Due to the combinatorial nature of the clustering result, which is a partition rather than a set of parameters or a function, the notions of mean and variance are not clear-cut. This intrinsic difficulty hinders the development of methods to improve clustering by aggregation or to assess the uncertainty of clusters generated. We overcome the barrier by aligning clusters via soft matching solved by optimal transport. Equipped with this technique, we propose a new algorithm to enhance clustering by any baseline method using bootstrap samples. In addition, the cluster alignment enables us to quantify variation in the clustering result at the levels of both overall partitions and individual clusters. Topological relationships between clusters such as match, split, and merge can be revealed. A confidence point set for each cluster, a concept kin to the confidence interval, is proposed. The tools we have developed here will help address the crucial question of whether any cluster is an intrinsic or spurious pattern. Experimental results on both simulated and real data sets are provided.