Algorithms for clustering data
Algorithms for clustering data
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Computational Geometry: Theory and Applications
Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications
Data Mining and Knowledge Discovery
Incremental Clustering for Mining in a Data Warehousing Environment
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
A Fast Algorithm for Density-Based Clustering in Large Database
PAKDD '99 Proceedings of the Third Pacific-Asia Conference on Methodologies for Knowledge Discovery and Data Mining
Dynamic half-space reporting, geometric optimization, and minimum spanning trees
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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We present new geometric approximation and exact algorithms for the density-based data clustering problem in d-dimensional space Rd (for any constant integer d 驴 2). Previously known algorithms for this problem are efficient only for uniformly-distributed points. However, these algorithms all run in 驴(n2) time in the worst case, where n is the number of input points. Our approximation algorithm based on the 驴-fuzzy distance function takes O(n log n) time for any given fixed value 驴 0, and our exact algorithms take sub-quadratic time. The running times and output quality of our algorithms do not depend on any particular data distribution. We believe that our fast approximation algorithm is of considerable practical importance, while our sub-quadratic exact algorithms are more of theoretical interest. We implemented our approximation algorithm and the experimental results show that our approximation algorithm is efficient on arbitrary input point sets.