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Information Processing and Management: an International Journal
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Algorithms for clustering data
BIRCH: an efficient data clustering method for very large databases
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
Automatic subspace clustering of high dimensional data for data mining applications
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Linear Differential Algorithm for Motion Recovery: AGeometric Approach
International Journal of Computer Vision
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Euclidean Reconstruction and Reprojection Up to Subgroups
International Journal of Computer Vision - Special issue on Genomic Signal Processing
Motion Recovery from Image Sequences: Discrete Viewpoint vs. Differential Viewpoint
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Efficient and Effective Clustering Methods for Spatial Data Mining
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
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Several pattern recognition problems can be reduced in a natural way to the problem of optimizing a nonlinear function over a Lie manifold. However, optimization on Lie manifolds involves, in general, a large number of nonlinear equality constraints and is hence one of the hardest optimization problems. We show that exploiting the special structure of Lie manifolds allows one to devise a method for optimizing on Lie manifolds in a computationally efficient manner. The new method relies on the differential geometry of Lie manifolds and the underlying connections between Lie groups and their associated Lie algebras. We describe an application of the new Lie group method to the problem of diagnosing malignancy in the cytological extracts of breast tumors. The diagnosis method that we present has a mean sensitivity of 98.086% and a predictive index of 0.0602, making it the most accurate and reliable diagnostic method reported thus far.