On the minimum node degree and connectivity of a wireless multihop network
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Threshold Functions, Node Isolation, and Emergent Lacunae in Sensor Networks
IEEE Transactions on Information Theory
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Spectral clustering based on k-nearest neighbor graph
CISIM'12 Proceedings of the 11th IFIP TC 8 international conference on Computer Information Systems and Industrial Management
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Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are "identified": that is, the subgraph induced by points from the same cluster is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds on the probability that cluster identification is successful, and use them to predict "optimal" values of kfor the mutual and symmetric k-nearest-neighbor graphs. We point out different properties of the mutual and symmetric nearest-neighbor graphs related to the cluster identification problem.