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Autoencoders have achieved great success in various computer visionapplications. The autoencoder learns appropriate low dimensional imagerepresentations through the self-supervised paradigm, i.e., reconstruction.Existing studies mainly focus on the minimizing the reconstruction error onpixel level of image, while ignoring the preservation of Intrinsic Dimension(ID), which is a fundamental geometric property of data representations in DeepNeural Networks (DNNs). Motivated by the important role of ID, in this paper,we propose a novel deep representation learning approach with autoencoder,which incorporates regularization of the global and local ID constraints intothe reconstruction of data representations. This approach not only preservesthe global manifold structure of the whole dataset, but also maintains thelocal manifold structure of the feature maps of each point, which makes thelearned low-dimensional features more discriminant and improves the performanceof the downstream algorithms. To our best knowledge, existing works are rareand limited on exploiting both global and local ID invariant properties on theregularization of autoencoders. Numerical experimental results on benchmarkdatasets (Extended Yale B, Caltech101 and ImageNet) show that the resultingregularized learning models achieve better discriminative representations fordownstream tasks including image classification and clustering.

Autoencoders with Intrinsic Dimension Constraints for Learning Low Dimensional Image Representations