Intelligent transportation management requires not only statistical information on users' mobility patterns, but also real-time knowledge of their selected transportation modes. The research area of GPS-based transportation mode identification aims to infer users' travel modes from their mobility data as captured by GPS sensors in their smartphones or vehicles. The recently demonstrated prevalence of deep neural networks in learning from data makes them a promising candidate for transportation mode identification. However, the massive geospatial data produced by GPS sensors are typically unlabeled. To address this problem, we first pretrain a deep convolutional autoencoder (CAE) using fixed-size trajectory segments. Then, we attach a clustering layer to the CAE's embedding layer, the former maintaining cluster centroids as trainable weights. Finally, we retrain the composite clustering model, encouraging the encoder's learned representation of the input data to be clustering-friendly by striking a balance between the model's reconstruction and clustering losses. By further incorporating features computed over each segment, we achieve a clustering accuracy of 80.5% on Microsoft's Geolife dataset without using any labels. To the best of our knowledge, this is the first work to leverage unsupervised deep learning for clustering of GPS trajectory data by transportation mode.