—In this paper we present a vectorial representation of the HMM states that is inspired by the Subspace Gaussian Mixture Models paradigm (SGMM). This vectorial representation of states will make possible a large number of applications, such as HMM-states clustering and graphical visualization. Thanks to this representation, the Hidden Markov Model (HMM) states can be seen as sets of points in multi-dimensional space and then can be studied using statistical data analysis techniques. In this paper, we show how this representation can be obtained and used for tying states of an HHM-based automatic speech recognition system without any use of linguistic or phonetic knowledge. In experiments, this approach achieves significant and stable gain, while conserving the classical approach based on decision trees. We also show how it can be used for graphical visualization, which can be useful in other domains like phonetics or clinical phonetics.