The automatic speaker identification procedure is used to extract features that help to identify the components of the acoustic signal by discarding all the other stuff like background noise, emotion, hesitation, etc. The acoustic signal is generated by a human that is filtered by the shape of the vocal tract, including tongue, teeth, etc. The shape of the vocal tract determines and produced, what signal comes out in real time. The analytically develops shape of the vocal tract, which exhibits envelop for the short time power spectrum. The ASR needs efficient way of extracting features from the acoustic signal that is used effectively to makes the shape of the individual vocal tract. To identify any acoustic signal in the large collection of acoustic signal i.e. corpora, it needs dimension compactness of total variability space by using the GMM mean super vector. This work presents the efficient way to implement dimension compactness in total variability space and using cosine distance scoring to predict a fast output score for small size utterance.