USER'S MANUAL - Department of Electrical Engineering
Contents
1. Evaluation on training data accuracy 100 0000 GENERATING RULES WITH THE PRUNING OPTION If you consider the data set may contain noise you can use the pruning option when running elem2v3 exe as follows elem2v3 exe examplel p In this case the file example rule contains the following generated rules Rules for D 1 Rule 1 C 0 Rule Accuracy 1 000000 Rule Quality 1 322219 The positive cases covered by the rule are 4 cases 1357 The negative cases covered by the rule are 0 cases Rule 2 A 0 B 0 Rule Accuracy 1 000000 Rule Quality 0 698970 The positive cases covered by the rule are 2 cases 78 The negative cases covered by the rule are 0 cases 14 Rules for D 0 Rule 1 C 0 Rule Accuracy 0 750000 Rule Quality 1 322219 The positive cases covered by the rule are 3 cases 246 The negative cases covered by the rule are 1 cases 8 Rule Numbers are Rule number for D 1 is 2 Rule number for D 0 is 1 Total number of rules 3 Average Length of the rules 1 333333 Evaluation on training data accuracy 87 5000 Note that in this case the eighth example 1 1 1 1 is interpreted ELEM2 as a noisy case for the class D 0 EXAMPLE 2 PROBLEM DESCRIPTION Example 2 is also artificially designed It involves two continuous condition attributes one symbolic condition attribute and two classes The description file example2 fmf describes the domains2. 0 0 0 0 1 1 1 1 The description file is as follows in which we give all the attributes the same priority lt 0 5201 gt lt 0 5201 gt lt C0CS201 gt lt D0DS210 gt 12 GENERATING RULES WITHOUT USING PRUNING Use the following command to generate rules that describe the data exactly without using the option elem2v3 exe 1 The following rules are generated which are contained in the file example7 ruke Rules for D 1 Rule 1 C 0 Rule Accuracy 1 000000 Rule Quality 1 322219 The positive cases covered by the rule are 4 cases 13 57 The negative cases covered by the rule are 0 cases Rule 2 A 0 B 0 Rule Accuracy 1 000000 Rule Quality 0 698970 The positive cases covered by the rule are 2 cases 78 The negative cases covered by the rule are 0 cases Rules for D 0 Rule 1 A 0 C 0 Rule Accuracy 1 000000 Rule Quality 1 263241 The positive cases covered by the rule are 2 cases 24 The negative cases covered by the rule are 0 cases Rule 2 B 0 C 0 Rule Accuracy 1 000000 Rule Quality 1 263241 The positive cases covered by the rule are 2 cases 13 26 The negative cases covered by the rule are 0 cases Rule Numbers are Rule number for D 1 is 2 Rule number for D 0 is 2 Total number of rules 4 Average Length of the rules 1 750000
3. of each attribute lt C 0 al I gt lt C 0 a2 R gt lt C 0 color S 4 red blue yellow green gt lt D 0 class 5 2 1 0 gt where the attribute al is of integer type the attribute a2 is of real valued type the attribute color has 4 symbolic values red blue yellow and green The relationship between the classes and the condition attributes in the data set is designed as follows LS If 30 lt a1l lt 60 and 1 5 lt a2 lt 3 5 and color blue or green then class 1 otherwise class 0 TRAINING AND TESTING DATA The file example2 tst contains 440 examples that satisfy the above relationship 60 of these examples are randomly chosen as training examples which are contained in the file example2 dat RULES GENERATED BY ELEM2 Using the following command elem2v3 exe example2 the following rules shown in example2 rule are generated from the data file example2 dat Rules for class 1 Rule 1 30 lt 1 lt 60 1 500000 lt 2 lt 3 500000 color blue or green Rule Accuracy 1 000000 Rule Quality 4 132932 The positive cases covered by the rule are 13 cases 118 120 122 124 126 146 148 150 152 170 172 173 175 The negative cases covered by the rule are 0 cases Rules for class 0 Rule 1 color blue or green Rule Accuracy 1 000000 Rule Quality 1 427917 The positive cases covered by the rule are 125 cases 1 3 114 13 16 18 20 23 26 27 28 30 32 33 34 36 39 40 42 44 46 49 50 51 53 55 57 61 62 64
4. 22 Run 5 Total number of rules 7 Average length of the rules 2 000000 Prediction accuracy in the testing data 100 000000 Run 6 Total number of rules 7 Average length of the rules 2 000000 Prediction accuracy in the testing data 100 000000 Run 7 Total number of rules 7 Average length of the rules 1 857143 Prediction accuracy in the testing data 100 000000 Run 8 Total number of rules 6 Average length of the rules 1 666667 Prediction accuracy in the testing data 93 333336 Run 9 Total number of rules 8 Average length of the rules 2 250000 Prediction accuracy in the testing data 100 000000 Run 10 Total number of rules 6 Average length of the rules 2 000000 Prediction accuracy in the testing data 100 000000 Average number of rules 6 800000 Average length of rules 2 046667 Average testing accuracy 97 333328 Standard deviation of the accuracy 4 661306 ACKNOWLEDGEMENT The authors are members of the Institute for Robotics and Intelligent Systems IRIS and wish to acknowledge the support of the Networks of Centres of Excellence Program of the Government of Canada the Natural Sciences and Engineering Research Council and the participation of PRECARN Associates Inc 23 REFERENCES An A and Cercone N 1998 ELEM2 A Learning System for More Accurate Classifications In Proceedings of the 12 Biennial Conference of the Canadian Society for Computa
5. ELEM2 is based on an entropy minimization theory 3 either the number of equal width intervals or the cutpoints for decision attribute of type I or R ELEM2 cannot use a supervised method to discretize a decision attribute automatically An example for a description file is lt C 3 a1 I gt lt C 2 a2 R 0 5 0 D 5 gt lt C 0 a3 I 30 60 M 5 0 20 35 51 gt lt C 1 color S 4 red blue yellow green gt lt D 0 class S 2 0 1 gt where there are four condition attributes and a decision attribute in total The attribute a2 has the highest priority among the three condition attributes and a1 the lowest The order of these entries should be consistent with the order of attribute values in each case in the training data file In this example there are three integer or real valued attributes named al a2 and a3 respectively The attribute al will be discretized using an automatic supervised discretization method the attribute a2 will be discretized into 5 equal width intervals and a3 will be discretized using the specified cut points Depending on the training data file the entry for the decision attribute is not necessary to be the last one If no attribute is specified as a decision attribute i e all the attributes are labeled as either C or X then the last attribute with C is considered to be the decision attribute If more than one attributes are specified as decision attributes ELEM2 only considers the first attribute with D is the
6. Rule 4 1 gt 60 Rule Accuracy 1 000000 Rule Quality 1 118648 The positive cases covered by the rule 82 cases 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 The negative cases covered by the rule are 0 cases Rule 5 a2 gt 3 500000 Rule Accuracy 1 000000 Rule Quality 1 054322 The positive cases covered by the rule are 74 cases 22 23 24 25 26 27 28 29 49 50 51 52 53 54 55 56 79 80 81 82 83 84 85 86 87 104 105 106 107 108 109 127 128 129 130 131 132 133 134 135 153 154 155 156 157 158 176 177 178 179 180 181 182 203 204 205 206 207 208 209 210 211 231 232 233 234 235 258 259 260 261 262 263 264 The negative cases covered by the rule are 0 cases 17 Rule Numbers are Rule number for class 1 is 1 Rule number for class 0 is 5 Total number of rules 6 Average Length of the rules 1 833333 Evaluation on training data accuracy 100 0000 TESTING ON THE TEST DATA To evaluate how these rules perform on the testing data in file example2 tst use the following command test exe example2 The program will read rules from example2 inir and classify each case in example2 tst The classification results are sh
7. are used to describe the conditions under which a case belongs to a certain class Each condition attribute also has a name and a value domain For example age can be a condition attribute for the risk evaluating domain and it takes a value between 0 and 150 A case in the training data file is represented by values of a set of condition and decision attributes The training data file used ELEM2 is named as fi estem dat Each line in the file describes case providing the values of all the condition and decision attributes separated by spaces or tabs For example 20 98 red O 127 85 1 9 10 6 blue 2 116 79 0 are two cases in a training data file where each case consists of values for six condition attributes and one class attribute The attribute values must appear in the same order in all the cases and in the same order that the attributes are given in the description file see below The order of cases themselves does not matter Numeric values may be given in integer fixed point or floating point form so that all the following are acceptable as attribute values 7 12 7 2 5 3 23E 5 0 000026 DATA DESCRIPTION FILE The description file is fundamental to the induction task The file named i estemfmf provides information about each attribute and class including attribute names class names attribute types priorities of attributes attribute values for symbolic attributes and a numeric range for each continuous att
8. examples which demonstrates the use of elem2v3 exe test exe and cvelem2 exe DATA PREPARATION In this section we describe how to prepare the training data file test data file and their description file The training data file is used by ELEM2 to generate rules The test data is used to test generated rules The description file describes the training or testing data and is required by the system for rule induction and cross validation FILE NAMES All files read and written by the ELEM2 system are in plain text format and have a name of filestem extension where extension characterizes the type of information contained in the file A filestem can be any string of characters that is acceptable as a file name to your operating system The maximum length of a filestem is 60 characters TRAINING DATA FILE The training data file is used to represent the training cases from which ELEM2 constructs decision rules Training cases are described in terms of condition attributes and a decision attribute The decision attribute also called the class attribute is used to describe the class that a case belongs to Each value of the decision attribute represents a class For example if a case in a risk evaluating domain belongs to a ow medium or high class then the decision attribute say named as risk for the training data in this domain has a value domain which contains ow medium and high each of which represents a class Condition attributes
9. files The intermediate files are generated at the beginning of the program execution and will be deleted automatically by the program after rules are generated As user you will not have to worry about the intermediate files other than to make sure that you do not delete or modify them while they are still relevant The intermediate file extensions fct 47 471 and neg Three results files are generated by the program Their extensions are e rule containing description and information about the rules that generated by the program This file is the results file for users e intr also containing description of rules but in a format not readable by users The file is for the program test exe to read induced rules in order to classify testing data e fmc containing the information about condition and decision attributes especially the cutpoints that the system generated for continuous attributes This file is needed when running test exe It serves as a data description file for test exe as filestem fmf for elem2v3 exe HOW TO INTERPRET THE RULES We describe how to interpret the generated rules in the file festem rule A tule is listed according to the class value it predicts For example if there are two classes in the problem denoted as 0 and 1 respectively in the entry for the decision attribute of the file fi estem ff as follows lt D 0 Class 2 0 1 gt then in the file fi estem rule the rules that predict Class 0 i
10. is lt C 3 pressure R gt If the second format is used ELEM2 uses an equal width interval binning method that divides the range of values for this attribute into Number_of_partitions equal sized bins where Number_of_partitions is a user supplied parameter in the entry For example if you would like to discretize the above pressure attribute into 10 equal sized value ranges the entry for this attribute in the description file is suppose the range of values for this attribute is between 0 and 500 lt C 3 pressure R 0 500 D 10 gt which means that the value range of the pressure attribute is divided into 0 50 50 100 450 500 If the third format for the attribute entry is used ELEM2 discretizes the attribute using the provided cut points For example if you want to discretize the pressure attribute into ranges of 0 80 80 120 120 170 170 250 250 400 and 400 500 then the attribute s entry in the data description file is as follows lt C 3 pressure R 0 500 M 80 120 170 250 400 gt Note that either the second or the third format has to be used for a decision attribute if the decision attribute is an integer 1 or a real valued R attribute That is the user has to provide 4 A supervised discretization method makes use of the class labels in the training cases in the discretization process while unsupetvised methods do not utilize the class labels The supervised discretization method used in
11. 63 268 269 281 283 284 The negative cases covered by the rule are 0 cases 21 EXAMPLE 4 DATASET DESCRIPTION Example 4 is also taken from the UCI repository of machine learning databases 5 The data set is dat concerns classification of iris flowers It contains 150 examples Each example is described by 4 condition attributes all continuous and one decision attribute A description file 27772 for this data set is lt C 0 sepal_length R gt lt C 0 sepal_width R gt lt C 0 petal_length R gt lt C 0 petal_width R gt lt D 0 class S 3 1 2 3 gt CROSS VALIDATION To evaluate ELEM2 on the iris data set we can use command cvelem2 exe elem2v3 exe iris 10 which evaluates e m2v3 exe with the pruning option and the default rule quality formula on the ivis dat data set using 10 fold cross validation The evaluation result is recorded in the 7s cv file the content of which is shown below Run 1 Total number of rules 7 Average length of the rules 2 142857 Prediction accuracy in the testing data 93 333336 Run 2 Total number of rules 8 Average length of the rules 2 750000 Prediction accuracy in the testing data 100 000000 Run 3 Total number of rules 7 Average length of the rules 2 000000 Prediction accuracy in the testing data 100 000000 Run 4 Total number of rules 5 Average length of the rules 1 800000 Prediction accuracy in the testing data 86 666664
12. 66 68 70 71 73 78 81 83 84 86 88 89 90 92 94 96 97 101 102 104 106 107 109 110 111 114 116 119 121 123 125 128 130 132 134 138 140 142 144 147 149 151 153 155 156 157 159 160 161 163 165 167 169 171 174 177 179 182 186 189 191 193 195 199 204 206 208 210 213 216 219 221 224 225 226 227 229 232 234 236 237 240 242 244 246 249 250 252 253 255 257 258 259 260 262 The negative cases covered by the rule are 0 cases Rule 2 1 lt 30 Rule Accuracy 1 000000 Rule Quality 1 316963 16 The positive cases covered by the rule are 109 cases 12345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 The negative cases covered by the rule are 0 cases Rule 3 a2 lt 1 500000 Rule Accuracy 1 000000 Rule Quality 1 231440 The positive cases covered by the rule are 97 cases 1234567 8 30 31 32 33 34 35 36 37 38 57 58 59 60 61 62 63 64 65 66 67 88 89 90 91 92 93 94 95 110 111 112 113 114 115 116 117 136 137 138 139 140 141 142 143 144 145 159 160 161 162 163 164 165 166 167 168 183 184 185 186 187 188 189 190 191 192 193 194 212 213 214 215 216 217 218 219 220 236 237 238 239 240 241 242 243 244 245 246 247 The negative cases covered by the rule are 0 cases
13. UNIVERSITY OF WATERLOO DEPARTMENT OF COMPUTER SCIENCE MACHINE LEARNING GROUP USER S MANUAL ELEM2 RULE INDUCTION SYSTEM VERSION 3 0 Aijun An and Nick Cercone USER S MANUAL ELEM2 RULE INDUCTION SYSTEM VERSION 3 0 TABLE OF CONTENTS TABLE OF CONTENTS 2 A E A 3 DATA PREPARA TION 3 RIE NAMES 3 TRAINING DATA FILES Soa ee aaa ba sede 3 DATA DESCRIPTION FILE ciran 4 TEST e AN 6 GENERATING RULES deduscsevcvecssvsuensensoedssductuussesssveseusscseeconsvuusesveaes 6 HOW TO RUN THE RULE INDUCTION PROGRAM ccsessssecccecsessssececececseseaeceeececseneasseeccecsenessaeceeeesenenseaeeeeees 6 FILES GENERATED BY THE SYSTEM 8 HOW TOAINTERPRET THE RULES Oo eae eae ae ae 8 TESTING I RULES E oi EE SeNi 10 HOW TO RUN THE TESTING PROGRAM sssssssscecececsssscececececsessaececececsessaececececsenssscaecececsesesaaeceeeceesensaaees 10 FILES GENERATED BY THE TESTING PROGRAM cccsssssssecec
14. a a es 22 Cross VOLAGHON seer fiche ard 22 ACKNOWLEDGEMENT cosessdesdesecccetssedad deseeceatessdoseodsesesedeesdovicecesese sass docecees 23 cdsseccvessccccsvscvaccessenseucdecddedessesvsdecctcssseedusedeccscedossosusvetices seduspueseucesssssebuetecdesdssusessoatewssessstes 24 INTRODUCTION ELEM2 1 is a rule induction system that generates rules from a set of data and uses the generated rules to classify new cases in another set of data In this manual we describe how to use the ELEM2 Version 3 0 rule induction system The system contains three executable programs elem2v3 exe testexe and cvelem2 exe The program elem2v3 exe is a rule induction program that generates a set of classification rules from a set of training data The program test exe is a classification program which uses the rules generated by elem2v3 exe and classifies the cases in a test data file The program cvelem2 exe is a cross validation program that can be used to evaluate ELEM2 on a data set using fold cross validation To run these programs the user has to prepare the training and testing data In this manual we describe how to prepare these data files how to run the three programs with the data files from the command line of an operating system and how to interpret the result files generated from the programs We also illustrate the use of the ELEM2 system by running the programs with some
15. ch case with the class label for that case in the fi estem tst file and calculates the predictive accuracy of the rules over these testing cases FILES GENERATED BY THE TESTING PROGRAM The test exe program also generates some intermediate and results files The intermediate files will be deleted by the program after testing is done The extensions of these files are 457 and 4377 Users should not be concerned with intermediate files other than to avoid deleting or modifying them while the program is still running Two results files are generated by test exe Their extensions ate 10 e tcover containing information about rules the test cases covered by each and at the end the predictive accuracy of the rules on the testing data The content of this file is the same as the f estem rule except that the cases covered by each rule and the predictive accuracy are in terms of testing data not the training data e result containing all the cases in the i estem tst file with the predicted class at the end of each case An example of this file is given in the next section CROSS VALIDATION The cross validation program is to evaluate the ELEM2 rule induction system on a data set by using fold cross validation At the expense of computational resources cross validation gives a more reliable estimate of accuracy of a learning system than a single run on a held out test set A 7 fold cross validation program randomly partitions a data set
16. decision attribute and others as condition attributes The value for the priority of a decision attribute does not affect the induction results because priority is designed to specify the relative importance of condition attributes However a number must be provided for the priority of a decision attribute for the purpose of syntax checking of the description file TEST DATA FILE To evaluate the classification rules the system has produced from the training data you may reserve part of the available data as a test data set or generate a separate test data set The test data appears in the file fi estem tst in exactly the same format as the training data file Testing the classification rules is optional GENERATING RULES HOW TO RUN THE RULE INDUCTION PROGRAM After training data and description files have been prepared inducing rules from the training data can be as simple as running the following command elem2v3 exe filestem in Command Prompt window under the directory where elem2v3 exe filestem dat and filestem fmf reside The options that can be used with this command are p Default no pruning This option allows the program to use a pruning technique 1 to post prune the rules in order to deal with possible noise in the training data It is used as follows elem2v3 exe filestem p The default is no pruning in which case the program generates rules that fit the training data as well as possible Use of the pruning opt
17. eceessaececececsesessececececsenesaaeceeeceeseaaeeeeeeeeeentaaeas 10 CROSS VALIDATION custedececccsvedetess sstisevescdscetesaedvouevevsdesuseteseuseddevovenseucstsededebusateces ieddvs thes 11 HOW TO RUN THE CROSS VALIDATION PROGRAM csssssccececsesssscecececeesesneceeeeeceeseeaeceecesenennsaeeeeeeeeeeneaaees 11 FILES GENERATED BY THE CROSS VALIDATION PROGRAM csessssecccecsesessecesececsesesseaecececeenenssaeeeeseeeeensaaes 11 EXAMPLES sodbescesess nee SE 12 EXAMPLE 12 PHO DEM DeSCHIPUON 12 Training data and its 12 Generating rules Without USING pruning 13 Generating rules with the pruning OPtiOn cccccccccececsseseesseeecnseescesesseesecteeecseescesecseeseceeeeenseeseeaeeaeeas 14 15 Problem Description serien uen EEE AA EER Nah RoR Eas 15 Training Gnd TestinG oni kad seh eae ae eee Ae ni 16 Rules generated cena hk ak eagle ae a eA ais 16 Testing onthe Lest atd a adsense een eee Akela kodns 18 eee tte ae ater 19 Dataset Description ees ooh ae aE 19 Generating RUles spenntre EENE ETA E OTA EA A E SNEEN 20 ENNA Ee ESV A E ASEN EES EE Wives it EE S D EE EAEN OEE eas 22 Dataset description u ia E a ek oe E e
18. evaluation on the elem2v3 exe program on the data set 275 427 with the pruning option and the rule quality formula C2 FILES GENERATED BY THE CROSS VALIDATION PROGRAM The cvelem2 exe program generates some intermediate and result files The intermediate files are the training testing intermediate or result files used or generated in each of the runs These files will be deleted by the program after the evaluation is done The cvelem2 exe program generates one result file Its extension is 11 e containing the information about each run such as the number of generated rules the average length of the rules and the predictive accuracy on the test subset The file also contains a summary of the results from the runs such as the average number of rules the average length of rules the average testing accuracy and standard deviation over the runs EXAMPLES We illustrate the use of ELEM2 with some examples EXAMPLE 1 PROBLEM DESCRIPTION This example is designed to illustrate how to use elem2v3 exe with or without pruning the option p The problem contains two classes and three symbolic condition attributes A B and C each of which has two values 0 1 The two classes denoted as D 1 and D 0 respectively are described as follows If A 1 and B 1 or C 0 then D 1 otherwise D 0 TRAINING DATA AND ITS DESCRIPTION The training data file example1 dat contain all the eight possible examples which are
19. g data accuracy 100 0000 Description of each rule consists of the condition part of the rule rule accuracy on the training data rule quality in which higher numbers indicate better rules and the positive and negative cases covered by the rule The condition part of a rule consists of one attribute value or a conjunction of two more attribute value pairs For example the second rule for Class 1 is interpreted as If the attribute a1 is equal to 3 and the attribute a2 is equal to 3 then Class 1 At the end of the file festem rule a summary is given which states how many rules are generated for each class the total number of rules average length of the rules in terms of the number of attribute value pairs in the condition part of rules and classification accuracy of the rules evaluated over the training data TESTING RULES After rules are generated you can test the predictive performance of the rules on another set of available data called test data The test data should appear in the file f estem tst The file can be the same as different from the training data file i estem dat but it must be in the same format HOW TO RUN THE TESTING PROGRAM The command for invoking the testing program is test exe filestem This program reads attribute descriptions from fi estem fme and the rules from fi estem intr It uses these rules to classify the cases in the file i estem tst then compares the class it predicts for ea
20. into disjoint subsets then provides the learning program with 7 of them as training data and uses the remaining one as test cases This process is repeated times using different possible test subsets Each time a classification accuracy 15 obtained on the test subset The mean of the accuracies from the runs and the standard deviation of the accuracy are then calculated to measure the testing performance HOW TO RUN THE CROSS VALIDATION PROGRAM The command for invoking the cross validation program is cvelem2 exe elem2_rule_induction_program filestemn p rule_quality_no where e em2_rule_induction is the name of the ELEM2 rule induction program to be evaluated filestem is the prefix of the data file filestem dat that the cross validation is conducted on and is the number of folds Similar to the elem2v3 exe program two options and q rw_quality_no can be used with cvelem2 exe They are used in the same way as used with elem2v3 exe and passed from the cvelem2 exe program to the rule induction program to be evaluated such as elem2v3 exe Other inputs to the cvelem2 exe program which are not shown in the command include a filestem fmf file and the test exe program The filestem fmf file provides description of the data in filestem dat The test exe program is used to classify test cases during cross validation An example of running cvelem2 exe is cvelem2 exe elem2v3 exe iris 10 p 9 3 which conducts 10 fold
21. ion is recommended q rule_quality_no Default 1 The option allows the user to choose one of the 12 rule quality formulas 4 encoded in the elem2v3 exe program by specifying a number between 1 and 12 inclusive The selected formula is used in the ELEM2 s post pruning and classification procedures The 12 formulas are shown in the following table see 4 for the description of these formulas Formula Number Rule Quality Formula Measure of Discrimination p Weighted Sum of Consistency and Coverage C2 C1 Degree of Logical Sufficiency Coleman s Formula Product of Consistency and Coverage G2 Likelihood Ratio Statistic Measure of Information 2 3 4 5 6 7 8 9 ra Pearson Chi Square Statistic Version 1 j jax Cohen s formula N Pearson Chi square Statistic Version 2 The default value of this option is 1 in which case the formula Measure of Discrimination is used An example of using this option is elem2v3 exe filestem p q 5 which causes the elem2v3 exe program to use Degree of Logical Sufficiency as the rule quality formula In summary the elem2v3 exe program can be invoked as elem2v3 exe filestem p q rmle_quality_no The two options can appear in either order and either of them can be missing FILES GENERATED BY THE SYSTEM The program elem2v3 exe generates some intermediate and results files with the same filestem as used by the training data and description
22. n the housing rule file generated by the above command Rules for MEDV lt 10 000000 Rule 1 CRIM gt 7 526010 NOX gt 0 671000 RM gt 5 272000 DIS lt 2 002600 LSTAT gt 26 639999 Rule Accuracy 1 000000 Rule Quality 2 616550 The positive cases covered by the rule are 7 cases 386 399 400 401 405 416 439 The negative cases covered by the rule are 0 cases Rule 2 NOX gt 0 605000 RM lt 6 152000 DIS lt 2 002600 B lt 68 949997 LSTAT gt 19 879999 Rule Accuracy 1 000000 Rule Quality 2 325986 The positive cases covered by the rule are 4 cases 419 426 438 439 20 The negative cases covered by the rule are 0 cases Rules for 10 000000 lt MEDV lt 20 000000 Rule 1 CRIM lt 15 023400 NO X gt 0 583000 RM lt 6 525000 AGE gt 82 500000 B gt 50 919998 14 100000 lt LSTAT lt 19 879999 Rule Accuracy 1 000000 Rule Quality 2 279597 The positive cases covered by the rule are 44 cases 128 129 130 134 135 136 137 138 140 147 154 155 156 157 171 357 362 364 391 394 395 396 397 421 422 431 434 435 442 443 444 447 448 449 450 453 459 460 462 475 477 479 489 492 The negative cases covered by the rule are 0 cases Rules for MEDV gt 40 000000 Rule 1 RM gt 7 079000 DIS lt 6 640700 PTRATIO lt 14 900000 LSTAT lt 7 440000 Rule Accuracy 1 000000 Rule Quality 3 005333 The positive cases covered by the rule are 16 cases 162 163 164 167 196 203 204 205 258 262 2
23. onding column of data in the training data file will be ignored by the induction program We allow X attributes in a training set because at times a data set contains irrelevant attributes such as the index of the training cases which is usually irrelevant to the learning task 3 An attribute name can be any string of characters without spaces in between The maximum length of an attribute name is 19 characters lt C 5 color 5 4 red blue yellow green gt 2 For an integer or real valued attribute its entry takes one of the following three formats depending on how you would like the attribute to be discretized lt C D X Priority Name I R gt ot lt C D X Priority Name I R Min_value Max_value D Numbet_of_pattitions gt ot lt C D X Priority Name I R Min_value Max_value M List_of_cutpoints gt where C D X Priority Name have the same meaning as for symbolic attributes I R takes the values of I or R and indicates whether the attribute is an integer or a real valued attribute Min_value gives the minimum value of the attribute and Max_value is the maximum value for the attribute If the first format is used ELEM2 invokes an automatic supervised discretization method to symbolize the values of this attribute in the training cases For example if a real valued condition attribute named pressure has the priority of 3 and you would like to use the automatic supervised method to discretize this attribute then its entry in the description file
24. own in the file examp e2 result as follows 0 0 000000 red 0 gt 0 0 0 000000 blue 0 gt 0 0 0 000000 yellow 0 gt 0 0 0 000000 green 0 gt 0 0 0 500000 red 0 gt 0 0 0 500000 blue 0 gt 0 0 0 500000 yellow 0 gt 0 0 0 500000 green 0 gt 0 0 1 000000 red 0 gt 0 40 2 000000 red 0 gt 0 40 2 000000 blue 1 gt 1 40 2 000000 yellow 0 gt 0 40 2 000000 green 1 gt 1 40 2 500000 red 0 gt 0 40 2 500000 blue 1 gt 1 40 2 500000 yellow 0 gt 0 40 2 500000 green 1 gt 1 40 3 000000 red 0 gt 0 40 3 000000 blue 1 gt 1 Number of testing cases 440 Number of cases classified correctly 440 18 Predictive Accuracy 100 000000 In this file each row shows a test case with the column before gt representing the actual class for the case as shown in the test date file and the column after gt representing the predicted class generated by the test exe program A summary of the prediction results is shown at the end of the file EXAMPLE 3 DATASET DESCRIPTION Example 3 is taken from the UCI repository of machine learning databases 5 The data set bousing dal concerns housing values in suburbs of Boston It contains 506 training examples Each example is described by 13 condition attributes 12 continuous and 1 binary valued attributes and 1 decision attribute continuous and representing house values This data set is used here to illustrate the use of continuous decision attribu
25. ribute The description file consists of a series of entries Each entry occupies one line and describes attribute An entry starts with lt and ends with a gt There are three kinds of attributes symbolic integer and real valued attributes A symbolic attribute has discrete values an integer attribute has integer values and a real valued attribute has continuous values Depending on the type of the attribute the entry can be in one of the following formats 1 Fora symbolic attribute its entry takes the following fomat lt C D X Priority Name S Number_of_values List_of_values gt where C D X takes the values of C D or X and indicates whether the attribute is a condition attribute indicated by C a decision class attribute indicated by D or an ignored attribute indicated by X Priority specifies the priority of this attribute among all the condition attributes and takes an integer value with lower number indicating higher priority Name specifies the name for this attribute S means symbolic attribute Number_of_values indicates the number of symbolic values of the attribute and List_of_values lists the symbolic values For example a condition attribute co or has the values of red blue yellow and green Suppose its priority is 5 The entry for this attribute is The maximum number of attributes currently allowed by ELEM2 V2 0 is 100 2 If an attribute is labeled as an X attribute then its corresp
26. s listed first under the title Rules for Class 0 before the rules predicting Class 1 which are listed later under the title Rules for Class 1 as follows Rules for Class 0 Rule 1 a1 1 a2 1 a5 1 Rule Accuracy 1 000000 Rule Quality 2 096910 The positive cases covered by the rule are 31 cases 11 12 13 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 39 40 41 43 44 45 The negative cases covered by the rule are 0 cases Rule 2 a1 1 a2 1 a5 1 Rule Accuracy 1 000000 Rule Quality 1 780275 The positive cases covered by the rule are 20 cases 46 47 50 51 52 53 54 55 56 57 58 59 60 61 91 92 94 95 96 97 The negative cases covered by the rule are 0 cases Rules for Class 1 Rule 1 a5 1 Rule Accuracy 1 000000 Rule Quality 2 041687 The positive cases covered by the rule are 29 cases 9 10 14 31 37 42 48 49 66 67 71 77 78 80 84 85 88 89 90 93 98 100 102 103 105 108 113 117 121 The negative cases covered by the rule are 0 cases Rule 2 1 3 2 3 Rule Accuracy 1 000000 Rule Quality 1 681937 The positive cases covered by the rule 17 cases 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 The negative cases covered by the rule are 0 cases Rule Numbers are Rule number for Class 0 is 4 Rule number for Class 1 is 4 Total number of rules 8 Average Length of the rules 2 375000 Evaluation on trainin
27. tes The condition and decision attributes of the data set are listed as follows oee RIM per capita crime rate by town proportion of residential land zoned for lots over 25 000 square feet proportion of non retail business acres per town CHAS Charles River dummy variable 1 if tract bounds river 0 otherwise NOX nitric oxides concentration parts per 10 million RM average ma of rooms per dwelling AGE proportion of owner occupied units built prior to 1940 Dis weighted distances to five Boston employment centres where MEDV is the decision attribute and others are condition attributes A description file housing fmj for this data set is 19 lt C 0 CRIM R gt lt C 0 ZN R gt lt C 0 INDUS R gt lt C 0 CHAS S 20 1 gt lt C 0 NOX R gt lt C 0 RM R gt lt C 0 AGE R gt lt C 0 DIS R gt lt C 0 RADI 1 24D 10 gt lt C 0 TAX R gt lt C 0 PTRATIO R gt lt C 0 B R gt lt C 0 LSTAT R gt lt D 0 MEDV R 5 0 50 0 M 10 20 30 40 gt where MEDV is a real valued decision attribute and cut points 10 20 30 and 40 are specified to discretize the attribute whose values range from 5 0 and 50 0 Thus there are five classes in this data set denoted as MEDV lt 10 0 10 lt MEDV lt 20 20 lt MEDV lt 30 30 lt MEDV lt 40 and MEDV gt 40 GENERATING RULES To generate rules from housing dat use command elem2v3 exe housing The following are samples of rules i
28. tional Studies of Intelligence Vancouver Canada An A Cercone N Chan C and Shan N 1995 ELEM A Method for Inducing Rules from Examples In Proceedings of the 15 Annual Technical Conference of the British Computer Society Specialist Group on Expert Systems Cambridge U K An A and Cercone N 1999 Discretization of Continuous Attributes for Learning Classification Rules Proceedings of the Third Pacific Asia Conference on Knowledge Discovery and Data Mining PAKDD 99 Beijing China An A and Cercone N 2000 Rule Quality Measures Improve the Accuracy of Rule Induction an Experimental Approach Proceedings of 12th International Symposium on Methodologies for Intelligent Systems Charlotte North Carolina Murphy P M and Aha D W 1994 UCI Repository of Machine Learning Databases URL http www ics uci edu AI ML MLDBRepository html 24
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