Optimization of the number of clusters: a case study on multivariate quality control results of segment installation

When encountering too many records, each of which has several attributes, clustering of the data is an important issue on mining and classification. Recently many advances on clustering algorithms have been made such that clustering of data is done precisely and quickly. Clustering algorithms use optimization algorithms which simultaneously provide the number of clusters as default. These algorithms cluster the data so that those which belong to a cluster have maximum similarity and those in different clusters have minimum similarity. The k-means algorithm is a traditional algorithm for clustering problems. One of the most important difficulties of clustering algorithms is determining the number of clusters before starting the algorithm. In other words, by having knowledge on distribution of data, the number of clusters should be estimated and then imported to the problem as an input. In this paper, the data collected on quality control of mechanized tunneling are analyzed. They consist of measurements of 16 characteristics for 200 initial installed rings of segments on the tunnel walls inspected by the quality control team. A dynamic validity index is used and combined to the k-means algorithm for clustering the data so that the optimal number of clusters can be determined simultaneously. The application of the algorithm shows that the total installed rings can be clustered into four clusters. These four classes of quality can best describe the total installed rings on the tunnel in comparison of other number of classes (or clusters). Furthermore, this approach helps the quality team to determine the most effective or best performance executive team whom their installed rings have best class and minimum variations.