This paper introduces a new unsupervised approach for dialogue act induction. Given the sequence of dialogue utterances, the task is to assign them the labels representing their function in the dialogue. Utterances are represented as real-valued vectors encoding their meaning. We model the dialogue as Hidden Markov model with emission probabilities estimated by Gaussian mixtures. We use Gibbs sampling for posterior inference. We present the results on the standard Switchboard-DAMSL corpus. Our algorithm achieves promising results compared with strong supervised baselines and outperforms other unsupervised algorithms.