In this paper, we propose an intuitive, training-free and label-free method for intent clustering in conversational search. Current approaches to short text clustering use LLM-generated pseudo-labels to enrich text representations or to identify similar text pairs for pooling. The limitations are: (1) each text is assigned only a single label, and refining representations toward a single label can be unstable; (2) text-level similarity is treated as a binary selection, which fails to account for continuous degrees of similarity. Our method LUMI is designed to amplify similarities between texts by using shared pseudo-labels. We first generate pseudo-labels for each text and collect them into a pseudo-label set. Next, we compute the mean of the pseudo-label embeddings and pool it with the text embedding. Finally, we perform text-level pooling: Each text representation is pooled with its similar pairs, where similarity is determined by the degree of shared labels. Our evaluation on four benchmark sets shows that our approach achieves competitive results, better than recent state-of-the-art baselines, while avoiding the need to estimate the number of clusters during embedding refinement, as is required by most methods. Our findings indicate that LUMI can effectively be applied in unsupervised short-text clustering scenarios.