PATTERN CLUSTERING: AN ARTIFICIAL INTELLIGENCE APPROACH. B. Shekar, M. Narasimha Murty and G. Krishna. Department of Computer Science and ...
PATTERN CLUSTERING: AN ARTIFICIAL INTELLIGENCE APPROACH
B. Shekar, M. Narasimha Murty and G. Krishna Department of Computer Science and Automation I n d i a n I n s t i t u t e o f Science Bangalore 560 012 INDIA
ABSTRACT The n o t i o n of * concept* based on f u n c t i o n a l i t y of o b j e c t s is d e f i n e d and made use o f i n the c o n t e x t o f p a t t e r n c l u s t e r i n g . A n approach t o p a r t i t i o n o b j e c t s u s i n g a knowledge base is p r e s e n t e d . A d i f f e r e n t c l a s s o f concepts c a l l e d conceptual t r a n s formers i s proposed and i t s e f f e c t s on c l u s t e r i n g i s looked i n t o . I
INTRODUCTION
C l u s t e r i n g is a process of g r o u p i n g o b j e c t s based on a s i m i l a r i t y measure. Con v e n t i o n a l s i m i l a r i t y measures are c o n t e x t -free and g e s t a l f property-independent in n a t u r e . A r e c e n t development to o v e r c o me such problems, is the measure ( M i c h a l s k i 1980): S i m i l a r i t y ( A , B ) = f ( A , B , E , C ) where A and B are the o b j e c t s being compared and E and C are the environment and a set of p r e d e f i n e d concepts r e s p e c t i v e l y . Here we d e f i n e the term concept from the f u n c t i o n a l p o i n t of view based on the p h y s i c a l p r o p e r t i e s which imply the f u n c t ion. A knowledge-based approach t o p a r t i t i o n objects is o u t l i n e d . An i n t e r e s t i n g subset o f concepts c a l l e d conceptual t r a n s f o r m e r s , which i s a n a b s t r a c t i o n from r e a l l i f e , i s s t u d i e d i n d e t a i l . The e f f e c t s of t h i s type of concepts on the c l u s t e r i n g mechanism i s looked i n t o . II CONCEPTS AND CONCEPTUAL TRANSFORMERS A concept can be r e c u r s i v e l y d e f i n e d as f o l l o w s : ( a ) A concept is a p a r t i a l mapp i n g f r o m , e i t h e r the powerset o f the i n s tances o f the p h y s i c a l d e s c r i p t o r s o f o b j e c t s , o r the powerset o f u s e r - d e f i n e d f u n c t i o n s , to a domain of l a b e l s , (b) A concept is a p a r t i a l mapping from the powerset of l a b e l s to a set of l a b e l s . Observe t h a t the above d e f i n i t i o n is an e x t e n s i o n of "concept' g i v e n by Winston (Winston 1984). I n the c o n t e x t o f c l u s t e r ing, there is a c e r t a i n category of concepts which cannot be t r e a t e d the same way in which we view a concept as d e f i n e d above. T h i s c l a s s (Co) of c o n c e p t s , which i n a d d i t i o n t o s a t i s f y i n g the above d e f i n ition will a l s o s a t i s f y the transformer
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KNOWLEDGE ACQUISITION
r e l a t i o n R on Co d e f i n e d by the f i r s t order l o g i c statement:
