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
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
IEEE Transactions on Mobile Computing
Threshold Functions, Node Isolation, and Emergent Lacunae in Sensor Networks
IEEE Transactions on Information Theory
Extending mobility to publish/subscribe systems using a pro-active caching approach
Mobile Information Systems
Extending mobility to publish/subscribe systems using a pro-active caching approach
Mobile Information Systems
State of the art versus classical clustering for unsupervised word sense disambiguation
Artificial Intelligence Review
CoNLL '11 Proceedings of the Fifteenth Conference on Computational Natural Language Learning
An iterated graph laplacian approach for ranking on manifolds
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
| Hi-index | 5.23 |
We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in order to obtain optimal clustering results. Which type of neighborhood graph should one choose, mutual k-nearest-neighbor or symmetric k-nearest-neighbor? What is the optimal parameter k? In our setting, clusters are defined as connected components of the t-level set of the underlying probability distribution. Clusters are said to be identified in the neighborhood graph if connected components in the graph correspond to the true underlying clusters. Using techniques from random geometric graph theory, we prove bounds on the probability that clusters are identified successfully, both in a noise-free and in a noisy setting. Those bounds lead to several conclusions. First, k has to be chosen surprisingly high (rather of the order n than of the order logn) to maximize the probability of cluster identification. Secondly, the major difference between the mutual and the symmetric k-nearest-neighbor graph occurs when one attempts to detect the most significant cluster only.