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Effective representation of objects in irregular and unordered point clouds is one of the core challenges in 3D vision. Transforming point cloud into regular structures, such as 2D images and 3D voxels, are not ideal. It either obscures the inherent geometry information of 3D data or results in high computational complexity. Learning permutation invariance feature directly from raw 3D point clouds using deep neural network is a trend, such as PointNet and its variants, which are effective and computationally efficient. However, these methods are weak to reveal the spatial structure of 3D point clouds. Our method is delicately designed to capture both global and local spatial layout of point cloud by proposing a Local k-NNs Pattern in Omni-Direction Graph Convolution Neural Network architecture, called LKPO-GNN. Our method converts the unordered 3D point cloud into an ordered 1D sequence, to facilitate feeding the raw data into neural networks and simultaneously reducing the computational complexity. LKPO-GNN selects multi-directional k-NNs to form the local topological structure of a centroid, which describes local shapes in the point cloud. Afterwards, GNN is used to combine the local spatial structures and represent the unordered point clouds as a global graph. Experiments on ModelNet40, ShapeNetPart, ScanNet, and S3DIS datasets demonstrate that our proposed method outperforms most existing methods, which verifies the effectiveness and advantage of our work. Additionally, a deep analysis towards illustrating the rationality of our approach, in terms of the learned the topological structure feature, is provided. Source code is available at https://github.com/zwj12377/LKPO-GNN.git. [ABSTRACT FROM AUTHOR]

• Replace hard codematrix with soft codematrix. • Use the regression outputs of the base classifiers to replace the traditional classification outputs. • Iteratively softens codematrix elements using global loss tuning. • Conveniently merge the proposed algorithm into other ECOC algorithms to further improve performance. The technique of error-correcting output codes (ECOC) has been proven to be of high discriminative ability in many classification applications. However, most algorithms on the ECOC were designed based on the binary or ternary codes (referred to as the hard codes), which might fail to precisely correct errors in dealing with tough tasks. In this study, a Soft-Recoding strategy based on a self-adaptive algorithm is proposed, which replaces the traditional hard codes with the real-value elements to better fit the output distribution of the base learners. This is achieved by minimizing the ratio of two distances: the distance of the output vector to the ground-truth class, and the average distance of the output vector to the remaining classes. Extensive experiments using five different hard ECOC algorithms and the corresponding softened versions on twenty datasets with diversified numbers of features and classes confirm the effectiveness of our Soft-Recoding strategy in promoting the performance of the original ECOC algorithms. Our source code and additional results are available at: github.com/MLDMXM2017/SA-soft-recoding. [ABSTRACT FROM AUTHOR]