We present a novel deep neural network architecture for unsupervised subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel self-expressive layer between the encoder and the decoder to mimic the "self-expressiveness" property that has proven effective in traditional subspace clustering. Being differentiable, our new self-expressive layer provides a simple but effective way to learn pairwise affinities between all data points through a standard back-propagation procedure. Being nonlinear, our neural-network based method is able to cluster data points having complex (often nonlinear) structures. We further propose pre-training and fine-tuning strategies that let us effectively learn the parameters of our subspace clustering networks. Our experiments show that the proposed method significantly outperforms the state-of-the-art unsupervised subspace clustering methods.
Auto-encoders (AEs) can non-linearly transform data into a latent space. When this latent space has lower dimension than the original one @cite_36 , this can be viewed as a form of non-linear PCA. An auto-encoder typically consists of an encoder and a decoder to define the data reconstruction cost. With the success of deep learning @cite_11 , deep (or stacked) AEs have become popular for unsupervised learning. For instance, deep AEs have proven useful for dimensionality reduction @cite_36 and image denoising @cite_51 . Recently, deep AEs have also been used to initialize deep embedding networks for unsupervised clustering @cite_27 . A convolutional version of deep AEs was also applied to extract hierarchical features and to initialize convolutional neural networks (CNNs) @cite_52 .
@cite_36 @cite_52 @cite_27 @cite_51 @cite_11
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The success of deep neural networks often relies on a large amount of labeled examples, which can be difficult to obtain in many real scenarios. To address this challenge, unsupervised methods are strongly preferred for training neural networks without using any labeled data. In this paper, we present a novel paradigm of unsupervised representation learning by Auto-Encoding Transformation (AET) in contrast to the conventional Auto-Encoding Data (AED) approach. Given a randomly sampled transformation, AET seeks to predict it merely from the encoded features as accurately as possible at the output end. The idea is the following: as long as the unsupervised features successfully encode the essential information about the visual structures of original and transformed images, the transformation can be well predicted. We will show that this AET paradigm allows us to instantiate a large variety of transformations, from parameterized, to non-parameterized and GAN-induced ones. Our experiments show that AET greatly improves over existing unsupervised approaches, setting new state-of-the-art performances being greatly closer to the upper bounds by their fully supervised counterparts on CIFAR-10, ImageNet and Places datasets. A novel variational autoencoder is developed to model images, as well as associated labels or captions. The Deep Generative Deconvolutional Network (DGDN) is used as a decoder of the latent image features, and a deep Convolutional Neural Network (CNN) is used as an image encoder; the CNN is used to approximate a distribution for the latent DGDN features code. The latent code is also linked to generative models for labels (Bayesian support vector machine) or captions (recurrent neural network). When predicting a label caption for a new image at test, averaging is performed across the distribution of latent codes; this is computationally efficient as a consequence of the learned CNN-based encoder. Since the framework is capable of modeling the image in the presence absence of associated labels captions, a new semi-supervised setting is manifested for CNN learning with images; the framework even allows unsupervised CNN learning, based on images alone. A novel variational autoencoder is developed to model images, as well as associated labels or captions. The Deep Generative Deconvolutional Network (DGDN) is used as a decoder of the latent image features, and a deep Convolutional Neural Network (CNN) is used as an image encoder; the CNN is used to approximate a distribution for the latent DGDN features code. The latent code is also linked to generative models for labels (Bayesian support vector machine) or captions (recurrent neural network). When predicting a label caption for a new image at test, averaging is performed across the distribution of latent codes; this is computationally efficient as a consequence of the learned CNN-based encoder. Since the framework is capable of modeling the image in the presence absence of associated labels captions, a new semi-supervised setting is manifested for CNN learning with images; the framework even allows unsupervised CNN learning, based on images alone. In this work we propose a novel model-based deep convolutional autoencoder that addresses the highly challenging problem of reconstructing a 3D human face from a single in-the-wild color image. To this end, we combine a convolutional encoder network with an expert-designed generative model that serves as decoder. The core innovation is our new differentiable parametric decoder that encapsulates image formation analytically based on a generative model. Our decoder takes as input a code vector with exactly defined semantic meaning that encodes detailed face pose, shape, expression, skin reflectance and scene illumination. Due to this new way of combining CNN-based with model-based face reconstruction, the CNN-based encoder learns to extract semantically meaningful parameters from a single monocular input image. For the first time, a CNN encoder and an expert-designed generative model can be trained end-to-end in an unsupervised manner, which renders training on very large (unlabeled) real world data feasible. The obtained reconstructions compare favorably to current state-of-the-art approaches in terms of quality and richness of representation.