A distance metric of patterns is crucial to hotspot cluster analysis and classification. In this paper, we propose an improved tangent space (ITS)-based distance metric for hotspot cluster analysis and classification. The proposed distance metric is an important extension of the well-developed tangent space method in computer vision. It can handle patterns containing multiple polygons, while the traditional tangent space method can only deal with patterns with a single polygon. It inherits most of the advantages of the traditional tangent space method, e.g., it is easy to compute and is tolerant with small variations or shifts of the shapes. The ITS-based distance metric is a more reliable and accurate metric for hotspot cluster analysis and classification. We also propose a hierarchical density-based clustering method for hotspot clustering. It is more suitable for arbitrary shaped clusters.