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- Keywords: variational autoencoder, latent space, basis, disentangled representation
- TL;DR: Construct orthogonal latent space for deep disentangled representation based on a basis in the linear algebra
- Abstract: The variational autoencoder, one of the generative models, defines the latent space for the data representation, and uses variational inference to infer the posterior probability. Several methods have been devised to disentangle the latent space for controlling the generative model easily. However, due to the excessive constraints, the more disentangled the latent space is, the lower quality the generative model has. A disentangled generative model would allocate a single feature of the generated data to the only single latent variable. In this paper, we propose a method to decompose the latent space into basis, and reconstruct it by linear combination of the latent bases. The proposed model called BasisVAE consists of the encoder that extracts the features of data and estimates the coefficients for linear combination of the latent bases, and the decoder that reconstructs the data with the combined latent bases. In this method, a single latent basis is subject to change in a single generative factor, and relatively invariant to the changes in other factors. It maintains the performance while relaxing the constraint for disentanglement on a basis, as we no longer need to decompose latent space on a standard basis. Experiments on the well-known benchmark datasets of MNIST, 3DFaces and CelebA demonstrate the efficacy of the proposed method, compared to other state-of-the-art methods. The proposed model not only defines the latent space to be separated by the generative factors, but also shows the better quality of the generated and reconstructed images. The disentangled representation is verified with the generated images and the simple classifier trained on the output of the encoder.