In the data of laser interferometric gravitational wave detectors, transient noise with non-stationary and non-Gaussian features occurs at a high rate. It often causes problems such as instability of the detector, hiding and/or imitating gravitational-wave signals. This transient noise has various characteristics in the time-frequency representation, which is considered to be associated with environmental and instrumental origins. Classification of transient noise can offer one of the clues for exploring its origin and improving the performance of the detector. One approach for the classification of these noises is supervised learning. However, generally, supervised learning requires annotation of the training data, and there are issues with ensuring objectivity in the classification and its corresponding new classes. On the contrary, unsupervised learning can reduce the annotation work for the training data and ensuring objectivity in the classification and its corresponding new classes. In this study, we propose an architecture for the classification of transient noise by using unsupervised learning, which combines a variational autoencoder and invariant information clustering. To evaluate the effectiveness of the proposed architecture, we used the dataset (time-frequency two-dimensional spectrogram images and labels) of the LIGO first observation run prepared by the Gravity Spy project. We obtain the consistency between the label annotated by Gravity spy project and the class provided by our proposed unsupervised learning architecture and provide the potential for the existence of the unrevealed classes.