Point cloud analysis, arising from computer graphics, remains a fundamental but challenging problem, mainly due to the non-Euclidean property of point cloud data modality. With the snap increase in the amount and breadth of related research in deep learning for graphs, many important works come in the form of graphs representing the point clouds. In this paper, we present a sampling adaptive graph convolutional network that combines the powerful representation ability of random walk subgraph searching and the essential success of the Fisher vector. Extending from those existing graph representation learning or embedding methods with multi-hop neighbor random searching, we sample multi-scale walk fields by using asteerableexploration-exploitationsecond order random walk, which endows our model with the most flexibility compared with the original first order random walk. To encode each-scale walk field consisting of several walk paths, specifically, we characterize these paths of walk field by Gaussian mixture models (GMMs) so as to better analogize the standard CNNs on Euclidean modality. Each Gaussian component implicitly defines a direction and all of them properly encode thespatial layoutof walk fields after the gradient projecting to the space of Gaussian parameters, i.e. the Fisher vectors. Thereby, we introduce and name our deep graph convolutional network asPointFisher. Comprehensive evaluations on several public datasets well demonstrate the superiority of our proposed learning method over other state-of-the-arts for point cloud classification and segmentation.

Lei Ji, Xianglin Guo, Haoyang Huang, Xilin Chen. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

While current block diagonal constrained subspace clustering methods are performed explicitly on the original data space, in practice, it is often more desirable to embed the block diagonal prior into the reproducing kernel Hilbert feature space by kernelization techniques, as the underlying data structure in reality is usually nonlinear. However, it is still unknown how to carry out the embedding and kernelization in the models with block diagonal constraints. In this paper, we shall take a step in this direction. First, we establish a novel model termed implicit block diagonal low-rank representation (IBDLR), by incorporating the implicit feature representation and block diagonal prior into the prevalent low-rank representation method. Second, mostly important, we show that the model in IBDLR could be kernelized by making use of a smoothed dual representation and the specifics of a proximal gradient-based optimization algorithm. Finally, we provide some theoretical analyses for the convergence of our optimization algorithm. Comprehensive experiments on synthetic and real-world data sets demonstrate the superiorities of our IBDLR over state-of-the-art methods.