3D Point Cloud Denoising via Deep Neural Network based Local Surface Estimation

We present a neural-network-based architecture for 3D point cloud denoising called neural projection denoising (NPD). In our previous work, we proposed a two-stage denoising algorithm, which first estimates reference planes and follows by projecting noisy points to estimated reference planes. Since the estimated reference planes are inevitably noisy, multi-projection is applied to stabilize the denoising performance. NPD algorithm uses a neural network to estimate reference planes for points in noisy point clouds. With more accurate estimations of reference planes, we are able to achieve better denoising performances with only one-time projection. To the best of our knowledge, NPD is the first work to denoise 3D point clouds with deep learning techniques. To conduct the experiments, we sample 40000 point clouds from the 3D data in ShapeNet to train a network and sample 350 point clouds from the 3D data in ModelNet10 to test. Experimental results show that our algorithm can estimate normal vectors of points in noisy point clouds. Comparing to five competitive methods, the proposed algorithm achieves better denoising performance and produces much smaller variances

Signal Recovery on Graphs: Random versus Experimentally Designed Sampling

We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited class and is similar to the globally smooth class. We then propose two recovery strategies based on random sampling and experimentally designed sampling. The proposed recovery strategy based on experimentally designed sampling is similar to the leverage scores used in the matrix approximation. We show that while both strategies are unbiased estimators for the low-frequency components, the convergence rate of experimentally designed sampling is much faster than that of random sampling when a graph is irregular. We validate the proposed recovery strategies on three specific graphs: a ring graph, an Erd\H{o}s-R\'enyi graph, and a star graph. The simulation results support the theoretical analysis.Comment: Correct some typo

CORPORATE CASH HOLDINGS: STUDY OF CHINESE FIRMS

This study focuses on the determinants of cash holdings in the period of 2003-2012 for Chinese manufacturing industry and how Chinese firms manage cash holdings. In general, when firms are more financially constrained, they are more likely to hold more cash. According to our investigation, firms with lower leverage, less net working capital (NWC), and lower capital expenditures, are more likely to increase cash holdings. In addition, China has different economic environment from developed countries, most of manufacturing firms are state owned; thus, the government policies influence the motivations of firms

Hypergraph Structure Inference From Data Under Smoothness Prior

Hypergraphs are important for processing data with higher-order relationships involving more than two entities. In scenarios where explicit hypergraphs are not readily available, it is desirable to infer a meaningful hypergraph structure from the node features to capture the intrinsic relations within the data. However, existing methods either adopt simple pre-defined rules that fail to precisely capture the distribution of the potential hypergraph structure, or learn a mapping between hypergraph structures and node features but require a large amount of labelled data, i.e., pre-existing hypergraph structures, for training. Both restrict their applications in practical scenarios. To fill this gap, we propose a novel smoothness prior that enables us to design a method to infer the probability for each potential hyperedge without labelled data as supervision. The proposed prior indicates features of nodes in a hyperedge are highly correlated by the features of the hyperedge containing them. We use this prior to derive the relation between the hypergraph structure and the node features via probabilistic modelling. This allows us to develop an unsupervised inference method to estimate the probability for each potential hyperedge via solving an optimisation problem that has an analytical solution. Experiments on both synthetic and real-world data demonstrate that our method can learn meaningful hypergraph structures from data more efficiently than existing hypergraph structure inference methods