CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C                                                                   C
C                                                                   C
C       CMS DSN  =  MIX1CM CLUSPAC                                  C
C                                                                   C
C      "MIX1CM CLUSPAC" IS A PROGRAM FOR CLUSTERING UNIVARIATE DATA C
C  (DATA ON THE LINE) BY ITERATIVE MAXIMIZATION OF THE MIXTURE-     C
C  MODEL LIKELIHOOD                                                 C
C                                                                   C
C                 N   K                                             C
C                --- --                                             C
C          L  =  | | >  P(C)*F(X(I)|C)                              C
C                | | --                                             C
C                I=1 C=1                                            C
C                                                                   C
C                                                                   C
C      REFERENCE:                                                   C
C                                                                   C
C  WOLFE (1970).                                                    C
C                                                                   C
C          MANUAL MODE:  NUMBER OF CLUSTERS AND INITIAL MEANS ARE   C
C          INPUT.  (USE PROGRAM  MIX1CMA  FOR AUTOMATIC SETTING OF  C
C          NUMBERS OF CLUSTERS AND INITIAL MEANS.)                  C
C                                                                   C
C                                                                   C
C          PROGRAMMED BY                                            C
C              DR. STANLEY L. SCLOVE                 312/996-2681   C
C              DEPARTMENT OF                                        C
C                 INFORMATION & DECISION SCIENCES         M/C 294   C
C              COLLEGE OF BUSINESS ADMINISTRATION                   C
C              UNIVERSITY OF ILLINOIS  AT CHICAGO                   C
C              BOX 4348                                             C
C              CHICAGO, IL  60680-4348                              C
C                                                                   C
C                                                                   C
C          VERSION 3.2   30-OCT-89                                  C
C                                                                   C
C     COPYRIGHT (C) 1988  STANLEY L. SCLOVE                         C
C                                                                   C
C                                                                   C
C                                                                   C
C          RESTRICTIONS (CAN BE MODIFIED):                          C
C     N, SAMPLE SIZE, AT MOST 999;                                  C
C     K, NUMBER OF CLUSTERS, AT MOST 29;                            C
C     ITER, MAXIMUM NUMBER OF ITERATIONS, 20.                       C
C                                                                   C
C                                                                   C
C                                                                   C
C     CONTROL CARDS:                                                C
C                                                                   C
C     (1) DATASET TITLE                                             C
C     (2) N, IN FORMAT (2X,I4)                                      C
C     (3) FMT, IN FORMAT (18A4), E.G.,  (1X,F4.1).                  C
C         ALLOW AT LEAST ONE BLANK IN FMT:  IT WILL ALSO BE USED    C
C         FOR OUTPUT, WHERE CC1 IS FOR CARRIAGE CONTROL.            C
C         ALLOW A CC FOR THE DECIMAL POINT ON OUTPUT,               C
C         WHETHER OR NOT THERE IS ONE ON INPUT.                     C
C     (4) DATA, IN FORMAT SPECIFIED BY FMT                          C
C     (5) K, NUMBER OF CLUSTERS, IN FORMAT (2X,I1)                  C
C     (6) K INITIAL VALUES OF PRIOR PROBABILITIES AND MEANS,        C
C         IN FORMAT (5X,F3.2,2X,F8.2).                              C
C     (7) INITIAL VALUE OF THE VARIANCE.  (THE RESULTS DO NOT       C
C         DEPEND UPON THIS VALUE IF THE INITIAL PRIOR PROBABILITIES C
C         ARE EQUAL.)                                               C
C                                                                   C
C                                                                   C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C                                                                   C
C                                                                   C
C
C
C     WRITE PROGRAM INFORMATION.
C
C
C     READ SAMPLE SIZE, N.
C
C     READ DATA FORMAT.
C
C     READ DATA AND
C     COMPUTE STATISTICS OF WHOLE SAMPLE:
C
C     THE NEXT STMT WAS FOR USE WITH THE WATFOR COMPILER:
C          READ (5,*) X(I)
C
C     WRITE DATA:
C     WRITE SUMMARY STATISTICS FOR WHOLE SAMPLE:
C
C
C       READ K, NUMBER OF CLUSTERS.
C
C       READ INITIAL PRIOR PROBS AND MEANS:
C       READ INITIAL VARIANCE:
C
C
C
C     WRITE INITIAL PRIOR PROBS, MEANS AND VARIANCE:
C
C     SET CONSTANTS.
C
C       IF THE INITIAL PRIOR PROBABILITIES ARE EQUAL, THEN THE
C     FIRST ITERATION IS EQUIVALENT TO  MINIMUM DISTANCE CLUSTERING
C     TO INITIAL MEANS (I.E., "ISODATA").
C     IN GENERAL, THE CLUSTERING IS BY     MAXIMUM POSTERIOR
C     PROBABILITY CLUSTERING.
C
C
C     STORE OLD CLUSTERING:
C
C     COMMENCE DISTANCE COMPUTATIONS.
C       NOTE THAT A PROB. DENSITY FUNCTION OTHER THAN THE GAUSSIAN
C     COULD BE USED HERE:
C     XMNDSQ(I) = MIN SQ. DISTANCE FROM X(I) TO ANY MEAN
C
C
C
C
C     COMPUTE POSTERIOR PROBABILITIES OF GROUP MEMBERSHIP:
C     IF ( DENOM(I) .EQ. 0.0 ) DENOM(I)=0.0001
C
C       COMPUTE NEW LABELS BY MAX POSTERIOR PROBABILITY:
C
C       WRITE NEW LABELS:
C
C       UPDATE CLUSTER PRIOR PROBABILITIES P(IC), MEANS XMEAN(IC) AND
C     VARIANCE VARHAT:
C       XNC(IC) WILL BE THE SUM OVER ALL N OBSERVATIONS OF THEIR
C     POSTERIOR PROBABILITIES OF MEMBERSHIP IN CLUSTER IC.
C     IF ( VAR(IC) .LE. 0.0 ) VAR(IC) = 0.0001
C
C       COUNT NUMBERS IN CLUSTERS:
C
C
C
C
C
C
C
C
C     B(IC) IS BOUNDARY BETWEEN G-TH AND G+1-ST CLASSES.
C
C
C
C     VARHAT  IS MLE OF VARIANCE.
C
C
C
C
C     COMPUTE MODEL-SELECTION CRITERIA:
C     NO. PARAMETERS = K MEANS + 1 VARIANCE + (K-1) PROBS.
C
C     SCHWARZ' CRITERION IS FIRST-DEGREE EXPANSION OF
C     LOG POSTERIOR PROBABILITY OF THE MODEL.
C     KASHYAP'S CRITERION IS SECOND-DEGREE EXPANSION OF SAME.
C
C
C
C
C     WITH THE WATFOR COMPILER, USE THE FOLLOWING STMT AFTER END
C     INSTEAD OF //GO.SYSIN DD * .
C     $DATA
 
       Sample deck set-up:
TRYPANOSOMES DATA:  LENGTHS OF 500 ROUNDWORMS
N=0500
(1X,F2.0)
 15
 15
 15
 
 . . .
 
 35
K=2
C1   .50  15.
C2   .50  29.
VAR 25.00
/*