کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
533833 870177 2005 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimization on Lie manifolds and pattern recognition
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر چشم انداز کامپیوتر و تشخیص الگو
پیش نمایش صفحه اول مقاله
Optimization on Lie manifolds and pattern recognition
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Pattern Recognition - Volume 38, Issue 12, December 2005, Pages 2286–2300
نویسندگان
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