In this paper, a new framework for data analysis based on the “key points” in data distribution is proposed. Here, the key points contain three types of data points: bridge points, border points, and skeleton points, where our main contribution is the bridge points. For each type of key points, we have developed the corresponding detection algorithm and tested its effectiveness with several synthetic data sets. Meanwhile, we further developed a new hierarchical clustering algorithm SPHC (Skeleton Point based Hierarchical Clustering) to demonstrate the possible applications of the key points acquired. Based on some real-world data sets, we experimentally show that SPHC performs better compared with several classical clustering algorithms including Complete-Link Hierarchical Clustering, Single-Link Hierarchical Clustering, KMeans, Ncut, and DBSCAN.