Cluster Analysis

Description of Cluster Analysis
Cluster analysis is a data analysis tool for solving classification problems. Its object is to sort cases into groups, or clusters, so that the degree of association is strong between members of the same cluster and weak between members of different clusters. Group members will share certain properties in common and it is hoped that the resultant classification will provide some insight into our research topic. The general categories of cluster analysis methods include Joining (Tree Clustering), Two-way Joining, K-means Clustering, et al. A detailed description of the cluster analysis can be found at http://www.statsoftinc.com/textbook/stcluan.html.

In this study, cluster analysis is used to identify similar and dissimilar aerosol monitoring sites so that we can test the ability of the Causes of Haze Assessment methods to explain the similarities and differences. The major clustering algorithm used in this study is joining or tree clustering.

Joining (Tree Clustering)
The purpose of this algorithm is to join together objects into successively larger clusters, using some measure of similarity or distance. A typical result of this type of clustering is a hierarchical tree as shown below.

At the beginning, each object is in a class by itself. Then, we lower our threshold regarding the decision when to declare two or more objects to be members of the same cluster. As a result more and more objects are linked together following certain Amalgamation or linkage rules and aggregate larger and larger clusters of increasingly dissimilar elements. Finally, in the last step, all objects are joined together. In the plot, the vertical axis denotes the linkage distance. Thus the higher the level of aggregation, the less similar are the members in the respective class.