Clustering refers to a process to discover the internal structures of data or the potential data models in a dataset [1–۳] by data partitioning. Thanks to the outstanding capability of discover clusters of different shapes and sizes along with outliers, densitybased [4–۶] and grid-based [7] clustering technology are widely applied to the fields of health care [8], information security [9], internet [10] and etc [11–۱۵]. Data points are divided into core points, boundary points and noise points by the DBSCAN algorithm [16], and a cluster is formed when the data is expanding from the core points outwards the clustering boundary. As those methods are susceptible to parameter changes, different parameters may lead to different data dividing and clustering results. IS-DBSCAN [17], ISB-DBSCAN [18] and others [19–۲۱] are proposed by making use of the nearest neighbor relationship instead of the neighborhood density, which effectively reduce the influence of the parameters on the algorithm. However, for the multi-density datasets, the clustering results are not always favorable because neighbor relationships can misjudge the boundary points. Grid clustering technique divide grids into high-density ones and low-density ones with compressing expression and clusters are formed when high-density grids are connected. Grid-based clustering technologies, such as CLIQUE [22], MGM-GA [23] and etc [24,25], are efficient because grid clustering is formed with the. extension of grid cells. Such an approach can be efficient, however, in the clusters forming process, if a dense grid is adjacent to a sparse grid (we called boundary grid), which probably contains noises, the algorithm is of low clustering accuracy. Boundary points not only play a significant role in expansionbased clustering algorithms, but also in other fields of data mining. The PAC-Bayes boundary theory, a theoretical framework, combines Bayes theory [26–۲۸] with minimum structural analysis principle of random classifier, obtaining the most generalized risk boundary. The algorithms derived from PAC-Bayes boundary are actually the “average” of Hypothesis Space, thus achieving a better classification performance [29–۳۱]. Support Vector Machine (SVM) [32–۳۴] also uses boundary points to improve performance. Furthermore, on the occasion of supervised, Compression Nearest Neighbor (CNN) [35] can extract the neighboring data boundary points from different classes, and it can also used to reduce the number of support vectors in the SVM algorithm, which is helpful to reduce training costs [36–۳۹]. Besides, the study on boundary is also contributing to discover interesting models in data [40–۴۲]. For instance, in the medical field, the clustering boundary may represent a group of people, who carry virus but not affected. With regard to handwriting recognition, the clustering boundary may stand for handwriting images which are easily misjudged to be other characters.