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Learning from unlabeled or partially labeled data to alleviate human labeling remains a challenging research topic in 3D modeling. Along this line, unsupervised representation learning is a promising direction to auto-extract features without human intervention. This paper proposes a general unsupervised approach, named \textbf{ConClu}, to perform the learning of point-wise and global features by jointly leveraging point-level clustering and instance-level contrasting. Specifically, for one thing, we design an Expectation-Maximization (EM) like soft clustering algorithm that provides local supervision to extract discriminating local features based on optimal transport. We show that this criterion extends standard cross-entropy minimization to an optimal transport problem, which we solve efficiently using a fast variant of the Sinkhorn-Knopp algorithm. For another, we provide an instance-level contrasting method to learn the global geometry, which is formulated by maximizing the similarity between two augmentations of one point cloud. Experimental evaluations on downstream applications such as 3D object classification and semantic segmentation demonstrate the effectiveness of our framework and show that it can outperform state-of-the-art techniques.