Deep neural networks have been shown to excel in understanding multimedia by using latent representations to learn complex and useful abstractions. However, they remain unpractical for embedded devices due to memory constraints, high latency, and considerable power consumption at runtime. In this paper, we propose the compression of deep models based on learning lower dimensional subspaces from their latent representations while maintaining a minimal loss of performance. We leverage on the premise that deep convolutional neural networks extract many redundant features to learn new subspaces for feature representation. We construct a compressed model by reconstruction from representations captured by an already trained large model. As compared to state-of-the-art, the proposed approach does not rely on labeled data. Moreover, it allows the use of sparsity inducing LASSO parameter penalty to achieve better compression results than when used to train models from scratch. We perform extensive experiments using VGG-16 and wide ResNet models on CIFAR-10, CIFAR-100, MNIST and SVHN datasets. For instance, VGG-16 with 8.96M parameters trained on CIFAR-10 was pruned by 81.03 % with only 0.26 % generalization performance loss. Correspondingly, the size of the VGG-16 model is reduced from 35MB to 6.72MB to facilitate compact storage. Furthermore, the associated inference time for the same VGG-16 model is reduced from 1.1 secs to 0.6 secs so that inference is accelerated. Particularly, the proposed student models outperform state-of-the-art approaches and the same models trained from scratch.