On the Classification of Patterns by the Karhunen-Loeve Orthogonal System Without Supervisor
نویسندگان
چکیده
In t h i s paper we show how t h e p a t t e r n samples g e n e r a t e d f r o m t h e unknown asymmet r i c f i n i t e m i x t u r e d i s t r i b u t i o n a re d i c h o t o m i z e d b y t h e Karhunen-Loeve o r t h o g o n a l sys tem i n t h e o p t i m a l way. We i n t r o d u c e t h e concep t o f t h e d i f f e r e n c e o f f e a t u r e s o f two c a t e g o r i e s and p r o v e t h a t d e c r e a s i n g t h e e r r o r p r o b a b i l i t y o f d i c h o t o m y i s e q u a l t o i n c r e a s i n g t h e d i f f e r e n c e o f f e a t u r e s o f two c a t e g o r i e s . And i t can be shown t h a t t h e maximum d i f f e r e n c e o f f e a t u r e s o b t a i n e d by t h e K L sys tem i s e q u i v a l e n t t o t h a t w h i c h i s o b t a i n e d by the Bayes s o l u t i o n . Moreover i t can b e p roved t h a t t h e r e e x i s t s a d i c h o t o m y w h i c h conve rges t o t h e Bayes s o J u t i o n by i n c r e a s i n g the number o f s a m p l e s .
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