These are rules obtained with the representation RT01,
from data generated by the author.
All the material in typewriter font has been
output in that form by one of the programs. Many lines of output
have been taken out, but what is left has not been altered.
Inconsistencies are due to the different versions of the programs
used as program development proceeded.
The rules are presented here in order to illustrate the operation
of CN2, and the general nature of the induced rules.
However, these rules are not presented as
plausible candidates for rules that humans might use.
The figures in square brackets indicate how many of each class is
covered by that rule. Thus, [15 0 0] means that all 15 of
the examples falling into the category defined by the three
conditions have Port_Ths_Half_Ahead as their action
decision class. Similarly, [23 11 14] indicates that
there were 48 examples within the scope of the two conditions,
and of those, 23 had class Port_Ths_Half_Ahead,
11 had class Stbd_Ths_Half_Ahead and 14 had the class
value NO_KEY. This latter rule is less accurate than the
former one.
The larger the numbers, the broader
the coverage, and the more the numbers are other than in the
appropriate place, the less accurate is the rule.
*------------------------*
| UN-ORDERED RULE LIST |
*------------------------*
IF 0.65 < rov_speed < 2.33
AND rov_port_revs_demand = stop
AND rov_stbd_revs_demand = h_ahd
THEN class = Port_Ths_Half_Ahead [15 0 0]
IF rov_height > 1.80
AND rov_port_revs_demand = stop
AND rov_stbd_revs_demand = h_astn
THEN class = Port_Ths_Half_Ahead [7 0 0]
IF rov_degrees < 31.50
AND rov_speed > 0.31
AND rov_target_range < 10.10
THEN class = Port_Ths_Half_Ahead [7 0 0]
IF rov_target_range > 137.35
AND sub_display = rov
THEN class = Port_Ths_Half_Ahead [23 11 14]
IF rov_target_range < 56.75
AND rov_port_revs_demand = f_ahd
THEN class = Port_Ths_Half_Ahead [16 12 10]
IF rov_target_head > 135.00
AND rov_speed > 0.22
AND rov_r < 0.17
AND 6.75 < rov_target_range < 7.45
AND sub_display = rov
THEN class = Port_Ths_Half_Ahead [7 0 0]
IF rov_height > 31.75
AND rov_port_revs_demand = f_ahd
THEN class = Port_Ths_Half_Ahead [36 25 36]
IF rov_target_range < 34.40
THEN class = Port_Ths_Half_Ahead [89 79 148]
IF rov_height < 17.05
AND rov_speed > 0.48
AND rov_port_revs_demand = h_ahd
AND rov_stbd_revs_demand = stop
THEN class = Stbd_Ths_Half_Ahead [0 15 0]
IF rov_speed < 0.58
AND 0.13 < rov_r < 0.31
AND rov_target_range > 5.00
AND rov_stbd_revs_demand = stop
THEN class = Stbd_Ths_Half_Ahead [0 12 0]
IF rov_target_range < 59.80
AND rov_port_revs_demand = h_ahd
AND rov_stbd_revs_demand = f_ahd
THEN class = Stbd_Ths_Half_Ahead [0 7 0]
IF rov_target_head < 243.00
AND rov_port_revs_demand = h_astn
AND rov_stbd_revs_demand = stop
THEN class = Stbd_Ths_Half_Ahead [0 6 0]
IF rov_r > -0.01
AND rov_target_range < 32.60
AND rov_stbd_revs_demand = f_ahd
THEN class = Stbd_Ths_Half_Ahead [1 5 0]
IF rov_degrees < 104.00
AND rov_stbd_revs_demand = f_ahd
THEN class = Stbd_Ths_Half_Ahead [10 27 21]
IF rov_target_range > 124.15
AND sub_display = rov
THEN class = Stbd_Ths_Half_Ahead [38 37 36]
IF 5.45 < rov_target_range < 10.50
THEN class = Stbd_Ths_Half_Ahead [35 36 52]
IF rov_target_range < 97.15
AND rov_stbd_revs_demand = f_ahd
THEN class = Stbd_Ths_Half_Ahead [29 41 35]
IF sub_display = ship
THEN class = NO_KEY [0 0 340]
IF sub_display = umb
THEN class = NO_KEY [0 0 61]
IF rov_speed < 0.65
AND rov_r > -0.09
AND rov_target_range > 4.95
AND rov_stbd_revs_demand = h_ahd
THEN class = NO_KEY [0 0 21]
(DEFAULT) class = NO_KEY [194 185 654]
And these are the results of testing those rules, first with the data from which they were derived, and second from another similar set of data. The default rule accuracy in these cases would be 654 / 1033 = 63.3 % and 320 / 444 = 72.0 %.
PREDICTED
ACTUAL Port_Th Stbd_Th NO_KEY Accuracy
Port_Ths 79.00 21.00 94.00 41 %
Stbd_Ths 56.00 38.00 91.00 21 %
NO_KEY 85.00 34.00 535.00 82 %
Overall accuracy: 63 %
PREDICTED
ACTUAL Port_Th Stbd_Th NO_KEY Accuracy
Port_Ths 31.00 9.00 21.00 51 %
Stbd_Ths 42.00 5.00 16.00 8 %
NO_KEY 60.00 16.00 244.00 76 %
Overall accuracy: 63 %
*------------------------*
| UN-ORDERED RULE LIST |
*------------------------*
IF rov_off_head > 43.00
AND rov_height < 40.20
AND rov_speed < 1.33
AND rov_target_range < 133.35
AND sub_display = rov
THEN class = Pure_Turn_Stbd [14 0 0]
IF rov_off_head > 8.50
AND 6.25 < rov_target_range < 7.60
THEN class = Pure_Turn_Stbd [6 0 0]
IF rov_off_head > 29.50
AND rov_height > 34.45
AND rov_speed < 1.15
AND rov_target_range > 121.75
AND sub_display = rov
AND rov_turn_demand = strait
THEN class = Pure_Turn_Stbd [12 0 0]
IF 10.85 < rov_height < 42.95
AND rov_speed < 0.15
THEN class = Pure_Turn_Stbd [5 1 0]
IF rov_off_head < -29.50
AND rov_height > 4.20
AND 0.09 < rov_speed < 2.85
AND sub_display = rov
THEN class = Pure_Turn_Port [0 17 0]
IF sub_display = ship
THEN class = NO_KEY [0 0 224]
IF -10.50 < rov_off_head < 11.00
THEN class = NO_KEY [0 0 73]
(DEFAULT) class = NO_KEY [34 23 331]
The performance of these rules looks better, but in fact this is due to the greater proportion of NO_KEY events. The overall accuracy is still very similar to the performance of the default rule by itself.
PREDICTED
ACTUAL Pure_Tu Pure_Tu NO_KEY Accuracy
Pure_Tur 34.00 0.00 0.00 100 %
Pure_Tur 6.00 17.00 0.00 74 %
NO_KEY 52.00 0.00 279.00 84 %
Overall accuracy: 85 %
PREDICTED
ACTUAL Pure_Tu Pure_Tu NO_KEY Accuracy
Pure_Tur 8.00 1.00 0.00 89 %
Pure_Tur 7.00 4.00 1.00 33 %
NO_KEY 17.00 2.00 182.00 91 %
Overall accuracy: 87 %
The accuracy of the default rule in the first case (training examples) is 85.3 %. In the second case (test examples), it is 201 / (9 + 12 + 201) = 201 / 222 = 90.5%