Abstract: Most recent graph clustering methods have resorted to Graph Auto-Encoders (GAEs) to perform joint clustering and embedding learning. However, two critical issues have been overlooked. First, the accumulative error, inflicted by learning from noisy clustering assignments, degrades the effectiveness of the clustering model. This problem is called Feature Randomness. Second, reconstructing the adjacency matrix sets the model to learn irrelevant similarities for the clustering task. This problem is called Feature Drift. Furthermore, the theoretical relation between the aforementioned problems has not yet been investigated. We study these issues from two aspects: (1) there is a trade-off between Feature Randomness and Feature Drift when clustering and reconstruction are performed at the same level, and (2) the problem of Feature Drift is more pronounced for GAE models, compared with vanilla auto-encoder models. Thus, we reformulate the GAE-based clustering methodology. Our solution is two-fold. First, we propose a sampling operator that triggers a protection mechanism against Feature Randomness. Second, we propose an operator that triggers a correction mechanism against Feature Drift by gradually transforming the reconstructed graph into a clusteringoriented one. As principal advantages, our solution grants a considerable improvement in clustering effectiveness and can be easily tailored to GAE models.