Spectral clustering is a popular tool in many unsupervised computer vision and machine learning tasks. Recently, due to the encouraging performance of deep neural networks, many conventional spectral clustering methods have been extended to the deep framework. Although these deep spectral clustering methods are quite powerful and effective, learning the cluster number from data is still a challenge. In this paper, we aim to tackle this problem by integrating the spectral clustering, generative adversarial network and low rank model within a unified Bayesian framework. First, we adapt the low rank method to the cluster number estimation problem. Then, an adversarial-learning-based deep clustering method is proposed and incorporated. When introducing the spectral clustering method into our model clustering procedure, a hidden space structure preservation term is proposed. Via a Bayesian framework, the structure preservation term is embedded into the generative process, which can then be used to deduce a spectral clustering in the optimization procedure. Finally, we derive a variational-inference-based method and embed it into the network optimization and learning procedure. Experiments on different datasets prove that our model has the cluster number estimation capability and show that our method can outperform many similar graph clustering methods.

Multimanifold clustering separates data points approximately lying on a union of submanifolds into several clusters. In this paper, we propose a new nonparametric Bayesian model to handle the manifold data structure. In our framework, we first model the manifold mapping function between Euclidean space and topological space by applying a deep neural network, and then construct the corresponding generation process of multiple manifold data. To solve the posterior approximation problem, in the optimization procedure, we apply a variational auto-encoder-based optimization algorithm. Especially, as the manifold algorithm has poor performance on the real dataset where nonmanifold and manifold clusters are appearing simultaneously, we expand our proposed manifold algorithm by integrating it with the original Dirichlet process mixture model. Experimental results have been carried out to demonstrate the state-of-the-art clustering performance.

Deep spectral clustering is a popular and efficient algorithm in unsupervised learning. However, deep spectral clustering methods are organized into three separate steps: affinity matrix learning, spectral embedding learning, and K-means clustering on spectral embedding. In this case, although each step can achieve its own performance, it is still difficult to obtain robust clustering results. In this letter, we propose a one-step adaptive spectral clustering network to overcome the aforementioned shortcomings. The network embeds the three parts of affinity matrix learning, spectral embedding learning, and indicator learning into a unified framework. The affinity matrix is adaptively adjusted by spectral embedding in a deep subspace. We introduce spectral rotation to discretize spectral embedding, which makes the spectral embedding and indicator be learned simultaneously to improve clustering quality. Each part of the model can be iteratively updated based on other parts to optimize the clustering results. Experimental results on four real datasets show the effectiveness of our method on the ACC and NMI clustering evaluation metrics. In particular, our method achieves an NMI of 0.932 and an ACC of 0.973 on the MNIST dataset, a decent performance boost compared to the best baseline.

Deep spectral clustering techniques are considered one of the most efficient clustering algorithms in data mining field. The similarity between instances and the disparity among classes are two critical factors in clustering fields. However, most current deep spectral clustering approaches do not sufficiently take them both into consideration. To tackle the above issue, we propose Semantic Spectral clustering with Contrastive learning and Neighbor mining (SSCN) framework, which performs instance-level pulling and cluster-level pushing cooperatively. Specifically, we obtain the semantic feature embedding using an unsupervised contrastive learning model. Next, we obtain the nearest neighbors partially and globally, and the neighbors along with data augmentation information enhance their effectiveness collaboratively on the instance level as well as the cluster level. The spectral constraint is applied by orthogonal layers to satisfy conventional spectral clustering. Extensive experiments demonstrate the superiority of our proposed frame of spectral clustering.

Sparse subspace clustering, as one of the most effective subspace clustering method, is widely studied in the data processing realm. However, conventional sparse subspace clustering methods are organized with two separated steps, feature learning and indicator learning. This makes the algorithm suffer the difficulties that: (1) representation and cluster indicator learning cannot affect each other; (2) cluster number and sparse penalty coefficient should be specified a priori; (3) sparse subspace clustering method is designed for the linear subspace data and cannot be exploited in the general clustering task. In this letter, a novel sparse clustering method is proposed, in which we extend the conventional algebraic sparse subspace clustering approach to a Bayesian framework. Then, cluster number estimation and low rank constraint are coupled via a Dirichlet process parameter generation process, in which the rank are no more required to be low but can be generated with a suitable value. Finally, Generative Adversarial Network (GAN) is incorporated into the Bayesian sparse model, which extends the subspace clustering method to a normal clustering model. Experiments on different real world datasets validate our theory analysis and demonstrate the effective of the proposed algorithm.

As one of the most effective subspace clustering methods, the self-expression based sparsity method leverages the robust representational learning and non-linear transformation capacities of deep learning. This approach facilitates the mapping of data into a low-dimensional subspace, wherein the clustering operations are subsequently executed. However, most conventional self-expression methods do not handle the subspace clustering problem with sparse-labeled information. Considering the scarcity and value of labeled samples in various real-world applications, we propose a novel deep Few-Shot Subspace Clustering Learning (FS2CL) framework to improve the traditional self-expression-based techniques in the case of sparse label information, in which partial classes in the observation dataset have a scarcity of labeled samples and most other classes do not. We expect to obtain more discriminative low-rank representations that exhibit high cohesion among clusters. To overcome the limitation that the low-rank approximation is achieved by singular value decomposition, which is not differentiable and cannot be embedded in neural networks for gradient back-propagation, a Low-rank Representation Approximation (LRA) module is proposed to transform the non-differentiable singular value decomposition into a differentiable iterative process. This procedure produces a low-rank representation that maximizes the cohesion of features belonging to the same cluster. Subsequently, we propose a method for learning a low-dimensional learnable subspace bases matrix assisted by a small number of labeled samples, which captures the structure of each subspace. We then classify the data points belonging to the corresponding class by measuring the similarity between the instance and each subspace base. Due to the low dimension of the subspace bases matrix, it is possible to apply our method to large-scale datasets. The proposed method is superior to state-of-the-art clustering approaches through extensive comparison studies conducted on six benchmark datasets: MNIST, Fashion-MNIST, REUTERS-10K, STL-10, CIFAR10, and CIFAR100.