GACH: a grid-based algorithm for hierarchical clustering of high-dimensional data

This paper proposes a grid-based hierarchical clustering algorithm (GACH) as an efficient and robust method to explore clusters in high-dimensional data with no prior knowledge. It discovers the initial positions of the potential clusters automatically and then combines them hierarchically to obtain the final clusters. In this regard, GACH first projects the data patterns on a two-dimensional space (i.e., on a plane established by two features) to overcome the curse of dimensionality problem in high-dimensional data. To choose these two well-informed features, a simple and fast feature selection algorithm is proposed. Then, through meshing the plane with grid lines, GACH detects the crowded grid points. The nearest data patterns around these grid points are considered as initial members of some potential clusters. By returning the patterns back to their true dimensions, GACH refines these clusters. In the merging phase, GACH combines the closely adjacent clusters in a hierarchical bottom-up manner to construct the final clusters' members. The main features of GACH are: (1) it automatically discovers the clusters, (2) the obtained clusters are stable, (3) it is efficient for data sets with high dimensions, and (4) its merging process involves a threshold which can be obtained in advance for well-clustered data. To assess our proposed algorithm, it is applied on some benchmark data sets and the validity of obtained clusters is compared with the results of some other clustering algorithms. This comparison shows that GACH is accurate, efficient and feasible to discover clusters in high-dimensional data.