Data
trains

trains

active ARFF Publicly available Visibility: public Uploaded 06-04-2014 by Jan van Rijn
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Author: Source: Unknown - Please cite: 1. Title: INDUCE Trains Data set 2. Sources: - Donor: GMU, Center for AI, Software Librarian, Eric E. Bloedorn (bloedorn@aic.gmu.edu) - Original owners: Ryszard S. Michalski (michalski@aic.gmu.edu) and Robert Stepp - Date received: 1 June 1994 - Date updated: 24 June 1994 (Thanks to Larry Holder (UT Arlington) for noticing a translation error) 3. Past usage: - This set most closely resembles the data sets described in the following two publications: 1. R.S. Michalski and J.B. Larson "Inductive Inference of VL Decision Rules" In Proceedings of the Workshop in Pattern-Directed Inference Systems, Hawaii, May 1977. Also published in SIGART Newsletter, ACM No. 63, pp. 38-44, June 1977. 2. Stepp, R.E. and Michalski, R.S. "Conceptual Clustering: Inventing Goal-Oriented Classifications of Structured Objects" In R.S. Michalski, J.G. Carbonell, and T.M. Mitchell (Eds.) "Machine Learning: An Artificial Intelligence Approach, Volume II". Los Altos, Ca: Morgan Kaufmann. Both of these papers describe a set of 10 trains, 5 east-bound and 5 west bound. Both refer to the same 10 trains as seen by the figures in these publications. The differences are: 1) This dataset has 10 attributes, no wheel, or load color attributes 2) Reference 2 (Stepp, Michalski): does not completely list the attributes used, but does mention wheel color - an attribute not present in this dataset. 3) Reference 1 (Michalski, Larson): 12 attributes mentioned, but only 6 are explicitly described. These 6 are included in the dataset below and the Stepp and Michalski set. Results: [1] Michalski and Larson found the following decision rules: (1) There exists car1, car2, lod1 and lod2 such that [infront(car1, car2)][lcont(car1, lod1)][lcont(car2,lod2)] [load-shape(lod1)=triangle][load-shape(lod2)=polygon]=>[dir=east] (2) There exists a car1 such that [ln(car1)=short][car-shape(car1)=closed-top]=>[dir=east] (3) [ncar=3]v There exists car1 such that [car1(car-shape(car1)=jagged- top] =>[dir=west] There exists car1 such that (4) [#cars(ln=long)=2][cshape(car1)=open,trapezoind,u-shaped] v [location(car1)=2][cshape(car1)=closed, rectangle]=>[dir=west] (The first selector in rule 4 uses a meta descriptor generated by the program that counts the number of long cars in a train) [2] The goal of the cluster research is to develop a general method for clustering structured objects that can generate conjunctive descriptions that occur in human classifications or invent new concepts that have similar appeal. CLUSTER/S was able to find the following cognitively appealing clusters: 1) a) "There are two different car shapes in the train" b) "There are three or more different car shapes in the train" 2) a) Wheels on all cars have the same color, b) wheels on all cars do not have the same color." 4. Relevant information: - Additional "background" knowledge is supplied that provides a partial ordering on some of the attribute values. - We are providing this dataset both in its original form and in a form similar to the more typical propositional datasets in our repository. Since the trains dataset records relations between attributes, this transformation was somewhat challenging. However, it may shed some insight on this problem for people who are more familiar with the simple one-instance-per-line dataset format. - Hierarchy of values: if (cshape is one of {openrect,opentrap,ushaped,dblopnrect} then cshape is opentop if (cshape is one of {hexagon,ellipse,closedrect,jaggedtop,slopetop, engine} then cshape closedtop - Prediction task: Determine concise decision rules distinguishing trains traveling east from those traveling west. 5. Number of instances: 10 6. Number of attributes: - 10, not including the class attribute 1. ccont(train idx1, car idx2): car idx is contained in train idx 2. ncar(train idx): # of trains in car train idx (int) 3. infront(car idx1, car idx2): relative positions of cars in train 4. loc(car idx): absolute position of car in train (int) 5. nwhl(car idx): # of wheels of car idx (int) 6. ln(car idx): length of car idx (long, short) 7. cshape(car idx): shape of car (engine, dblopenrect, closedrect, openrect, opentrap, ushaped, hexagon, ellipse, jaggedtop, slopetop, opentop, closedtop) 8. npl(car idx): number of loads in car idx 9. lcont(car idx, load idx): description of which cars hold which loads 10. lhshape(load idx): description of load shape (trianglod, rectanglod, circlelod, hexagonlod) Class: direction (east, west) The following format was used for the "transformed" dataset representation as found in trains.transformed.data (one instance per line): Attributes: 33 1. Number_of_cars (integer in [3-5]) 2. Number_of_different_loads (integer in [1-4]) 3-22: 5 attributes for each of cars 2 through 5: (20 attributes total) - num_wheels (integer in [2-3]) - length (short or long) - shape (closedrect, dblopnrect, ellipse, engine, hexagon, jaggedtop, openrect, opentrap, slopetop, ushaped) - num_loads (integer in [0-3]) - load_shape (circlelod, hexagonlod, rectanglod, trianglod) 23-32: 10 Boolean attributes describing whether 2 types of loads are on adjacent cars of the train - Rectangle_next_to_rectangle (0 if false, 1 if true) - Rectangle_next_to_triangle (0 if false, 1 if true) - Rectangle_next_to_hexagon (0 if false, 1 if true) - Rectangle_next_to_circle (0 if false, 1 if true) - Triangle_next_to_triangle (0 if false, 1 if true) - Triangle_next_to_hexagon (0 if false, 1 if true) - Triangle_next_to_circle (0 if false, 1 if true) - Hexagon_next_to_hexagon (0 if false, 1 if true) - Hexagon_next_to_circle (0 if false, 1 if true) - Circle_next_to_circle (0 if false, 1 if true) 33. Class attribute (east or west) The number of cars vary between 3 and 5. Therefore, attributes referring to properties of cars that do not exist (such as the 5 attriubutes for the "5th" car when the train has fewer than 5 cars) are assigned a value of "-". 7. Distribution of classes: - There are 5 east-bound trains and 5 west-bound trains (i.e., 50% east, 50% west) Information about the dataset CLASSTYPE: nominal CLASSINDEX: last

33 features

class (target)nominal2 unique values
0 missing
Number_of_carsnominal3 unique values
0 missing
Number_of_different_loadsnominal4 unique values
0 missing
num_wheels_2nominal2 unique values
0 missing
length_2nominal2 unique values
0 missing
shape_2nominal5 unique values
0 missing
num_loads_2nominal2 unique values
0 missing
load_shape_2nominal3 unique values
0 missing
num_wheels_3nominal2 unique values
0 missing
length_3nominal2 unique values
0 missing
shape_3nominal8 unique values
0 missing
num_loads_3nominal2 unique values
0 missing
load_shape_3nominal3 unique values
0 missing
num_wheels_4nominal2 unique values
3 missing
length_4nominal2 unique values
3 missing
shape_4nominal4 unique values
3 missing
num_loads_4nominal3 unique values
3 missing
load_shape_4nominal4 unique values
4 missing
num_wheels_5nominal1 unique values
7 missing
length_5nominal1 unique values
7 missing
shape_5nominal2 unique values
7 missing
num_loads_5nominal1 unique values
7 missing
load_shape_5nominal2 unique values
7 missing
Rectangle_next_to_rectanglenominal2 unique values
0 missing
Rectangle_next_to_trianglenominal2 unique values
0 missing
Rectangle_next_to_hexagonnominal1 unique values
0 missing
Rectangle_next_to_circlenominal2 unique values
0 missing
Triangle_next_to_trianglenominal2 unique values
0 missing
Triangle_next_to_hexagonnominal2 unique values
0 missing
Triangle_next_to_circlenominal2 unique values
0 missing
Hexagon_next_to_hexagonnominal1 unique values
0 missing
Hexagon_next_to_circlenominal2 unique values
0 missing
Circle_next_to_circlenominal1 unique values
0 missing

62 properties

10
Number of instances (rows) of the dataset.
33
Number of attributes (columns) of the dataset.
2
Number of distinct values of the target attribute (if it is nominal).
51
Number of missing values in the dataset.
7
Number of instances with at least one value missing.
0
Number of numeric attributes.
33
Number of nominal attributes.
100
Percentage of nominal attributes.
0.25
Third quartile of mutual information between the nominal attributes and the target attribute.
8
The maximum number of distinct values among attributes of the nominal type.
Minimum skewness among attributes of the numeric type.
0.47
First quartile of entropy among attributes.
Third quartile of skewness among attributes of the numeric type.
Maximum skewness among attributes of the numeric type.
Minimum standard deviation of attributes of the numeric type.
First quartile of kurtosis among attributes of the numeric type.
Third quartile of standard deviation of attributes of the numeric type.
Maximum standard deviation of attributes of the numeric type.
50
Percentage of instances belonging to the least frequent class.
First quartile of means among attributes of the numeric type.
1.39
Standard deviation of the number of distinct values among attributes of the nominal type.
0.87
Average entropy of the attributes.
5
Number of instances belonging to the least frequent class.
0.01
First quartile of mutual information between the nominal attributes and the target attribute.
Mean kurtosis among attributes of the numeric type.
18
Number of binary attributes.
First quartile of skewness among attributes of the numeric type.
Mean of means among attributes of the numeric type.
First quartile of standard deviation of attributes of the numeric type.
0.89
Average class difference between consecutive instances.
0.19
Average mutual information between the nominal attributes and the target attribute.
0.8
Second quartile (Median) of entropy among attributes.
1
Entropy of the target attribute values.
3.65
An estimate of the amount of irrelevant information in the attributes regarding the class. Equals (MeanAttributeEntropy - MeanMutualInformation) divided by MeanMutualInformation.
Second quartile (Median) of kurtosis among attributes of the numeric type.
3.3
Number of attributes divided by the number of instances.
2.39
Average number of distinct values among the attributes of the nominal type.
Second quartile (Median) of means among attributes of the numeric type.
5.37
Number of attributes needed to optimally describe the class (under the assumption of independence among attributes). Equals ClassEntropy divided by MeanMutualInformation.
Mean skewness among attributes of the numeric type.
0.11
Second quartile (Median) of mutual information between the nominal attributes and the target attribute.
50
Percentage of instances belonging to the most frequent class.
Mean standard deviation of attributes of the numeric type.
Second quartile (Median) of skewness among attributes of the numeric type.
5
Number of instances belonging to the most frequent class.
0
Minimal entropy among attributes.
Second quartile (Median) of standard deviation of attributes of the numeric type.
2.92
Maximum entropy among attributes.
Minimum kurtosis among attributes of the numeric type.
54.55
Percentage of binary attributes.
1.36
Third quartile of entropy among attributes.
Maximum kurtosis among attributes of the numeric type.
Minimum of means among attributes of the numeric type.
70
Percentage of instances having missing values.
Third quartile of kurtosis among attributes of the numeric type.
Maximum of means among attributes of the numeric type.
0
Minimal mutual information between the nominal attributes and the target attribute.
15.45
Percentage of missing values.
0
Percentage of numeric attributes.
Third quartile of means among attributes of the numeric type.
1
Maximum mutual information between the nominal attributes and the target attribute.
1
The minimal number of distinct values among attributes of the nominal type.

18 tasks

693 runs - estimation_procedure: 10-fold Crossvalidation - evaluation_measure: predictive_accuracy - target_feature: class
368 runs - estimation_procedure: 33% Holdout set - evaluation_measure: predictive_accuracy - target_feature: class
345 runs - estimation_procedure: 5 times 2-fold Crossvalidation - evaluation_measure: predictive_accuracy - target_feature: class
216 runs - estimation_procedure: 10 times 10-fold Crossvalidation - evaluation_measure: predictive_accuracy - target_feature: class
31 runs - estimation_procedure: 10-fold Crossvalidation - evaluation_measure: precision - target_feature: class
0 runs - estimation_procedure: Leave one out - evaluation_measure: predictive_accuracy - target_feature: class
213 runs - estimation_procedure: 10 times 10-fold Learning Curve - evaluation_measure: predictive_accuracy - target_feature: class
82 runs - estimation_procedure: 10-fold Learning Curve - evaluation_measure: predictive_accuracy - target_feature: class
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: class
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: class
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: class
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: class
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: class
0 runs - estimation_procedure: 10-fold Learning Curve - target_feature: class
25 runs - estimation_procedure: Interleaved Test then Train - target_feature: class
0 runs - estimation_procedure: 50 times Clustering
0 runs - estimation_procedure: 50 times Clustering
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