupervised learning algorithms, graphs, and new applications of clustering algorithms to graphs. Unsupervised learning algorithms are automated methods for exploring and finding the interesting aspects of a high-dimensional data set. The grand tour is a multivariate data visualization technique used to observe the unsupervised learning algorithms. Making the plots interactive and utilizing linked brushing presents more information to the user. A graph consists of nodes and edges. Graphically, nodes are small shapes like circles and edges are shown as lines connecting the nodes. Interaction with the visualization allows for structure modification such as node addition/deletion, edge addition/modification/deletion, and node and edge figure placement. The nodes and edges of a graph can have multiple properties, or variables, associated with them, and these values can be shown in the visualization by mapping them to visual attributes of the nodes and edges, like node shape or edge color. A path is a sequence of nodes and edges of a graph and a cycle is a path that leads back to the starting node. Many of these cycles in a graph will contain some of the same nodes and edges. Groups of similar cycles can be found by using a clustering algorithm on the cycles of the graph. A suitable distance metric for comparing cycles and a definition of the median of a set of cycles are required by the clustering algorithm. Once the clusters of similar cycles are found, dynamic graphics methods can be used to visualize them effectively.