Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Clustering in large graphs and matrices
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Clustering for edge-cost minimization (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-time approximation schemes for geometric min-sum median clustering
Journal of the ACM (JACM)
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
SIAM Journal on Computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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Modeling data sets as points in a high dimensional vector space is a trendy theme in modern information retrieval and data mining. Among the numerous drawbacks of this approach is the fact that many of the required processing tasks are computationally hard in high dimension. We survey several algorithmic ideas that have applications to the design and analysis of polynomial time approximation schemes for nearest neighbor search and clustering of high dimensional data. The main lesson from this line of research is that if one is willing to settle for approximate solutions, then high dimensional geometry is easy. Examples are included in the reference list below.