You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Traditional image clustering methods take a two-step approach, feature learning and clustering, sequentially. However, recent research results demonstrated that combining the separated phases in a unified framework and training them jointly can achieve a better performance. In this paper, we first introduce fully convolutional auto-encoders for image feature learning and then propose a unified clustering framework to learn image representations and cluster centers jointly based on a fully convolutional auto-encoder and soft @math -means scores. At initial stages of the learning procedure, the representations extracted from the auto-encoder may not be very discriminative for latter clustering. We address this issue by adopting a boosted discriminative distribution, where high score assignments are highlighted and low score ones are de-emphasized. With the gradually boosted discrimination, clustering assignment scores are discriminated and cluster purities are enlarged. Experiments on several vision benchmark datasets show that our methods can achieve a state-of-the-art performance.

Cited Abstract(s):
[1]: Autoencoders play a fundamental role in unsupervised learning and in deep architectures for transfer learning and other tasks. In spite of their fundamental role, only linear autoencoders over the real numbers have been solved analytically. Here we present a general mathematical framework for the study of both linear and non-linear autoencoders. The framework allows one to derive an analytical treatment for the most non-linear autoencoder, the Boolean autoencoder. Learning in the Boolean autoencoder is equivalent to a clustering problem that can be solved in polynomial time when the number of clusters is small and becomes NP complete when the number of clusters is large. The framework sheds light on the different kinds of autoencoders, their learning complexity, their horizontal and vertical composability in deep architectures, their critical points, and their fundamental connections to clustering, Hebbian learning, and information theory.

[2]: High-dimensional data can be converted to low-dimensional codes by training a multilayer neural network with a small central layer to reconstruct high-dimensional input vectors. Gradient descent can be used for fine-tuning the weights in such “autoencoder” networks, but this works well only if the initial weights are close to a good solution. We describe an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data.

[3]: We explore an original strategy for building deep networks, based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs. The resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders. It is however shown on a benchmark of classification problems to yield significantly lower classification error, thus bridging the performance gap with deep belief networks (DBN), and in several cases surpassing it. Higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent SVM classifiers. Qualitative experiments show that, contrary to ordinary autoencoders, denoising autoencoders are able to learn Gabor-like edge detectors from natural image patches and larger stroke detectors from digit images. This work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations.

[4]: We show how to use "complementary priors" to eliminate the explaining-away effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that fine-tunes the weights using a contrastive version of the wake-sleep algorithm. After fine-tuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The low-dimensional manifolds on which the digits lie are modeled by long ravines in the free-energy landscape of the top-level associative memory, and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind.

[5]: There has been much interest in unsupervised learning of hierarchical generative models such as deep belief networks. Scaling such models to full-sized, high-dimensional images remains a difficult problem. To address this problem, we present the convolutional deep belief network, a hierarchical generative model which scales to realistic image sizes. This model is translation-invariant and supports efficient bottom-up and top-down probabilistic inference. Key to our approach is probabilistic max-pooling, a novel technique which shrinks the representations of higher layers in a probabilistically sound way. Our experiments show that the algorithm learns useful high-level visual features, such as object parts, from unlabeled images of objects and natural scenes. We demonstrate excellent performance on several visual recognition tasks and show that our model can perform hierarchical (bottom-up and top-down) inference over full-sized images.

[6]: The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, autoencoders, manifold learning, and deep networks. This motivates longer term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation, and manifold learning.

[7]: Complexity theory of circuits strongly suggests that deep architectures can be much more efficient (sometimes exponentially) than shallow architectures, in terms of computational elements required to represent some functions. Deep multi-layer neural networks have many levels of non-linearities allowing them to compactly represent highly non-linear and highly-varying functions. However, until recently it was not clear how to train such deep networks, since gradient-based optimization starting from random initialization appears to often get stuck in poor solutions. recently introduced a greedy layer-wise unsupervised learning algorithm for Deep Belief Networks (DBN), a generative model with many layers of hidden causal variables. In the context of the above optimization problem, we study this algorithm empirically and explore variants to better understand its success and extend it to cases where the inputs are continuous or where the structure of the input distribution is not revealing enough about the variable to be predicted in a supervised task. Our experiments also confirm the hypothesis that the greedy layer-wise unsupervised training strategy mostly helps the optimization, by initializing weights in a region near a good local minimum, giving rise to internal distributed representations that are high-level abstractions of the input, bringing better generalization.

[8]: We present a novel convolutional auto-encoder (CAE) for unsupervised feature learning. A stack of CAEs forms a convolutional neural network (CNN). Each CAE is trained using conventional on-line gradient descent without additional regularization terms. A max-pooling layer is essential to learn biologically plausible features consistent with those found by previous approaches. Initializing a CNN with filters of a trained CAE stack yields superior performance on a digit (MNIST) and an object recognition (CIFAR10) benchmark.
Stacked auto-encoders [3] [1] [6] [4] [2] [7] have been studied in the past years for unsupervised deep feature extraction and nonlinear dimension reduction. Their extensions for dealing with images are convolutional stacked auto-encoders [8] [5] . Most of these methods contain a two-stage training procedure [7] : one is layer-wise pre-training and the other is overall fine-tuning. One of the significant drawbacks of this learning procedure is that the layer-wise pre-training is time-consuming and tedious, especially when the base layer is a Restricted Boltzmann Machine (RBM) rather than a traditional auto-encoder or when the overall network is very deep.