c/EPA
                       Environmental Monitoring
                       Systems Laboratory
                       P.O. Box 15027
                       Las Vegas NV 89114-5027
                        March 1984
            Research and Development
Feasibility of Using Infrared
Spectroscopy and Pattern
Classification for Screening
Organic Pollutants in
Waste Samples

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                                                    600R84110
FEASIBILITY  OF  USING  INFRARED SPECTROSCOPY AND PATTERN
   CLASSIFICATION  FOR SCREENING ORGANIC POLLUTANTS
                   IN WASTE SAMPLES

                         by

                   Donald E. Leyden
               Department of Chemistry
             Colorado State University
                Fort  Collins, CO 80523
       Interagency Agreement No. DW 930078-01-1
                  Project Officer
                  Chas Fitzsimmons
         Advanced Monitoring Systems Division
     Environmental Monitoring Systems Laboratory
           Environmental Protection Agency
                Las Vegas, NV 89114
     This  study was conducted in cooperation with
    National  Aeronautics and Space Administration
               Langley Research Center
                  Hampton, VA 23665
     ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
          OFFICE  OF RESEARCH AND DEVELOPMENT
         U.S.  ENVIRONMENTAL PROTECTION AGENCY
                 LAS VEGAS, NV 89114

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                                     NOTICE
     The information in this document has been funded wholly or in part by the
United States Environmental  Protection Agency under Interagency Agreement
Number DW 930078-01-1 to the National Aeronautics and Space Administration,
Langley Research Center.  It has not been subjected to the Agency's peer and
administrative review, and therefore does not necessarily reflect the views  of
the Agency.  Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
                                       11

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                                    ABSTRACT
     This project was undertaken to determine the feasibility  of using  pattern
classification techniques and infrared spectroscopy to screen  hazardous waste
samples in the field.  The technique would require a portable  IR spectrometer
and a microcomputer to perform a binary pattern classification of the spectra.
The classification scheme requires "training" on a main frame  computer  to  pro-
duce weighting vectors from infrared library spectra.  The weighting vectors,
when applied to pattern vectors obtained from sample spectra,  could classify
samples in the field as being likely or not likely to contain  hazardous sub-
Stances as defined by the spectral library.

     Preliminary tests of the scheme using 50 compounds from the U.S. Environ-
mental Protection Agency Priority Pollutant List are encouraging.  The  ability
of the simple, linear, binary pattern classification scheme to predict  whether
a compound is in the class known as hazardous pollutants appears feasible.

     This report was submitted in partial  fulfillment of Interagency Agreement
No. DW89930548-01-1 by Colorado State University (CSU) under the sponsorship of
the EPA.  CSU was a subcontractor to Martin-Marietta, the prime contractor  for
this project.  The contract was administered by the National Aeronautics and
Space Administration under the Agreement with EPA.  This report covers  a period
from March 7, 1983 to December 1, 1983 and work was completed  as of December 1,
1983.

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                                    CONTENTS

Abstract	iii
Acknowledgment 	     v
1.   Introduction  	     1
2.   Conclusions   	     2
3.   Infrared Spectroscopy 	     3
4.   Experimental  	     9
5.   Results	    12
6.   Suggested Further Research  	    14
References	    16
Appendices
Appendix A - Binary Pattern Recognition Code 	    17
Appendix B - Output run one	    20
Appendix C - Output run two	    21
Appendix D - Output run three	    22
                                       iv

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                                 ACKNOWLEDGMENT
     The assistance of Mr.  Jeff Cornell,  a  student at Colorado State University,
and the assistance of Mr. John Coates  and Mr.  Dennis Schaff, Perkin-Elmer
Corporation, are acknowledged.

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                                   SECTION 1
                                  INTRODUCTION

     This feasibility study was part of a larger project jointly funded by EPA
and NASA under an interagency agreement entitled Electronic Methods for In-Situ
Monitoring of Hazardous Wastes.  Two approaches were under investigation, x-ray
fluorescence spectroscopy and infrared spectroscopy.  Martin-Marietta,  Denver
Division, was the prime contractor (to NASA) and was responsible for both
efforts.  The infrared feasibility study was subcontracted to Coloraado State
University and composed only 5% of the total project budget, the major  effort
being the development of x-ray fluorescence spectrometry as a viable field
screening technique for hazardous wastes.

     The goal of this project was to perform a feasibility study to determine
whether it is possible to screen environmental samples, especially industrial
wastes and sludges in the field, and thus to determine if hazardous pollutants
are likely present.  The proposed instrumental technique is infrared spectroscopy,
most likely some form of Fourier transform infrared spectroscopy.  The  proposed
decision making technique is pattern recognition or pattern classification.

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                                   SECTION  2



                                  CONCLUSIONS





     By using a limited data set  of infrared  spectra  and  limited  time,  it  has



been determined that the ability  of a  simple, linear,  binary,  pattern clas-



sification scheme to predict whether a compound  is  in  the class known as



hazardous pollutants appears feasible.







     This study also has shown that preliminary  investigations using infrared



spectra and pattern classification schemes  can be conducted  on a  microcomputer.

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                                   SECTION 3
                             INFRARED SPECTROSCOPY

     The coupling of infrared and pattern classification has precedents in the
literature (1,2).  A brief introduction will be given for each.

INFRARED SPECTROSCOPY

       Organic molecules contain a variety of forms of energy.   One of these
is that manifested as vibration of the chemical bonds.  The absorption of
electromagnetic radiation in the region known as infrared (2.5-15 micrometer
wavelengths) can cause transitions in the level or state of these vibrations.
Scanning through this wavelength range results in a plot of absorption versus
wavelength, or an infrared spectrum, which is characteristic of the compound or
mixture of compounds in a sample.  Fourier transform infrared spectroscopy is
an instrumental and mathematical method of collecting many such scans in a
short period of time, thus improving the signal-to-noise ratio.   The signal-to-
noise ratio increases proportionally to the square root of the  number of repet-
itive scans.  Thus, for example, by scanning 100 times, improvement by a factor
of 10 is usually realized experimentally.  As a result of Fourier transform
techniques, it is reasonable to expect to obtain a spectrum from less than
microgram quantities of many types of organic molecules.  Thus,  infrared spec-
troscopy has found use in environmental analyses (3).  It is expected that in

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many types of matrices, a few hundred parts per billion of several  molecular
types can be detected, but not quantitatively determined.   The detection limit
will depend upon the type of infrared chromophore (color producing group) in
the molecular structure.

PATTERN CLASSIFICATION

     The availability of high-speed computers for processing large amounts of
data has led to the consideration of volumes of data which were previously
implausible to treat.  One outcome of this ability has been the use of pattern
recognition or pattern classification techniques in chemistry.  According to
Jurs and Isenhour (4), pattern recognition "includes the detection, perception,
and recognition of regularities (invariant properties) among sets of measure-
ments describing objects or events."  Pattern recognition  is normally used by
chemists and others to classify a set of experimental  data as a member of a
class.  This technique has been applied to many types of problems.

     A basic pattern recognition system usually contains the units shown in
Figure 1 (4, p.3).
        Figure 1.  Block diagram of a basic pattern recognition system.
                                       4

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The transducer converts information from the laboratory format into the pattern



space of the pattern recognition system.  Often, this entails no more than



converting the raw data into a suitable computer format.  The preprocessor



accepts the data and converts it into a form which is dealt with more easily by



the classifier.  The classifier treats the data by some algorithm to produce a



classification decision.  The classifier may be based on various branches of



applied mathematics, statistical decision theory, information theory, or geom-



etric theory.  There exists a variety of pattern classification systems includ-



ing those for multicategory classification.  However, in this report only a



binary classification system is considered and discussed.







     The object of this feasibility study is to determine whether the presence



of hazardous organic pollutants such as, but not limited to, those on the



Environmental Protection Agency Priority Pollutant List can be predicted from



an infrared spectrum of industrial  waste samples.  Thus, only a binary classi-



fier is required to determine whether or not the samples contain such compounds.



The hazardous pollutants often contain such organofunctional groups as C-C1



bonds, phenolic groups, polyaromatic hydrocarbons (PAH's)  and other structural



units represented in infrared spectra.  Usually, determining even the likely



presence of such compounds requires extensive preanalytical separation for



successful detection by IR spectroscopy.  A fast inexpensive method of sample



classification could be an effective cost-saving aid.







     Chemical data such as infrared spectral information may be represented as



a d-dimensional pattern vector:

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                                X = xljx2s...xd                             (1)

The components Xj are observable quantities such as the wavelength  of a  peak  in
an infrared spectrum of a compound.  Alternatively, the spectral  region  may  be
divided into subregions, and the x,- values would then  represent  the intensity
of the absorption in each subregion.  If there were 100 such  subregions, there
would be 100 dimensions of data, or a set of vectors in 100-space,  one set for
each of the subregions of the infrared spectrum.  If thousands  of compounds  are
considered, clearly a vast amount of data could result.

     For a binary classifier, the two classes of data  should  fall  on either
side of a decision surface.  For a simple two-space case,  this  amounts to
tracing a line (not necessarily a straight one) that runs  between the two
classes of data.   In hyperspace, the analogy is a hyperplane  that may or may
not be linear and separates the two classes of data.  The  case  is simpler if  a
linear hyperplane can be used as it can be represented by  a vector  from  the
origin.  In such a case, the sign of the dot product of the normal  vector W  and
a pattern vector X defines on which side of the hyperplane a  given  pattern
point lies (4, p.11):

                              W-X = |W| |X| cos 0                         (2)

where 9 is the angle between the two vectors.  Since the normal  vector is
perpendicular to the hyperplane, all patterns having dot products that are
positive lie on the same side of the plane as the normal vector,  and all  those
with negative dot products lie on the opposite side.  Although  decision

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surfaces need not be linear, their simplicity is appealing.

     Often a concept called Threshold Logic Units (TLU) is used for linear,
binary classification.  This method uses some function which generates one of
two results based on the input data.  A decision is based upon whether the
result is greater or less than the threshold value.  The result may be computed
by weighted components, wj, of the normal  vector, W, applied to each term in
the data set
                 W-X = |W| |X| cos 0 = w1x1+w2x2+...+wrfxc|+w(.|+1           (3)

where W^+i is added to project the vector from the origin.  The weight compo-
nents are determined by "training" the classifier with a set of data of known
classification.  These data are known as the "training set" which is considered
by the classifier one set at a time.  The weight vector components w
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be used with a single Read Only Memory (ROM)  for the program and data.
                                        x   x
                                          x x  .•
                                             • *
                                         X..'
                                    ,x O   .''a  O  O
                                          o    o
       Figure 2.   Example of a  two-space,  linear,  binary  classification.
           Two classes of data  represented by  x  and  o,  respectively,
            fall  on either side of the  decision  plane  represented  by
            the dashed line. An upper  and lower threshold  (TLU) are
             represented by dotted lines.   Data  which  fall  between
                    the threshold limits are not classified.

                                       8

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                                   SECTION 4



                                  EXPERIMENTAL







     This feasibility study was performed with  limited resources.   However,  the



success that was obtained illustrates the possibility of using  small  computers



for the application of using pattern classification and infrared  spectrometry



to screen hazardous waste samples in the field.   Appendix A shows  the listing



of a computer program for linear, binary pattern classification written  in



Apple Computer Applesoft language.  This program was translated from  the FORTRAN



program given in the appendix of the book by Jurs and Isenhour  (4).   The program



was executed on an APPLE 11+ (Apple Computer, Cupertino, CA)  computer.







     The original plan for this study was to use a computer data  station from a



vendor of infrared instrumentation along with infrared data on  diskette.



Several unfortunate events occurred.  The liaison from the vendor  failed for



several months to arrange the loan of a data station.  Once obtained, no soft-



ware support or manuals were available.  The form of the data on  the  diskettes



was found to be unsatisfactory for use in a classification program.   Therefore,



as described below, an alternative was found.  Although not considered to be



completely satisfactory, a meager amount of data were utilized  which  shed some



insight to the question at hand.







     The spectra for 100 compounds were encoded  for use in this study.   Fifty

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compounds were selected from the Environmental  Protection Agency Priority



Pollutant List.  An additional  50 compounds were selected which  are not  on



either the EPA Priority Pollutant List or in Appendix VIII,  40CFR261  (RCRA).



Data for the Priority Pollutants were derived from spectra published  by  Sadtler



(5) and data for the other compounds were derived from spectra published by  the



Aldrich Chemical Co. (6).  The infrared spectra of these compounds  were  divided



into eight regions (Table 1).  Each region is in units of cm~l,  and the  data



entry is a one (1) if a peak is present in the region and zero (0)  if no peak



is present in the region.







                                    TABLE 1.
Spectral
Region
1
2
3
4
Range of Wave
Numbers (cm*l)
200-500
501-1000
1001-1500
1501-2000
Spectral
Region
5
6
7
8
Range of Wave
Numbers (cm-1)
2001-2500
2501-3000
3001-3500
3501-4000
The data set was assigned a "dot product" or class of one (1)  if the compound



were a hazardous pollutant, or a negative one (-1) if it were  not.   A training



set was made up from 80 of the 100 compounds, 40 from the Priority  Pollutant



List (hazardous), and 40 from the Aldrich library (nonhazardous).   This  left



the spectra of 20 compounds (10 from each classification) to be used as  test



data.  Although this is a meager and greatly simplified data set, the results



are encouraging.  These data were analyzed using the program shown  in Appendix





                                    10

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A, requiring approximately 45 seconds  to execute  on  the APPLE  11+ computer.
                                     11

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                                   SECTION 5
                                    RESULTS

     The results of the use of the data described  above  executed  in  the
Applesoft program are shown in Appendix B. The first  line  indicates that 60
data sets are to be used in training,  that there are  eight  data in each  set,
and that the TLU has been set to 0.75  on each  side of  a  linear surface.  The
nine weight vectors (including the w^+i component) are the  weight vectors for
each datum.  There were 26 feedback iterations to  determine the weight vectors;
each were set initially at 0.1 in line 130 of  the  program.   With  a deadzone
(TLU) about the decision surface of 0.75, 13 of the 20 data sets  were predicted
and 7 were not.  Of the 13 predicted,  1 was predicted  incorrectly.   With a
deadzone (TLU) about the decision surface of 0, 20 of  the 20 data sets were
predicted and 5 predicted incorrectly.  Thus,  with this  simple set of data, 75
percent of the test set were correctly predicted with  a  training  of  26 feed-
backs.

     Appendix C shows a modified run of the program in which 70 data sets were
used as the training set and a TLU of  1 was specified.   The increased TLU
increased the magnitude of the weight  vector components  which has the effect of
spreading the vectors in hyperspace.  All  10 compounds of the test set were
predicted when 500 feedbacks were allowed, but when the  TLU was reduced  to
zero, 3 were incorrectly predicted.
                                    12

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     Appendix D shows the results of a run in which 80 data  sets  were  used  to



train for the prediction of 20 data sets,  all  of which were  known to fall into



one of two classes.  All 20 compounds of the test set were predicted correctly



with 100 iterations and the TLU set at both 0.75 and zero.







     Although this feasibility study was not as  extensive as desired because of



a variety of problems including limited funding  and delays in the loan of equip-



ment, some encouraging results were obtained.   If an appropriate  number of



training data were to be used, the execution time on a microcomputer would  be



prohibitively long, but this study shows that preliminary work can be  conducted



on such a computer.  The majority of the computer time is spent  in the training



session.  Once the weight vectors are obtained,  the prediction takes only a few



seconds to determine, as this is a direct, not an iterative  computation.



Clearly, a small microcomputer such as those associated with modern spectrom-



eters can perform this computation.  Most  importantly, although  the data set



used was small, the ability of the simple, linear, binary pattern classifica-



tion scheme to predict whether a compound  is in  the class known  as hazardous



pollutants appears feasible.
                                     13

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                                   SECTION 6

                           SUGGESTED FURTHER RESEARCH



     The results and conclusions of this feasibility study suggest the probable

success of further research.  Provided that an infrared spectrometer containing

even the most basic microcomputer can be designed with sufficient sensitivity

and portability, a research plan to develop a system for the rapid, inexpensive,

and reliable screening of hazardous waste samples for as little as a few micro-

grams of organic pollutant is recommended.  First, a large data file of infrared

spectra suitable for use in a pattern recognition scheme would be obtained on a

lease basis.  The most obvious of these data bases is that from Sadtler.  The

general pattern classification program "ARTHUR"£/ would be obtained for execu-

tion on a large mainframe computer.  This program permits the use of a wide

variety of pattern classification techniques.  Therefore, one would not be

restricted to the linear, binary classification used here.  However, linear,

binary classification would be explored in detail first because of its mathe-

matical simplicity.  The judicious use of asymmetric TLU's would be explored to

"bias" the decision to predict the presence of probable pollutants even when

they might not be present, j_f that were a desired result.
   ARTHUR is a generalized pattern classification program available from
   Infometrix, Seattle, Washington.  It is planned to be made available in
   a microcomputer version.
                                       14

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     These studies would be required on pure compound spectra  first.    Then,



computer-generated spectra of mixtures simulated by linear addition  of the



spectra of pure compounds would be investigated.  For example,  the reliability



of the prediction when a trace of pollutant was  mixed with a  large amount of



some other compound would be tested.  This would be a severe  and  critical test.



Fortunately, it can be performed using computer-generated  data.   Preparation  of



laboratory mixtures would only be necessary to test the instrumentation.







     It is estimated that this research could be conducted during one  year  at a



cost of approximately $70,000.
                                       15

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                                   REFERENCES








1.   B. R. Kowalski, P.  C.  Jurs,  T.  L.  Isenhour and C. N. Reilley, Anal. Chem.,



     4U 1945 (1969).








2.   R. W. Liddell, III, and  P. C.  Jurs,  Appl. Spectres., 27_, 371, (1973).








3.   A. L. Smith, APPLIED INFRAFRED  SPECTROSCOPY, FUNDAMENTALS, TECHNIQUES AND



     ANALYTICAL  PROBLEM-SOLVING,  Wiley-Interscience, New York, New York, 1979.








4.   P. C. Jurs  and T.  L. Ishenhour,  CHEMICAL APPLICATIONS OF PATTERN



     RECOGNITION, Wiley-Interscience, New York, NY, 1975.







5.   INFRARED SPECTRA HANDBOOK OF PRIORITY POLLUTANTS AND TOXIC CHEMICALS,



     Sadtler Research Laboratories,  Philadelphia, PA, 1982.








6.   C. J. Pouchert, THE ALDRICH  LIBRARY  OF  INFRARED SPECTRA, 2ND EDITION,



     Aldrich Chemical Co.,  Inc.,  Milwaukee,  WI, 1978.
                                       16

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                          APPENDIX  A
TO  REM  »»»*>*»*»»*»» BINARY PATTERN RECOGNITION »***»»*********»»I»»«»»»

30  REM
40  REM
49  REM    t«***»»****»**»*********t»**t*»************»****»
50  REM  THIS PROGRAM WAS TRANSLATED FROM
51  REM  A FORTRAN VERSION IN THE BOOK
52  REM  "CHEMICAL APPLICATIONS OF PATTERN RECOGNITION"
53  REM  P.C. OURS AND T.L. 1SENHOUR
54  REM  WILEY 1NTERSCIENCE,  NY. 1975
55  REM  TRANSLATION BY D.E.  LEYDEN
56  REM  DEPT. OF CHEMISTRY
57  REM  COLORADO STATE UNIVERSITY
58  REM  FORT COLLINS CO 80523
59  REM   *****S****S******************tt****************t*
80  RESTORE
90  HOME
95  PRINT  CHR* <4);"PR#1"
98  PRINT  CHR* <9>"BON"
100  DIM D<5,100>,W<6>,L<1OO),ID<100>,ICUOO>,NS<100>,KP<20>
110 NT = 80
120 NP = 2O
130 WI = .1
140 TS = .75
150 NO = NT + NP
160 NA = 1000
170 NU = 5
180  REM  READ DATA SET
190  FOR I = 1 TO NO
2OO  READ L(I)
210  FOR J = 1 TO NU
220  READ D
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1000  REM  SOUBROUTINE TRAIN
1010 NC = O
1O20  PRINT "TRAINING ":NT,NU,TS
1030 NV = NU * 1
1040 NF = 0
1O50 KK = O
1060 KV = O
1070  REM   STARTING POINT OF MAIN LOOP & RETURN FROM LINE NUMBER 1520
1O90 KZ = O
1090  IF KV <  =0 GOTO 1120
110O ND = KV
111O  GOTO 1170
1120 ND = NT
1130  FOR I = 1 TO NT
114O NSU) = ID(I)
1150  NEXT I
1160  REM   THE NEXT LOOP CLASSIFIES THE ND MEMBERS OF THE CURRENT SUBSET
1170  FOR IR = 1 TO ND
1180 I = NS(IR)
1185  REM  THE NEXT LOOP CALCULATES THE DDT PRODUCT
119O S = W(NV)
120O  FOR 0 = 1 TO NU
1210 S = S + D(J.I)  * W(J)
1220  NEXT 0
1230  REM  THE NEXT THREE STATEMENTS TEST FOR CORRECT ANSWER
1240  IF L 0 GOTO 1260
1250  IF  (S + TS) <   =0 GOTO 1420
1255  GOTO 1290
1260  IF  (S - TS) > O GOTO 1420
1265  REM  1270 OR 129O CALCULATES THE CORRECTION INCREMENT
1270 C = 2 « (TS - S)
1280  GOTO 1300
129O C = 2 * ( - TS - S)
1300 XX = 1.0
1310  FOR J = 1 TO NU
1320 XX = XX + D  ~ 2
1330  NEXT J
1340 C = C / XX
135O  REM  THE NEXT LOOP PERFORMS THE FEEDBACK
136O  FOR J = 1 TO NU
137O W(0) = W<0) + C * D(0,I)
1375  NEXT J
1330 W(NV) = W O GOTO 1550
1510  REM  TEST WHETHER CURRENT SUBSET IS INTIRE TRAINING SET
1520  IF  (ND - NT)  <  > O GOTO 1080
1530  REM  TEST FOR ZERO ERROR
1540  IF KV <  > 0 GOTO 1080
1550 NC = 1

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1!:'.60  REM  SUMMARY OUTPUT OF TRAINING ROUTINE
1570  FOR K = 1 TO KK
17,30  PRINT  INT (KP(K»:
1590  NEXT K
1595  PRINT
1600  PRINT "WEIGHT VECTOR"
161O  FOR J = 1 TO NV
1620  PRINT W(J)
1630  NEXT J
1640  PRINT "FEEDBACKS ":NF
1650  RETURN
2000  REM  SUBROUTINE PREDICTION
2010 LI = O
2O2O L2 = O
203O KW = 0
2040 Nl = 0
205O N2 = 0
2060  FOR II = 1 TO NP
207O I = IC(II)
2090 S = W 0 GOTO 2150
2130 K'W = KW + 1
2140  GOTO 2230
2150  IF L(I) > 0 GOTO 2200
2160 N2 = N2 + 1
2170  IF < - S - TS) > 0 GOTO 2230
2180 LI = LI -i- 1
2190  GOTO 2230
2200 Nl = Nl + 1
2210  IF  0 GOTO 2230
2220 L2 = L2 + 1
2230  NEXT II
2240  PRINT "PREDICTION WITH DEADZONE = ";TS
2250 LT = LI * L2
2260 JW = Nl + N2
2270 PW = 100 - (100 * LT / JW)
2280 PI = 100 - (100 * LI / N2)
2290 P2 = 100 - (100 » L2 / Nl)
2300  PRINT "NUMBER PREDICTED = ";OW
2310  PRINT "NUMBER NOT PREDICTED = ";KW
232O  PRINT "NUMBER PREDICTED INCORRECTLY = ";LT
2330  PRINT
2340  PRINT LT;"/";JW;"  "; INT (PW)
235O  PRINT L1;"/";N2;"  "; INT (PI)
2360  PRINT L2;"/";N1;"  "; INT (P2)
2365  PRINT
237O  RETURN

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                          APPENDIX  B
TRAINING 60     8               .75

WEIGHT VECTOR
-2.32670578
1.938407BB
-2.80600923
-2.90653334
1.72147704
-.949600764
1.82722324
1.7296907
.512025906

FEEDBACKS 26
PREDICTION WITH DEADZONE = .75
NUMBER PREDICTED =13
NUMBER NOT PREDICTED = 7
NUMBER PREDICTED INCORRECTLY = 1

1/13  92
1/4  75
O/9  100

PREDICTION WITH DEADZONE = O
NUMBER PREDICTED = 2O
NUMBER NOT PREDICTED = O
NUMBER PREDICTED INCORRECTLY = 5

5/2O  75
5/8  37
O/12  100

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                    APPENDIX  C
         70     8
8               8
HEIGHT VECTOR
-14.1103004
50.9810323
-46.4651464
-48.769018
2.36107728
-7.01234953
5.69704767
12.8294714
-4.55528285

FEEDBACKS 50O
PREDICTION WITH DEADZONE = 1
NUMBER PREDICTED = 1O
NUMBER NOT PREDICTED = O
NUMBER PREDICTED INCORRECTLY = 3

3/10  70
1/5  80
2/5  60

PREDICTION WITH DEADZONE = 0
NUMBER PREDICTED =10
NUMBER NOT PREDICTED = 0
NUMBER PREDICTED INCORRECTLY = 3

3/10  70
1/5  80
2/5  60

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                     APPENDIX D
TRAINING 80     5               .75
8
3
1
O~>22104333332222100
WEIGHT VECTOR
.605293118
.959874479
.299292939 .
-.713884741
-.409&5779&
.0221140133
FEEDBACKS
PREDICTION WITH DEADZONE = .75
NUMBER PREDICTED = 2O
NUMBER NOT PREDICTED = O
NUMBER PREDICTED INCORRECTLY = 0

O/2O  100
O/9  100
O/ll  1OO

PREDICTION WITH DEADZONE = O
NUMBER PREDICTED = 20
NUMBER NOT PREDICTED = O
NUMBER PREDICTED INCORRECTLY = 0

O/20  100
0/9  1OO
O/ll  10O

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