With the existing of coverage holes, the Quality of Service (such as event response, package delay, and the life time et al.) of a Wireless Sensor Network (WSN) may become weaker. In order to recover the holes, one can locate them by identifying the boundary nodes on their edges. Little effort has been made to distinguish the boundary nodes in a model where wireless sensors are randomly deployed on a three-dimensional surface. In this paper, we propose a distributed method which contains three steps in succession. It first projects the 1-hop neighborhood of a sensor to the plane. Then, it sorts the projected nodes according to their angles and finds out if there exists any ring formed by them. At last, the algorithm validates a circle to confirm that it is a ring surrounding the node. Our solution simulates the behavior of rotating a semicircle plate around a sensor under the guidance of its neighbors. Different from the existing results, our method transforms a three-dimensional problem into a two-dimensional one and maintaining its original topology, and it does not rely on any complex Hamiltonian Cycle finding to test the existence of a circle in the neighborhood of a sensor. Simulation results show our method outperforms others at the correctness and effectiveness in identifying the nodes on the edges of a three-dimensional WSN.

In the age of big data, recommendation systems provide users with fast access to interesting information, resulting to a significant commercial value. However, the extreme sparseness of user assessment data is one of the key factors that lead to the poor performance of recommendation algorithms. To address this problem, we propose a spectral clustering recommendation scheme with low-rank matrix completion and spectral clustering. Our scheme exploits spectral clustering to achieve the division of a similar user group. Meanwhile, the low-rank matrix completion is used to effectively predict un-rated items in the sub-matrix of the spectral clustering. With the real dataset experiment, the results show that our proposed scheme can effectively improve the prediction accuracy of un-rated items.