Dealingwith numericattributesNumeric attributes are discretized: the range oftheattribute is divided into a set of intervalsInstances are sorted according toattribute's valuesBreakpoints areplaced wherethe (majority)classchanges(sothatthetotalerrorisminimized)Example:temperaturefromweather data648081838565757568697071.7272YesYesI No Yes Yes Yes I No No Yes I Yes YesI No IYesINO62026/9/22UniversityofWaikato
2026/9/22 University of Waikato 6 Dealing with numeric attributes ◼ Numeric attributes are discretized: the range of the attribute is divided into a set of intervals ◆ Instances are sorted according to attribute’s values ◆ Breakpoints are placed where the (majority) class changes (so that the total error is minimized) ◼ Example: temperature from weather data 64 65 68 69 70 71 72 72 75 75 80 81 83 85 Yes | No | Yes Yes Yes | No No Yes | Yes Yes | No | Yes Yes | No
Resultof overfittingavoidanceFinal result forfor temperature attribute:8081838564656869707172727575INoYesYes NoYes No Yes Yes Yes No No Yes Yes YesAttributeRulesErrorsTotalerrors2/54/14OutlookSunny→NoResulting0/4Overcast→Yes2/5Rainy→Yesrule sets:3/105/14Temperature≤77.5→Yes2/4>77.5→No*1/73/14Humidity≤82.5→Yes2/6>82.5and≤95.5→No0/1>95.5→Yes2/8WindyFalse→Yes5/143/6True →No*2026/9/22University of Waikato
2026/9/22 University of Waikato 7 Result of overfitting avoidance ◼ Final result for for temperature attribute: ◼ Resulting rule sets: 64 65 68 69 70 71 72 72 75 75 80 81 83 85 Yes No Yes Yes Yes | No No Yes Yes Yes | No Yes Yes No Attribute Rules Errors Total errors Outlook Sunny → No 2/5 4/14 Overcast → Yes 0/4 Rainy → Yes 2/5 Temperature 77.5 → Yes 3/10 5/14 > 77.5 → No* 2/4 Humidity 82.5 → Yes 1/7 3/14 > 82.5 and 95.5 → No 2/6 > 95.5 → Yes 0/1 Windy False → Yes 2/8 5/14 True → No* 3/6
Discussionof1R1Rwasdescribed inapaperbyHolte(1993)Containsanexperimental evaluationon16datasets (using cross-validationsothat results wererepresentative of performance on futuredata)Minimumnumber of instanceswas setto6aftersome experimentation1R'ssimplerulesperformednotmuchworsethanmuchmorecomplexdecisiontreesSimplicity first pays off!82026/9/22UniversityofWaikato
2026/9/22 University of Waikato 8 Discussion of 1R ◼ 1R was described in a paper by Holte (1993) ◆ Contains an experimental evaluation on 16 datasets (using cross-validation so that results were representative of performance on future data) ◆ Minimum number of instances was set to 6 after some experimentation ◆ 1R’s simple rules performed not much worse than much more complex decision trees ◼ Simplicity first pays off!
PARTVCredibility:Evaluatingg what'sbeenlearned2026/9/22University of Waikato
2026/9/22 University of Waikato 9 PART V Credibility: Evaluating what’s been learned
Classweka.classifiers.OneR-MicrosoftInternetExplorerFileEditViewToolsHelpFavoritesSearchFavoritesMediaBackAddressec:twekalweka-3-2-3idoctweka.classifiers.OneR.htmlWEKA's homeAll PackagesClass HierarchyIndexThis PackagePreviousNextClass weka.classifiers.OneRjava.lang.Object-weka.classifiers.Classifier-weka.classifiers.OneRpublic class OneRextends Classifierimplements OptionHandlerClass for building and using a iR classifier. For more information, seeR.C.Holte (1g93).Very simple classification rules performwell on most commonlyu11,pp.63-91.10
2026/9/22 University of Waikato 10 Weka