This letter aims to learn a global representation for each point in a random cluster using only purely local geometric or topological information. Based on this, distributed tags for indoor positioning break the atomicity of tags and make deployment more arbitrary. It also allows NP-hard matches to be quickly estimated with only one local observation. The novel self-supervised topological representation learning method only takes local point clusters as input and utilizes the proposed cluster-based sampling, training, and loss functions to form global self-comparison. The training samples are generated in real-time virtually, and there are few matching errors after being transferred to practice. The compact backbone network directly processes the coordinates of points and abandons the iterative optimization commonly used in matching. Moreover, it uses the representation to measure similarity directly, and the inference speed reaches the millisecond level. In the actual and virtual experiments, the local point clusters are surprisingly accurately matched to the random global ones. The localization based on this is also verified, and the relevant results prove the effectiveness of the proposed method.