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tic-tac-toe

tic-tac-toe

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Author: Source: Unknown - Please cite: 1. Title: Tic-Tac-Toe Endgame database 2. Source Information -- Creator: David W. Aha (aha@cs.jhu.edu) -- Donor: David W. Aha (aha@cs.jhu.edu) -- Date: 19 August 1991 3. Known Past Usage: 1. Matheus,~C.~J., & Rendell,~L.~A. (1989). Constructive induction on decision trees. In {it Proceedings of the Eleventh International Joint Conference on Artificial Intelligence} (pp. 645--650). Detroit, MI: Morgan Kaufmann. -- CITRE was applied to 100-instance training and 200-instance test sets. In a study using various amounts of domain-specific knowledge, its highest average accuracy was 76.7% (using the final decision tree created for testing). 2. Matheus,~C.~J. (1990). Adding domain knowledge to SBL through feature construction. In {it Proceedings of the Eighth National Conference on Artificial Intelligence} (pp. 803--808). Boston, MA: AAAI Press. -- Similar experiments with CITRE, includes learning curves up to 500-instance training sets but used _all_ instances in the database for testing. Accuracies reached above 90%, but specific values are not given (see Chris's dissertation for more details). 3. Aha,~D.~W. (1991). Incremental constructive induction: An instance-based approach. In {it Proceedings of the Eighth International Workshop on Machine Learning} (pp. 117--121). Evanston, ILL: Morgan Kaufmann. -- Used 70% for training, 30% of the instances for testing, evaluated over 10 trials. Results reported for six algorithms: -- NewID: 84.0% -- CN2: 98.1% -- MBRtalk: 88.4% -- IB1: 98.1% -- IB3: 82.0% -- IB3-CI: 99.1% -- Results also reported when adding an additional 10 irrelevant ternary-valued attributes; similar _relative_ results except that IB1's performance degraded more quickly than the others. 4. Relevant Information: This database encodes the complete set of possible board configurations at the end of tic-tac-toe games, where "x" is assumed to have played first. The target concept is "win for x" (i.e., true when "x" has one of 8 possible ways to create a "three-in-a-row"). Interestingly, this raw database gives a stripped-down decision tree algorithm (e.g., ID3) fits. However, the rule-based CN2 algorithm, the simple IB1 instance-based learning algorithm, and the CITRE feature-constructing decision tree algorithm perform well on it. 5. Number of Instances: 958 (legal tic-tac-toe endgame boards) 6. Number of Attributes: 9, each corresponding to one tic-tac-toe square 7. Attribute Information: (x=player x has taken, o=player o has taken, b=blank) 1. top-left-square: {x,o,b} 2. top-middle-square: {x,o,b} 3. top-right-square: {x,o,b} 4. middle-left-square: {x,o,b} 5. middle-middle-square: {x,o,b} 6. middle-right-square: {x,o,b} 7. bottom-left-square: {x,o,b} 8. bottom-middle-square: {x,o,b} 9. bottom-right-square: {x,o,b} 10. Class: {positive,negative} 8. Missing Attribute Values: None 9. Class Distribution: About 65.3% are positive (i.e., wins for "x") Information about the dataset CLASSTYPE: nominal CLASSINDEX: last

10 features

Class (target)nominal2 unique values
0 missing
top-left-squarenominal3 unique values
0 missing
top-middle-squarenominal3 unique values
0 missing
top-right-squarenominal3 unique values
0 missing
middle-left-squarenominal3 unique values
0 missing
middle-middle-squarenominal3 unique values
0 missing
middle-right-squarenominal3 unique values
0 missing
bottom-left-squarenominal3 unique values
0 missing
bottom-middle-squarenominal3 unique values
0 missing
bottom-right-squarenominal3 unique values
0 missing
Show all 10 features

107 properties

NumberOfInstances
958
Number of instances (rows) of the dataset.
NumberOfFeatures
10
Number of attributes (columns) of the dataset.
NumberOfClasses
2
Number of distinct values of the target attribute (if it is nominal).
NumberOfMissingValues
0
Number of missing values in the dataset.
NumberOfInstancesWithMissingValues
0
Number of instances with at least one value missing.
NumberOfNumericFeatures
0
Number of numeric attributes.
NumberOfSymbolicFeatures
10
Number of nominal attributes.
AutoCorrelation
1
Average class difference between consecutive instances.
CfsSubsetEval_DecisionStumpAUC
0.74
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_DecisionStumpErrRate
0.24
Error rate achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_DecisionStumpKappa
0.42
Kappa coefficient achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_NaiveBayesAUC
0.74
Area Under the ROC Curve achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_NaiveBayesErrRate
0.24
Error rate achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_NaiveBayesKappa
0.42
Kappa coefficient achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_kNN1NAUC
0.74
Area Under the ROC Curve achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_kNN1NErrRate
0.24
Error rate achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
CfsSubsetEval_kNN1NKappa
0.42
Kappa coefficient achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W
ClassEntropy
0.93
Entropy of the target attribute values.
DecisionStumpAUC
0.67
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.DecisionStump
DecisionStumpErrRate
0.3
Error rate achieved by the landmarker weka.classifiers.trees.DecisionStump
DecisionStumpKappa
0.34
Kappa coefficient achieved by the landmarker weka.classifiers.trees.DecisionStump
Dimensionality
0.01
Number of attributes divided by the number of instances.
EquivalentNumberOfAtts
49.45
Number of attributes needed to optimally describe the class (under the assumption of independence among attributes). Equals ClassEntropy divided by MeanMutualInformation.
J48.00001.AUC
0.85
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .00001
J48.00001.ErrRate
0.19
Error rate achieved by the landmarker weka.classifiers.trees.J48 -C .00001
J48.00001.Kappa
0.58
Kappa coefficient achieved by the landmarker weka.classifiers.trees.J48 -C .00001
J48.0001.AUC
0.85
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .0001
J48.0001.ErrRate
0.19
Error rate achieved by the landmarker weka.classifiers.trees.J48 -C .0001
J48.0001.Kappa
0.58
Kappa coefficient achieved by the landmarker weka.classifiers.trees.J48 -C .0001
J48.001.AUC
0.85
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .001
J48.001.ErrRate
0.19
Error rate achieved by the landmarker weka.classifiers.trees.J48 -C .001
J48.001.Kappa
0.58
Kappa coefficient achieved by the landmarker weka.classifiers.trees.J48 -C .001
MajorityClassPercentage
65.34
Percentage of instances belonging to the most frequent class.
MajorityClassSize
626
Number of instances belonging to the most frequent class.
MaxAttributeEntropy
1.56
Maximum entropy among attributes.
MaxKurtosisOfNumericAtts
Maximum kurtosis among attributes of the numeric type.
MaxMeansOfNumericAtts
Maximum of means among attributes of the numeric type.
MaxMutualInformation
0.09
Maximum mutual information between the nominal attributes and the target attribute.
MaxNominalAttDistinctValues
3
The maximum number of distinct values among attributes of the nominal type.
MaxSkewnessOfNumericAtts
Maximum skewness among attributes of the numeric type.
MaxStdDevOfNumericAtts
Maximum standard deviation of attributes of the numeric type.
MeanAttributeEntropy
1.54
Average entropy of the attributes.
MeanKurtosisOfNumericAtts
Mean kurtosis among attributes of the numeric type.
MeanMeansOfNumericAtts
Mean of means among attributes of the numeric type.
MeanMutualInformation
0.02
Average mutual information between the nominal attributes and the target attribute.
MeanNoiseToSignalRatio
80.7
An estimate of the amount of irrelevant information in the attributes regarding the class. Equals (MeanAttributeEntropy - MeanMutualInformation) divided by MeanMutualInformation.
MeanNominalAttDistinctValues
2.9
Average number of distinct values among the attributes of the nominal type.
MeanSkewnessOfNumericAtts
Mean skewness among attributes of the numeric type.
MeanStdDevOfNumericAtts
Mean standard deviation of attributes of the numeric type.
MinAttributeEntropy
1.47
Minimal entropy among attributes.
MinKurtosisOfNumericAtts
Minimum kurtosis among attributes of the numeric type.
MinMeansOfNumericAtts
Minimum of means among attributes of the numeric type.
MinMutualInformation
0.01
Minimal mutual information between the nominal attributes and the target attribute.
MinNominalAttDistinctValues
2
The minimal number of distinct values among attributes of the nominal type.
MinSkewnessOfNumericAtts
Minimum skewness among attributes of the numeric type.
MinStdDevOfNumericAtts
Minimum standard deviation of attributes of the numeric type.
MinorityClassPercentage
34.66
Percentage of instances belonging to the least frequent class.
MinorityClassSize
332
Number of instances belonging to the least frequent class.
NaiveBayesAUC
0.75
Area Under the ROC Curve achieved by the landmarker weka.classifiers.bayes.NaiveBayes
NaiveBayesErrRate
0.29
Error rate achieved by the landmarker weka.classifiers.bayes.NaiveBayes
NaiveBayesKappa
0.31
Kappa coefficient achieved by the landmarker weka.classifiers.bayes.NaiveBayes
NumberOfBinaryFeatures
1
Number of binary attributes.
PercentageOfBinaryFeatures
10
Percentage of binary attributes.
PercentageOfInstancesWithMissingValues
0
Percentage of instances having missing values.
PercentageOfMissingValues
0
Percentage of missing values.
PercentageOfNumericFeatures
0
Percentage of numeric attributes.
PercentageOfSymbolicFeatures
100
Percentage of nominal attributes.
Quartile1AttributeEntropy
1.53
First quartile of entropy among attributes.
Quartile1KurtosisOfNumericAtts
First quartile of kurtosis among attributes of the numeric type.
Quartile1MeansOfNumericAtts
First quartile of means among attributes of the numeric type.
Quartile1MutualInformation
0.01
First quartile of mutual information between the nominal attributes and the target attribute.
Quartile1SkewnessOfNumericAtts
First quartile of skewness among attributes of the numeric type.
Quartile1StdDevOfNumericAtts
First quartile of standard deviation of attributes of the numeric type.
Quartile2AttributeEntropy
1.53
Second quartile (Median) of entropy among attributes.
Quartile2KurtosisOfNumericAtts
Second quartile (Median) of kurtosis among attributes of the numeric type.
Quartile2MeansOfNumericAtts
Second quartile (Median) of means among attributes of the numeric type.
Quartile2MutualInformation
0.01
Second quartile (Median) of mutual information between the nominal attributes and the target attribute.
Quartile2SkewnessOfNumericAtts
Second quartile (Median) of skewness among attributes of the numeric type.
Quartile2StdDevOfNumericAtts
Second quartile (Median) of standard deviation of attributes of the numeric type.
Quartile3AttributeEntropy
1.56
Third quartile of entropy among attributes.
Quartile3KurtosisOfNumericAtts
Third quartile of kurtosis among attributes of the numeric type.
Quartile3MeansOfNumericAtts
Third quartile of means among attributes of the numeric type.
Quartile3MutualInformation
0.01
Third quartile of mutual information between the nominal attributes and the target attribute.
Quartile3SkewnessOfNumericAtts
Third quartile of skewness among attributes of the numeric type.
Quartile3StdDevOfNumericAtts
Third quartile of standard deviation of attributes of the numeric type.
REPTreeDepth1AUC
0.83
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 1
REPTreeDepth1ErrRate
0.2
Error rate achieved by the landmarker weka.classifiers.trees.REPTree -L 1
REPTreeDepth1Kappa
0.53
Kappa coefficient achieved by the landmarker weka.classifiers.trees.REPTree -L 1
REPTreeDepth2AUC
0.83
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 2
REPTreeDepth2ErrRate
0.2
Error rate achieved by the landmarker weka.classifiers.trees.REPTree -L 2
REPTreeDepth2Kappa
0.53
Kappa coefficient achieved by the landmarker weka.classifiers.trees.REPTree -L 2
REPTreeDepth3AUC
0.83
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 3
REPTreeDepth3ErrRate
0.2
Error rate achieved by the landmarker weka.classifiers.trees.REPTree -L 3
REPTreeDepth3Kappa
0.53
Kappa coefficient achieved by the landmarker weka.classifiers.trees.REPTree -L 3
RandomTreeDepth1AUC
0.77
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1
RandomTreeDepth1ErrRate
0.23
Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1
RandomTreeDepth1Kappa
0.5
Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1
RandomTreeDepth2AUC
0.77
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2
RandomTreeDepth2ErrRate
0.23
Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2
RandomTreeDepth2Kappa
0.5
Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2
RandomTreeDepth3AUC
0.77
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3
RandomTreeDepth3ErrRate
0.23
Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3
RandomTreeDepth3Kappa
0.5
Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3
StdvNominalAttDistinctValues
0.32
Standard deviation of the number of distinct values among attributes of the nominal type.
kNN1NAUC
1
Area Under the ROC Curve achieved by the landmarker weka.classifiers.lazy.IBk
kNN1NErrRate
0.03
Error rate achieved by the landmarker weka.classifiers.lazy.IBk
kNN1NKappa
0.94
Kappa coefficient achieved by the landmarker weka.classifiers.lazy.IBk
Show all 107 properties

11 tasks

Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: Test on Training Data - target_feature: Class
Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: 20% Holdout (Ordered) - target_feature: Class
Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: 10-fold Crossvalidation - target_feature: Class
Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: 10 times 10-fold Crossvalidation - target_feature: Class
Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: Leave one out - target_feature: Class
Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: 10% Holdout set - target_feature: Class
Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: 5 times 2-fold Crossvalidation - target_feature: Class
Supervised Classification on tic-tac-toe
0 runs - estimation_procedure: 33% Holdout set - target_feature: Class
Learning Curve on tic-tac-toe
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: Class
Learning Curve on tic-tac-toe
0 runs - estimation_procedure: 10 times 10-fold Learning Curve - target_feature: Class
Supervised Data Stream Classification on tic-tac-toe
0 runs - estimation_procedure: Interleaved Test then Train - target_feature: Class
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