10 Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 10, 2015 | http://pubs.acs.org Publication Date: November 6, 1985 | doi: 10.1021/bk-1985-0292.ch010
Monitoring Polycyclic Aromatic Hydrocarbons An Environmental Application of Fuzzy C-Varieties Pattern Recognition 1
2
R. W. Gunderson and K. Thrane 1
Department of Mathematics, Utah State University, Logan, UT 84322 Norsk Institutt for Luftforskning, N-2001 Lillestrøm, Norway
2
Data collected in a two year program to monitor polycyclic aromatic hydrocarbons in the vicinity of Sundsvall, Sweden, were analyzed by the Norwegian Institute for Air Research (NILU) to (1) determine the possibility of identifying emission sources, and (2) quantify the contribution from a local aluminum plant. NILU used the fuzzy c-varieties clustering program FOSE as one of two methods f o r c a r r y i n g out the i n v e s t i g a t i o n . The o r i g i n a l study was repeated using recent improvements in the fuzzy c-varieties technique and using the r e c u r s i v e c l u s t e r i n g o p t i o n and a quantitative measure of cluster quality which are features of a new program, FCVPC. The results of of these two investigations are discussed and compared. In general, the results and conclusions reached were in good agreement. I n 1 9 7 8 , t h e e m i s s i o n o f ben zo (a ) p y r ene ( B a P ) f r o m a n a l u m i n u m p l a n t i n t h e v i c i n i t y o f S u n d s v a l l , Sweden, was estimated t o be a b o u t f o u r t i m e s t h e t o t a l amount e m i t t e d from a l l t h e motor v e h i c l e s i n t h a t c o u n t r y . As m i g h t be e x p e c t e d , t h e r e s u l t o f t h i s e s t i m a t e c a u s e d c o n s i d e r a b l e c o n c e r n , and a s u r v e y o f t h e a i r q u a l i t y i n t h e S u n d s v a l l a r e a was made i n 1 9 8 0 - 8 1 . The p r o g r a m monitored concentrations of p o l y c y c l i c aromatic hydrocarbons (PAH) a n d f l u o r i d e i n a m b i e n t a i r , w i t h s a m p l e s b e i n g c o l l e c t e d once each week. C o n c e n t r a t i o n s o f f l u o r i d e and m e t e o r o l o g i c a l d a t a were measured by t h e a l u m i n u m c o m p a n y l a b o r a t o r y , w h i l e PAH c o n c e n t r a t i o n s were d e t e r m i n e d by t h e N o r w e g i a n I n s t i t u t e for Air Research (NILU). 0097-6156/85/ 0292-0130506.00/ 0 © 1985 American Chemical Society In Environmental Applications of Chemometrics; Breen, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
10.
GUNDERSON AND THRANE
Polycyclic Aromatic
Hydrocarbons
131
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 10, 2015 | http://pubs.acs.org Publication Date: November 6, 1985 | doi: 10.1021/bk-1985-0292.ch010
In a d d i t i o n t o s t u d y i n g t h e b e h a v i o u r and t r a n s p o r t o f t h e PAH c o m p o u n d s , NI LU was a s k e d to study the p o s s i b i l i t i e s o f i d e n t i f y i n g t h e main e m i s s i o n sources o f PAH, and o f q u a n t i f y i n g t h e c o n t r i b u t i o n s f r o m t h e aluminum plant. NILU e m p l o y e d two methods of i n v e s t i g a t i n g these questions. One o f t h o s e a p p r o a c h e s i n v o l v e d t h e a p p l i c a t i o n o f a r e l a t i v e l y new f a m i l y o f non-hierarchical c l u s t e r i n g algorithms, the f u z z y cv a r i e t i e s (FCV) a l g o r i t h m s (Bezdek, e t . a l . , J _ ) . One p u r p o s e o f t h i s p a p e r i s t o d e s c r i b e t h e FCV c l u s t e r i n g algorithms, u s i n g t h e NILU i n v e s t i g a t i o n as an example of t h e i r a p p l i c a t i o n t o environmental chemometrics. Another purpose i s to i n t r o d u c e a new measure o f c l u s t e r v a l i d i t y f o r t h e s e a l g o r i t h m s . This measure, t h e y_a_l_i_d_^t_y d i s c _ r i_m i n a η t_, provides a q u a n t i t a t i v e replacement f o r the s u b j e c t i v e evaluations o f c l u s t e r q u a l i t y w h i c h h a v e been r e q u i r e d i n p r e v i o u s a p p l i c a t i o n s o f FCV c l u s t e r i n g , i n c l u d i n g t h e o r i g i n a l NILU s t u d y . A p a r t o f t h e NILU s t u d y has been r e i n v e s t i g a t e d using the v a l i d i t y d i s c r i m i n a n t , both t o i l l u s t r a t e i t s use and t o a t t e m p t t o f u r t h e r v a l i d a t e the c o n c l u s i o n s o f t h a t i n v e s t i g a t i o n . The FCV C l u s t e r i n g Method I n t h e f o l l o w i n g , l e t X = {x«j,..,x } d e n o t e a d a t a s e t c o n s i s t i n g o f η measurement v e c t o r s , x , each w i t h d features ( a t t r i b u t e s ) , x ; i.e., x = ( k 1 » ·· » k d ^ · n
k
x
k i
There i s a b a s i c d i f f e r e n c e between b e t t e r known m e t h o d s o f c l u s t e r a n a l y s i s f a m i l y of c l u s t e r i n g a l g o r i t h m s . That concerns the t r a d i t i o n a l requirement m e a s u r e m e n t v e c t o r b_e_ e v e n t u a 11 y a s s i g n e d o n l y o n e , o f t_he_ c l u s t e r c l a s s e s . I n FCV that requirement i s r e p l a c e d with a p a i r of ( 1 ) t h a t a measurement " b e l o n g " t o more t h a n one o f d e g r e e of_ m e m b e r s h i p i n a represented by some v a l u e i n
x
k
most o f t h e a n d t h e FCV difference that every t o one , and clustering, conditions:
v e c t o r may simultaneously the data c l a s s e s , with i t s p a r t i c u l a r c l u s t e r being t h e i n t e r v a l Γρ,ΐΠ;
( 2 ) tnat the t o t a l "membership" of a given m e a s u r e m e n t v e c t o r o v e r a l l t h e c l u s t e r s must sum t o unity. If the n o t a t i o n u = ^ ( x ^ ) i s used to r e p r e s e n t the degree of membership of the measurement v e c t o r x ( k = 1 , 2 , . . , n ) i n c l u s t e r i ( i = 1 , 2 ,.., c ), t h e n t h e two c o n d i t i o n s a b o v e c a n be g i v e n a c o n v e n i e n t m a t h e m a t i c a l statement : i
k
k
In Environmental Applications of Chemometrics; Breen, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
ENVIRONMENTAL APPLICATIONS OF CHEMOMETRICS
132 f
(1 )
0
