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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

107 properties

958
Number of instances (rows) of the dataset.
10
Number of attributes (columns) of the dataset.
2
Number of distinct values of the target attribute (if it is nominal).
0
Number of missing values in the dataset.
0
Number of instances with at least one value missing.
0
Number of numeric attributes.
10
Number of nominal attributes.
Second quartile (Median) of skewness among attributes of the numeric type.
0.53
Kappa coefficient achieved by the landmarker weka.classifiers.trees.REPTree -L 3
0.34
Kappa coefficient achieved by the landmarker weka.classifiers.trees.DecisionStump
Maximum of means among attributes of the numeric type.
0.01
Minimal mutual information between the nominal attributes and the target attribute.
10
Percentage of binary attributes.
Second quartile (Median) of standard deviation of attributes of the numeric type.
0.77
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1
0.01
Number of attributes divided by the number of instances.
0.09
Maximum mutual information between the nominal attributes and the target attribute.
2
The minimal number of distinct values among attributes of the nominal type.
0
Percentage of instances having missing values.
1.56
Third quartile of entropy among attributes.
0.23
Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1
49.45
Number of attributes needed to optimally describe the class (under the assumption of independence among attributes). Equals ClassEntropy divided by MeanMutualInformation.
3
The maximum number of distinct values among attributes of the nominal type.
Minimum skewness among attributes of the numeric type.
0
Percentage of missing values.
Third quartile of kurtosis among attributes of the numeric type.
1
Average class difference between consecutive instances.
0.5
Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1
0.85
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .00001
Maximum skewness among attributes of the numeric type.
Minimum standard deviation of attributes of the numeric type.
0
Percentage of numeric attributes.
Third quartile of means among attributes of the numeric type.
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
0.77
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2
0.19
Error rate achieved by the landmarker weka.classifiers.trees.J48 -C .00001
Maximum standard deviation of attributes of the numeric type.
34.66
Percentage of instances belonging to the least frequent class.
100
Percentage of nominal attributes.
0.01
Third quartile of mutual information between the nominal attributes and the target attribute.
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
0.23
Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2
0.58
Kappa coefficient achieved by the landmarker weka.classifiers.trees.J48 -C .00001
1.54
Average entropy of the attributes.
332
Number of instances belonging to the least frequent class.
1.53
First quartile of entropy among attributes.
Third quartile of skewness among attributes of the numeric type.
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
0.5
Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2
0.85
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .0001
Mean kurtosis among attributes of the numeric type.
0.75
Area Under the ROC Curve achieved by the landmarker weka.classifiers.bayes.NaiveBayes
First quartile of kurtosis among attributes of the numeric type.
Third quartile of standard deviation of attributes of the numeric type.
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
0.77
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3
0.19
Error rate achieved by the landmarker weka.classifiers.trees.J48 -C .0001
Mean of means among attributes of the numeric type.
0.29
Error rate achieved by the landmarker weka.classifiers.bayes.NaiveBayes
First quartile of means among attributes of the numeric type.
0.83
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 1
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
0.23
Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3
0.58
Kappa coefficient achieved by the landmarker weka.classifiers.trees.J48 -C .0001
0.02
Average mutual information between the nominal attributes and the target attribute.
0.31
Kappa coefficient achieved by the landmarker weka.classifiers.bayes.NaiveBayes
1
Number of binary attributes.
0.01
First quartile of mutual information between the nominal attributes and the target attribute.
0.2
Error rate achieved by the landmarker weka.classifiers.trees.REPTree -L 1
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
0.5
Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3
0.85
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .001
80.7
An estimate of the amount of irrelevant information in the attributes regarding the class. Equals (MeanAttributeEntropy - MeanMutualInformation) divided by MeanMutualInformation.
First quartile of skewness among attributes of the numeric type.
0.53
Kappa coefficient achieved by the landmarker weka.classifiers.trees.REPTree -L 1
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
0.32
Standard deviation of the number of distinct values among attributes of the nominal type.
0.19
Error rate achieved by the landmarker weka.classifiers.trees.J48 -C .001
2.9
Average number of distinct values among the attributes of the nominal type.
First quartile of standard deviation of attributes of the numeric type.
0.83
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 2
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
1
Area Under the ROC Curve achieved by the landmarker weka.classifiers.lazy.IBk
0.58
Kappa coefficient achieved by the landmarker weka.classifiers.trees.J48 -C .001
Mean skewness among attributes of the numeric type.
1.53
Second quartile (Median) of entropy among attributes.
0.2
Error rate achieved by the landmarker weka.classifiers.trees.REPTree -L 2
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
0.03
Error rate achieved by the landmarker weka.classifiers.lazy.IBk
65.34
Percentage of instances belonging to the most frequent class.
Mean standard deviation of attributes of the numeric type.
Second quartile (Median) of kurtosis among attributes of the numeric type.
0.53
Kappa coefficient achieved by the landmarker weka.classifiers.trees.REPTree -L 2
0.93
Entropy of the target attribute values.
0.94
Kappa coefficient achieved by the landmarker weka.classifiers.lazy.IBk
626
Number of instances belonging to the most frequent class.
1.47
Minimal entropy among attributes.
Second quartile (Median) of means among attributes of the numeric type.
0.83
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 3
0.67
Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.DecisionStump
1.56
Maximum entropy among attributes.
Minimum kurtosis among attributes of the numeric type.
0.01
Second quartile (Median) of mutual information between the nominal attributes and the target attribute.
0.2
Error rate achieved by the landmarker weka.classifiers.trees.REPTree -L 3
0.3
Error rate achieved by the landmarker weka.classifiers.trees.DecisionStump
Maximum kurtosis among attributes of the numeric type.
Minimum of means among attributes of the numeric type.

15 tasks

14 runs - estimation_procedure: 10-fold Crossvalidation - target_feature: Class
0 runs - estimation_procedure: Test on Training Data - target_feature: Class
0 runs - estimation_procedure: 10-fold Crossvalidation - target_feature: bottom-left-square
0 runs - estimation_procedure: 10 times 10-fold Crossvalidation - target_feature: Class
0 runs - estimation_procedure: 10% Holdout set - target_feature: Class
0 runs - estimation_procedure: 20% Holdout (Ordered) - target_feature: Class
0 runs - estimation_procedure: 5 times 2-fold Crossvalidation - target_feature: Class
0 runs - estimation_procedure: Leave one out - target_feature: Class
0 runs - estimation_procedure: 10-fold Crossvalidation - target_feature: top-left-square
0 runs - estimation_procedure: 33% Holdout set - target_feature: Class
0 runs - estimation_procedure: 10-fold Crossvalidation - target_feature: bottom-middle-square
0 runs - estimation_procedure: 10-fold Crossvalidation - target_feature: middle-right-square
0 runs - estimation_procedure: 10 times 10-fold Learning Curve - target_feature: Class
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: Class
0 runs - estimation_procedure: Interleaved Test then Train - target_feature: Class
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