A Nonparametric Model for Multi-Manifold Clustering with Mixture of Gaussians and Graph Consistency.

Multi-manifold clustering is among the most fundamental tasks in signal processing and machine learning. Although the existing multi-manifold clustering methods are quite powerful, learning the cluster number automatically from data is still a challenge. In this paper, a novel unsupervised generative clustering approach within the Bayesian nonparametric framework has been proposed. Specifically, our manifold method automatically selects the cluster number with a Dirichlet Process (DP) prior. Then, a DP-based mixture model with constrained Mixture of Gaussians (MoG) is constructed to handle the manifold data. Finally, we integrate our model with the k-nearest neighbor graph to capture the manifold geometric information. An efficient optimization algorithm has also been derived to do the model inference and optimization. Experimental results on synthetic datasets and real-world benchmark datasets exhibit the effectiveness of this new DP-based manifold method.

Bayesian graph convolutional network with partial observations.

As a widely studied model in the machine learning and data processing society, graph convolutional network reveals its advantage in non-grid data processing. However, existing graph convolutional networks generally assume that the node features can be fully observed. This may violate the fact that many real applications come with only the pairwise relationships and the corresponding node features are unavailable. In this paper, a novel graph convolutional network model based on Bayesian framework is proposed to handle the graph node classification task without relying on node features. First, we equip the graph node with the pseudo-features generated from the stochastic process. Then, a hidden space structure preservation term is proposed and embedded into the generation process to maintain the independent and identically distributed property between the training and testing dataset. Although the model inference is challenging, we derive an efficient training and predication algorithm using variational inference. Experiments on different datasets demonstrate the proposed graph convolutional networks can significantly outperform traditional methods, achieving an average performance improvement of 9%.

Integrating biplane information and context for spine landmark detection.

Spine landmark detection is of great significance for spinal morphological parameter assessment and three-dimensional reconstruction of the human spine. This detection task generally involves locating spine landmarks in the anterior-posterior (AP) and lateral (LAT) X-rays of the spine. Recently, the two-stage methods for AP spine landmark detection achieve better performance. However, these methods perform poorly in LAT landmark detection because of poor detection accuracy of LAT vertebra due to occlusion. To solve this problem, this paper proposes a new two-stage spine landmark detection method. In the first stage, this paper propose a biplane vertebra detection network for vertebra detection on AP and X-rays simultaneously. Then an epipolar module and a context enhancement module are proposed to assist LAT vertebra detection by using the biplane information and the context information of the vertebrae respectively. In the second stage, the landmarks can be obtained in the detected vertebrae area. Extensive experiment results conducted on a dataset containing 328 pairs of X-rays demonstrate that our method improves the vertebra and landmark detection accuracy.

Bayesian Adversarial Spectral Clustering with Unknown Cluster Number.

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.

A Nonparametric Deep Generative Model for Multimanifold Clustering.

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.