Description of Air Pollution by Means of Pattern Recognition

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7 Description of Air Pollution by Means of Pattern Recognition Employing the A R T H U R Program F. W. Pijpers Department of Analytical Chemistry, University of Nijmegen, The Netherlands

Pattern recognition methods have been used for the des cription of air pollution in the industrialized region at the estuary of the river Rhine near Rotterdam. A selection of about eight chemical and physical-meteoro logical features offers a possibility for a description that accounts for about 70% of the information that is comprised in these features with two parameters only. Prediction of noxious air situations sometimes succeeds for a period of at most four hours in advance. Some times, however, no prediction can be made. Investiga tions pertaining to the correlation between air compo sition and complaints on bad smell by inhabitants of the area show that, apart from physical and chemical descriptors, other features are also involved that depend on human perception and behaviour. Description of the Problem In our laboratory, pattern recognition has been used i n s o l ving a variety of problems. Recently we set for ourselves a goal to investigate the p r o b a b i l i t y of describing a i r p o l l u t i o n i n h i g h l y i n d u s t r i a l i z e d regions i n such a way that, by taking appropriate measures, complaints from inhabitants of the area would be prevented. The DCMR* - a governmental organization i n The Netherlands c o l l e c t s data on various constituents of polluted a i r at a number of locations situated near and i n a highly i n d u s t r i a l i z e d area at the estuary of the r i v e r Rhine, near Rotterdam. Occasionally, when weather conditions demand i t , warnings for expectations of emergency a i r p o l l u t i o n situations are dispatched to the industries i n the area. These d i c t a t e a l i m i t a t i o n of the emission of S02, r e s u l t i n g from burning of sulfur-containing f u e l . In s p i t e of these well o r ganized actions, complaints from inhabitants of the area, who are stimulated to communicate t h e i r observations by telephone to the same o f f i c e that dispatches the warnings, cannot be precluded.

* Central Environmental Control Agency, Rijnmond 0097-6156/ 85/0292-0093506.00/ 0 © 1985 American Chemical Society Breen and Robinson; Environmental Applications of Chemometrics ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

ENVIRONMENTAL APPLICATIONS OF CHEMOMETRICS

94


Because of the complex s i t u a t i o n , which has to be described by a set of parameters pertaining to the c o n s t i t u t i o n of the atmosphere at various locations and to the weather conditions, the a p p l i c a t i o n of pattern recognition methods seems obvious. (1-5) The aim of t h i s investigation i s twofold: - Finding the relevant features that describe emergency s i t u a t i o n s . - P r e d i c t i o n of the evolution of these features i n time, i n order to enable a forecast of p o t e n t i a l emergency situations and allow the proper measures to be taken i n time. Thus, the burden on the inhabitants of the area may be a l l e v i a t e d . Without going into the d e t a i l s of the numerous techniques that are being used i n pattern recognition, a general outline of the method of problem handling by means of the ARTHUR package may be c l e a r l y i l l u s t r a t e d from an approach to the a i r p o l l u t i o n problem. (See Table I) - For a s t a r t , the pattern of an atmospheric composition and s i t u a t i o n , i . e . , a data vector comprising a l l available physical and/or chemical data pertaining to that s i t u a t i o n , i s positioned i n a multidimensional feature space that i s spanned by a l l physical ( i . e . , meteorological) and chemical ( i . e . , compos i t i o n a l ) named features. - When a number of s i t u a t i o n s , positioned i n that feature space, group together or c l u s t e r , i t i s obvious that t h e i r physical and chemical behaviour i s s i m i l a r . This w i l l be perceived by the population of the area i n the same way. In pattern recognition i t i s assumed that such behaviour not only holds f o r the known physi c a l and chemical data but also r e f l e c t s s i m i l a r behaviour of properties such as fresh a i r or noxious a i r . - In t h i s discussion we s e l e c t a number of consecutive days where a period with many complaints i s preceeded and followed by an about equal period of "good" days to see whether at l e a s t two d i f f e r e n t c l u s t e r s of patterns i n the feature space may be found that c o r r e spond with the property polluted a i r versus fresh a i r . - In case we succeed i n finding these c l u s t e r s we may proceed by sel e c t i n g those features that are most relevant for the d e f i n i t i o n of the c l u s t e r i n g . Here the techniques applied focus on c o r r e l a t i o n among the features themselves and a c o r r e l a t i o n between the features and the d i g i t i z e d property. (C0RREL and WEIGHT are the appropriate sub-routines i n the ARTHUR package). (6) - F i n a l l y the relevant feature combination f o r the description of the s i t u a t i o n s where complaints may occur can be used to predict the possible occurrence of bad situations i n the (near) future. Discussion of the results In Figure 1, a map i s presented of the estuary of the r i v e r Rhine near (west of) Rotterdam. The i n d u s t r i a l i z e d region i s situated around the harbors located south of the r i v e r near Hoogvliet. R e f i n e r i e s and f e r t i l i z e r plants are found there. In Table 1, various stages i n pattern recognition are l i s t e d . The subroutine CHANGE, i n combination with the INPUT-format i s used i n stages one and two. HIER, TREE and PLANE are useful i n stage three, whereas C0RREL and

Breen and Robinson; Environmental Applications of Chemometrics ACS Symposium Series; American Chemical Society: Washington, DC, 1985.


Royal Society of Chemistry.

Reproduced with permission from Ref. (7). Copyright 1984,

The

Figure 1. Map of the estuary of the r i v e r Rhine, near Rotterdam.



96


WEIGHT are employed i n stage four. Addition of an extra number of patterns i n a TEST-set allows v a l i d a t i o n of the learning machine developed i n the previous stages. Table II l i s t s the chemical and p h y s i c a l measurements that produce the feature space. A l i s t of complaints as coded from the communications from the population i s a l s o given. A p p l i c a t i o n of the inter-feature c o r r e l a t i o n c a l c u l a t i o n , CORREL, on the chemical and physical features l i s t e d here, results i n a l i m i t a t i o n of the number of features without s a c r i f i c i n g too much information. Apart from the s t a b i l i t y parameter, representing the meteorological conditions, some chemical constituents of polluted a i r are found to be of importance i n describing the s i t u a t i o n (see Table I I I ) . Construction of the interfeature variance-covariance matrix, followed by an eigenvector-eigenvalue c a l c u l a t i o n according to the Karhunen - Loéve procedure (KARLOV), produces a number of eigenvectors equal to the number of features. I t i s found that the two highest eigenvalues comprise 78% of the t o t a l information, and thus, should provide a reasonable picture of the s i t u a t i o n . The two c l u s ters representing "bad" and "good" situations r e s u l t i n g from a projection on the plane defined by the f i r s t two eigenvectors i s given i n Figure 2.

Table I . Various Stages i n Pattern Recognition 1. D e f i n i t i o n of problem space and data vectors 2. Selection of patterns f o r a t r a i n i n g set 3. Search for c l u s t e r s by various techniques 4. S e l e c t i o n , ordering and weighting of relevant ( i t e r a t i o n between step 3 and 4)

features

5. Predictions f o r a t e s t set

From t h i s figure one could get the f a l s e impression that the problem has been solved. This i s not true because t h i s r e s u l t could only be obtained with a c a r e f u l l y selected data set measured early i n May, 1979. The weather was stable during the e n t i r e observation p e r i o d , comprising two weeks with many complaints, followed and preceeded by two weeks of p r a c t i c a l l y no complaints. The other months of that year showed a much less predictable s i t u a t i o n . In order to see whether the development i n time of a given s i t u a t i o n could be followed, autocorrelation functions of a l l relevant features were constructed. From these functions i t was observed that, provided the weather was not too unstable, an autocorrelation time of about four hours was encountered. This autocorrelation was best defined f o r S02 concentrations that are measured hourly at various


7. P U P E R S

97

Description of Air Pollution


Table I I . L i s t of Observed Features

Chemical Compounds

Meteorological Conditions

Nitrous oxide N i t r i c oxide Sulfur dioxide Standardized smoke Saturated and O l e f i n i c Hydrocarbons Ozone

Direction of the wind Speed of the wind Relative humidity Temperature Sunlight r a d i a t i o n Amount of p r e c i p i t a t i o n A i r pressure Cloudiness Stability

Types of Complaint Soot, dust Noxious smell A c i d , chemical smell O i l y smell Smog Others

Table I I I . L i s t of Relevant Features S t a b i l i t y (Meteorological conditions) Ozone Saturated hydrocarbons O l e f i n i c hydrocarbons Sulfur dioxide at three d i f f e r e n t locations

locations i n contrast to other a i r constituents that are measured l e s s frequently. This time dependency has been translated into features that could be employed i n the pattern recognition process by introducing not only the actual concentration of S02 but also i t s time dependence as concluded from observations up to four hours i n the past.


98



Based upon these features another learning machine was constructed for the year 1982, describing the s i t u a t i o n with exclusion of the months September t i l l December when the weather was i n general too unstable. From that period 36 situations have been selected where complaints were registered f o r at l e a s t two consecutive hours. These data were completed by another 36 situations without complaints, selected exactly 24 hours before or a f t e r a period with complaints. The time dependence of the d i r e c t i o n of the wind was taken i n to account by integration over a period of four hours i n the past. These features were autoscaled, weighted and combined l i n e a r l y according to the Karhuhnen-Loeve transformation. (See Table IV). This table refers to the s i t u a t i o n i n the c i t y of Schiedam. The eigenvectors l i s t e d here are represented by the squares of the c o e f f i c i e n t s ; the two most important ones account f o r 68% of the variance of the e n t i r e set of features. I t i s seen i n Figure 3 that the projection of the patterns on the plane spanned by these two eigenvectors i s dominated by two complaint patterns with exeptional feature values. One may a l s o note the overlap between the c l u s t e r with complaints and that without complaints. In search f o r a better d e s c r i p t i o n , and taking into account that the impressions registered by the human nervous system should be rated on a l o g i r i t h m i c scale; a new transformation was t r i e d , t h i s time based upon logarithmized features. This resulted i n Table V, where i t i s seen that a somewhat enhanced information from the f i r s t two eigenvectors was obtained, i n comparison with that of Table IV (68% and 71% r e s p e c t i v e l y ) . The merits of t h i s learning machine are v i s u a l i z e d i n Figure 4, where apart from the t r a i n i n g set patterns an extra set of 13 patterns with complaints and 13 patterns without complaints i s added and projected as a t e s t set. According to the nearest neighbour voting system, eight out of t h i r t e e n non-complaint situations and nine out of thirteen complaint situations are positioned c o r r e c t l y . This i s not an impressive r e s u l t . Apparently the "reason" for complaints i s not exclusively described by physical or chemical parameters. This observation i s a l s o i l l u s t r a t e d by another c a l c u l a t i o n . In Figure 5, the hourly patterns of one day (24 hours) were p r o j e c ted on the t r a i n i n g set. This day, May 17th, 1982, at Schiedam comp r i s e s two hours with complaints, v i z . , 13 and 14 hour. I t i s seen that the s i t u a t i o n evolves from the area where no complaints are predicted towards the complaint area. About 8.00 hour the borderline i s crossed and indeed at 13.00 and 14.00 hour complaints are recorded. The 15th and 16th hour, that are c l e a r l y i n the complaint area, are not s i g n a l l e d , and the trace ends at 23 hours without complaints i n the non-complaint area as was expected. However, t h i s procedure f a i l e d completely with the hourly data set collected on July 7th and 8th i n the same location (See Figure 6). Here the evolution i n time of the a i r composition pattern vector c i r c l e s around i n the boundary area between complaint and non-complaint s i t u a t i o n s . There are complaints registered at 12 and 13 hours, however, why i s not c l e a r from the p i c t u r e . This i s another i l l u s t r a t i o n of the observation that features other than physical or chemical ones may be involved i n triggering complaints by the population.


7. PUPERS

99



Table TV. Karhuhnen-Loeve Transformation of "Schiedam" Data (Autoscaled and Weighted) Eigenvector Feature

First

Second

Sulfur dioxide (loc.10) Sulfur dioxide ( l o c . l l ) Direction of wind * V a r i a t i o n i n s u l f u r dioxide ( l o c . l l ) Sulfur dioxide (loc.12) Sulfur dioxide (loc.13) V a r i a t i o n i n s u l f u r dioxide (loc.10) Saturated hydrocarbons

0.30 0.15 0.01 0.12 0.16 0.12 0.12 0.02

0.00 0.23 0.49 0.04 0.09 0.!1 0.04 0.00

1.00

1.00

Eigenvalue ( i . e . , information) 54% + 14% = 68%

Table V. Karhunen-Loève Transformation of "Schiedam" Data (Ilogarithmized, Weighted and Autoscaled) Eigenvector Feature First Second

Log Sulfur dioxide Log Sulfur dioxide Log Sulfur dioxide Log Sulfur dioxide Log V a r i a t i o n S02 Log V a r i a t i o n S02 Direction of wind*

Eigenvalue ( i . e .

(loc.10) (loc.ll) (loc.12) (loc.13) (loc.10) (loc.ll)

information)

0.36 0.28 0.12 0.10 0.06 0.06 0.02

0.00 0.32 0.21 0.36 0.04 0.03 0.04

1.00

1.00

58% + 13% = 71%

* Integrated backwards i n time f o r 4 hours.


100


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F i g u r e 2. P r o j e c t i o n of hours Ο , w i t h c o m p l a i n t s , and • , w i t h o u t c o m p l a i n t s , of a i r p o l l u t i o n on the two most s i g n i f i c a n t e i g e n v e c t o r s of the Karhunen-Loeve t r a n s f o r m e d , s e v e n - d i m e n s i o n a l f e a t u r e space. Reproduced w i t h p e r m i s s i o n from Ref. 7. C o p y r i g h t 1984, The Royal S o c i e t y of C h e m i s t r y .

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F i g u r e 3. P r o j e c t i o n o f h o u r s # , w i t h c o m p l a i n t s , a n d O , w i t h o u t c o m p l a i n t s , of a i r p o l l u t i o n on the two most s i g n i f i c a n t e i g e n v e c t o r s . See T a b l e IV.


Description of Air

PUPERS

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F i g u r e 4. P r o j e c t i o n of hours · , w i t h c o m p l a i n t s , and O, w i t h o u t c o m p l a i n t s , i n c l u d i n g t e s t s e t p a t t e r n s • , w i t h c o m p l a i n t s , and • , w i t h o u t c o m p l a i n t s . See T a b l e V.

F i g u r e 5. P r o j e c t i o n of hours # , w i t h c o m p l a i n t s , and Ο » w i t h o u t c o m p l a i n t s , i n c l u d i n g a t e s t s e t o f 24 h o u r l y measurements on May 17, 1982,· , w i t h c o m p l a i n t s , and • , w i t h o u t c o m p l a i n t s , s t a r t i n g a t 0.00 h. Breen and Robinson; Environmental Applications of Chemometrics ACS Symposium Series; American Chemical Society: Washington, DC, 1985.


102


Figure 6. Projection of hours ·, with complaints, and °, without complaints, including a test set of hourly measurements on July 7 and 8 •, with complaints, and

D

without complaints·


7. PIJPERS


103

S t a t i s t i c a l and mathematical procedures In order to treat a l l features without preference, they are scaled such that a l l feature-axes i n the multi-dimensional feature space get an equal length according to


X

' i ,

k

-

( x

i , k - x i ) / t ( Ν - 1 ) ^ α ( x. ) }

1

which i s named autoscaling. Here χ . , represents the autoscaled Ν feature i f o r pattern k; χ. = Σ χ. ,/N; Ν the number of patterns ι k 1

1

and σ (

,

,

k

k

) the standard deviation of feature i ,

α ( χ. ) = { I * , ( x

i > k

according to

2

- \

) /(N-.) }*

Thus the center of each axis equals zero and the d i s t r i b u t i o n around the center becomes symmetrical

for Gaussian distributed feature

values; σ (x^) represents the unit length along the axes. The distance d. . between two patterns i and j i n the m u l t i dimensional feature space i s calculated according to the Euclidean distance d e f i n i t i o n :

d

where M

i,j

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{

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, k

, i

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-

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represents the number of features and thus the dimensiona

l i t y of the feature space. x

f

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feature k with pattern i . The distances are collected i n the d i s tance matrix with the dimension Ν * Ν. This matrix i s symmetrical around the diagonal; a l l diagonal elements are zero. The h i e r a r c h i c a l clustering procedure operates on the d i s tance matrix. Clustering of patterns i s searched f o r by combining patterns with high s i m i l a r i t y into gravity centres, i n between the s i m i l a r patterns. Here, a s i m i l a r i t y scale runs from 1 to 0 according



104

to


S. . = 1 - d. . / D i,J i , j max where D represents the highest numerical value encountered i n the distance matrix. After each combination of two patterns or of a pat tern and a gravity center, the distance matrix i s recalculated. The procedure i s followed graphically and ended when a preset number of clusters i s found or when the gravity centers of the clusters upon combination have to travel beyond a preset distance. The graphical representation of the c l u s t e r i n g retains distances or s i m i l a r i t i e s but omits the mutual o r i e n t a t i o n of various patterns. The minimal spanning tree also operates on the distance ma t r i x . Here, near by patterns are connected with lines i n such a way that the sum of the connecting lines i s minimal and no closed loops are constructed. Here too the information on distances i s retained, but the mutual o r i e n t a t i o n of patterns i s omitted. Both methods, h i e r a r c h i c a l clustering and minimal spanning tree, aim for making clusters i n the multi-dimensional space v i s i b l e on a plane. The c o r r e l a t i o n between two features ρ and g reads

C P

= '

g

1 (Ν=Τ).σ .σ Ρ g

if , (χ , - χ ' k

=

1

p

k

P

) (χ . - Χ ' g

k

)

g

where a l l symbols have the meanings as defined above. The weight of a feature depends on i t s a b i l i t y to separate two categories or clusters j and k from each other. The equation for the variance weight W. . for feature i reads.

2 2 W. . . = (x' ) · · + (Χ' ), ( M 2 )

i,j

+

( M 2 )

. - 2 χ'. . χ. .

i,k

Here χ'. . represents the autoscaled value for feature i f o r a pattern*'situated i n c l u s t e r j and (M2) the second moment for a l l feature values i of the N. patterns i n cluster j according to

N

(M2).

i .= Σ k=l

2

( x \ , - x \ . ), i,k i,k'/

M

The Karhuhnen-Loève transformation represents an eigenvalueeigenvector c a l c u l a t i o n based upon the variance- cοvariance matrix of the features. I t aims for a l i n e a r combination of features such that there are as much l i n e a r combinations as features. The l i n e a r combinations are mutually orthogonal and have a norm equal to one. Each l i n e a r combination (eigenvector) accounts for a part of the


7.

PIJPERS


105

t o t a l variance encompassed by the features. The vectors are ranked according to t h i s variance - the eigenvalue.


Conclusions Pattern recognition offers a useful t o o l f o r the d e s c r i p t i o n of a i r p o l l u t i o n i n i n d u s t r i a l i z e d areas. Depending on the weather conditions, sometimes even a p r e d i c t i o n of situations with bad-smell i n g a i r may be obtained. However, when the weather conditions are unstable, no v a l i d p r e d i c t i o n i s p o s s i b l e . Apart from p h y s i c a l , meteorological and chemical features, other factors must be accounted for to predict the burden f e l t by people l i v i n g i n the area. Acknowledgments Thanks are due to J . E . Evendijk, J . H . C . E i l e r s and P.J.W.M. Muskens, D . C . M . R . , for making the measured data on a i r constituents available to us; to G . A . P . E . Jacobs and G . J . H . Roelofs who d i d the computations and computer programming during t h e i r graduate studies at our laboratory; and to B.R. Kowalski f o r making the computer program "ARTHUR" available to us.

Literature Cited 1. Tan J.T., and Gonzales, R.C., "Pattern recognition Principles," Addison-Wesley, Reading, MA, 1979. 2. Jurs, R.C., and Isenhour, T.L., "Chemical Applications of Pattern Recognition," Wiley, New York, 1975. 3. Isenhour, T.L., Kowalski, B.R., and Jurs, R.C., CRC Crit. Rev. Anal. Chem. 1974, 4, July, 1. 4. Kateman, G., and Pijpers, F.W., "Quality Control in Analytical Chemistry," Wiley, New York, 1981. 5. Massart, D.L., and Kaufman, L., "The Interpretation of Analytical Chemical Data by the Use of Cluster Analysis," Wiley, New York, 1983. 6. Duewer, D.L., Koskinen, J.R., and Kowalski, B.R., "ARTHUR," Laboratory for Chemometrics, Department of Chemistry BGlO, University of Washington, Seattle, WA. 7. Pijpers, F.W., Analyst, 109 299 (1984) Received July 17, 1985


Description of Air Pollution by Means of Pattern Recognition

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