Most existing feature learning methods optimize inflexible handcrafted features and the affinity matrix is constructed by shallow linear embedding methods. Different from these conventional methods, we pretrain a generative neural network by stacking convolutional autoencoders to learn the latent data representation and then construct an affinity graph with them as a prior. Based on the pretrained model and the constructed graph, we add a self-expressive layer to complete the generative model and then fine-tune it with a new loss function, including the reconstruction loss and a deliberately defined locality-preserving loss. The locality-preserving loss designed by the constructed affinity graph serves as prior to preserve the local structure during the fine-tuning stage, which in turn improves the quality of feature representation effectively. Furthermore, the self-expressive layer between the encoder and decoder is based on the assumption that each latent feature is a linear combination of other latent features, so the weighted combination coefficients of the self-expressive layer are used to construct a new refined affinity graph for representing the data structure. We conduct experiments on four datasets to demonstrate the superiority of the representation ability of our proposed model over the state-of-the-art methods.
@cite_31: Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise behind the latter genre is that the data samples are obtained via linear transformation of latent representations that are easy to cluster; but in practice, the transformation from the latent space to the data can be more complicated. In this work, we assume that this transformation is an unknown and possibly nonlinear function. To recover the clustering-friendly' latent representations and to better cluster the data, we propose a joint DR and K-means clustering approach in which DR is accomplished via learning a deep neural network (DNN). The motivation is to keep the advantages of jointly optimizing the two tasks, while exploiting the deep neural network's ability to approximate any nonlinear function. This way, the proposed approach can work well for a broad class of generative models. Towards this end, we carefully design the DNN structure and the associated joint optimization criterion, and propose an effective and scalable algorithm to handle the formulated optimization problem. Experiments using different real datasets are employed to showcase the effectiveness of the proposed approach.
@cite_8: Subspace clustering aims to cluster unlabeled samples into multiple groups by implicitly seeking a subspace to fit each group. Most of existing methods are based on a shallow linear model, which may fail in handling data with nonlinear structure. In this paper, we propose a novel subspace clustering method -- deeP subspAce clusteRing with sparsiTY prior (PARTY) -- based on a new deep learning architecture. PARTY explicitly learns to progressively transform input data into nonlinear latent space and to be adaptive to the local and global subspace structure simultaneously. In particular, considering local structure, PARTY learns representation for the input data with minimal reconstruction error. Moreover, PARTY incorporates a prior sparsity information into the hidden representation learning to preserve the sparse reconstruction relation over the whole data set. To the best of our knowledge, PARTY is the first deep learning based subspace clustering method. Extensive experiments verify the effectiveness of our method.
@cite_6: We present a new technique called “t-SNE” that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map. t-SNE is better than existing techniques at creating a single map that reveals structure at many different scales. This is particularly important for high-dimensional data that lie on several different, but related, low-dimensional manifolds, such as images of objects from multiple classes seen from multiple viewpoints. For visualizing the structure of very large datasets, we show how t-SNE can use random walks on neighborhood graphs to allow the implicit structure of all of the data to influence the way in which a subset of the data is displayed. We illustrate the performance of t-SNE on a wide variety of datasets and compare it with many other non-parametric visualization techniques, including Sammon mapping, Isomap, and Locally Linear Embedding. The visualizations produced by t-SNE are significantly better than those produced by the other techniques on almost all of the datasets.
@cite_3: Recently deep learning has been successfully adopted in many applications such as speech recognition and image classification. In this work, we explore the possibility of employing deep learning in graph clustering. We propose a simple method, which first learns a nonlinear embedding of the original graph by stacked autoencoder, and then runs k-means algorithm on the embedding to obtain clustering result. We show that this simple method has solid theoretical foundation, due to the similarity between autoencoder and spectral clustering in terms of what they actually optimize. Then, we demonstrate that the proposed method is more efficient and flexible than spectral clustering. First, the computational complexity of autoencoder is much lower than spectral clustering: the former can be linear to the number of nodes in a sparse graph while the latter is super quadratic due to eigenvalue decomposition. Second, when additional sparsity constraint is imposed, we can simply employ the sparse autoencoder developed in the literature of deep learning; however, it is nonstraightforward to implement a sparse spectral method. The experimental results on various graph datasets show that the proposed method significantly outperforms conventional spectral clustering, which clearly indicates the effectiveness of deep learning in graph clustering.
@cite_15: 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.
@cite_34: Clustering is central to many data-driven application domains and has been studied extensively in terms of distance functions and grouping algorithms. Relatively little work has focused on learning representations for clustering. In this paper, we propose Deep Embedded Clustering (DEC), a method that simultaneously learns feature representations and cluster assignments using deep neural networks. DEC learns a mapping from the data space to a lower-dimensional feature space in which it iteratively optimizes a clustering objective. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods.
@cite_25: In this paper, we propose a new clustering model, called DEeP Embedded Regularized ClusTering (DEPICT), which efficiently maps data into a discriminative embedding subspace and precisely predicts cluster assignments. DEPICT generally consists of a multinomial logistic regression function stacked on top of a multi-layer convolutional autoencoder. We define a clustering objective function using relative entropy (KL divergence) minimization, regularized by a prior for the frequency of cluster assignments. An alternating strategy is then derived to optimize the objective by updating parameters and estimating cluster assignments. Furthermore, we employ the reconstruction loss functions in our autoencoder, as a data-dependent regularization term, to prevent the deep embedding function from overfitting. In order to benefit from end-to-end optimization and eliminate the necessity for layer-wise pre-training, we introduce a joint learning framework to minimize the unified clustering and reconstruction loss functions together and train all network layers simultaneously. Experimental results indicate the superiority and faster running time of DEPICT in real-world clustering tasks, where no labeled data is available for hyper-parameter tuning.
Tian @cite_3 use DNN to optimize the reconstruction loss function between the encoder and the decoder, but the input handcrafted feature is firstly optimized by subspace learning and then optimized by DNN secondly. Later, Peng @cite_8 also input handcrafted computer vision datasets for their DNN model resulting in that this method does not effectively utilize the representation ability of a convolutional neural network. As similar as Peng @cite_8 's method, Ji @cite_15 also make use of the autoencoder as pretraining and self-expressive property to learn the affinity matrix. The subtle difference that Ji @cite_15 's method inputs raw image data for a convolutional neural network rather than using handcrafted data in the Peng @cite_8 's model. Taking inspiration from @math -SNE @cite_6 , Xie @cite_34 define an centroid-based auxiliary target distribution to minimize Kullback-Leibler divergence, with parameters initialized by stacked autoencoders. Based on Xie 's @cite_34 algorithm, Dizaji @cite_25 use cluster assignments frequency as a regularization term to balance the cluster results. Yang @cite_31 jointly optimize a combination of the reconstruction error and @math -means objective function to achieve clustering-friendly' latent representations.