Haixin Zhang

Yongyong Cai, Jie Xu, Haixin Zhang

In tensor dynamics for liquid crystals derived from molecular models, a common problem is closure approximation. For rod-like molecules, the Bingham closure has proved to outperform other methods because it inherits the gradient flow structure of the molecular model, but is difficult to achieve efficient computations maintaining the gradient flow structure. We propose a closure approximation by the quasi-entropy that has been successfully applied to the free energy, based on which we construct the tensor gradient flow. The quasi-entropy closure has the same symmetry properties as the Bingham closure. The resulting tensor gradient flow is able to constrain the eigenvalues of the tensor within the physical range, guaranteeing the positive definiteness of the dissipation operator given by the higher-order tensors. The quasi-entropy closure is easy to implement since it can be reduced to minimizing an elementary function of three variables. As a result, we construct a numerical scheme preserving the eigenvalue constraints and energy dissipation, with the closure approximation decoupled from solving the scheme. Numerical simulations are carried out for the interface between the isotropic and the uniaxial nematic phase, as well as the defect evolutions, where the higher-order tensors indeed make a difference.

Haixin Zhang, Dong Huang

Previous contrastive deep clustering methods mostly focus on instance-level information while overlooking the member relationship within groups/clusters, which may significantly undermine their representation learning and clustering capability. Recently, some group-contrastive methods have been developed, which, however, typically rely on the samples of the entire dataset to obtain pseudo labels and lack the ability to efficiently update the group assignments in a batch-wise manner. To tackle these critical issues, we present a novel end-to-end deep clustering framework with dynamic grouping and prototype aggregation, termed as DigPro. Specifically, the proposed dynamic grouping extends contrastive learning from instance-level to group-level, which is effective and efficient for timely updating groups. Meanwhile, we perform contrastive learning on prototypes in a spherical feature space, termed as prototype aggregation, which aims to maximize the inter-cluster distance. Notably, with an expectation-maximization framework, DigPro simultaneously takes advantage of compact intra-cluster connections, well-separated clusters, and efficient group updating during the self-supervised training. Extensive experiments on six image benchmarks demonstrate the superior performance of our approach over the state-of-the-art. Code is available at https://github.com/Regan-Zhang/DigPro.

Haixin Zhang, Yongjun Li, Dong Huang

Image clustering, which involves grouping images into different clusters without labels, is a key task in unsupervised learning. Although previous deep clustering methods have achieved remarkable results, they only explore the intrinsic information of the image itself but overlook external supervision knowledge to improve the semantic understanding of images. Recently, visual-language pre-trained model on large-scale datasets have been used in various downstream tasks and have achieved great results. However, there is a gap between visual representation learning and textual semantic learning, and how to properly utilize the representation of two different modalities for clustering is still a big challenge. To tackle the challenges, we propose a novel image clustering framwork, named Dual-level Cross-Modal Contrastive Clustering (DXMC). Firstly, external textual information is introduced for constructing a semantic space which is adopted to generate image-text pairs. Secondly, the image-text pairs are respectively sent to pre-trained image and text encoder to obtain image and text embeddings which subsquently are fed into four well-designed networks. Thirdly, dual-level cross-modal contrastive learning is conducted between discriminative representations of different modalities and distinct level. Extensive experimental results on five benchmark datasets demonstrate the superiority of our proposed method.