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# System prepended metadata

title: Data sets for association rule mining

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# Data sets for association rule mining

|                  Scenario                   | Size of Rule (# relevant number of features) |      Distribution of 0/1      |      Noise      | # Data sets |
|:-------------------------------------------:|:--------------------------------------------:|:-----------------------------:|:---------------:|:-----------:|
|                     1_1                     |                  1 (color)                   |     Equivalent (250/250)      |        -        |     500     |
|                     1_2                     |                2 (color/pos)                 | Equivalent (250/250(125/125)) |        -        |     500     |
| 1_3 (= 1_2 with non-equivalent distribution |                2 (color/pos)                 | Non-Equivalent (167/166/166)  |        -        |     500     |
|           1_4 (= 1_1 with noise)            |                  1 (color)                   |     Equivalent (250/250)      | 1 (size, v = 5) |     500     |
|           1_5 (= 1_2 with noise)            |                2 (color/pos)                 | Equivalent (250/250(125/125)) | 1 (size, v = 5) |     500     |
|           1_6 (= 1_3 with noise)            |                2 (color/pos)                 | Non-Equivalent (167/166/166)  | 1 (size, v = 5) |     500     |
|       1_7 (= 1_2 with 1000 Data sets)       |                2 (color/pos)                 | Equivalent (250/250(125/125)) |        -        |    1000     |
|   1_8 (= 1_1 with smooth 25% prob. noise)   |                  1 (color)                   |     Equivalent (250/250)      | 1 (size, v = 2) |     500     |
|                     2_1                     |                2 (shape/pos)                 | Equivalent (250/250(random))  |        -        |     500     |
|           2_2 (= 2_1 with noise)            |                2 (shape/pos)                 | Equivalent (250/250(random))  | 1 (size, v = 3) |     500     |

# Rules:
Scenario 1_1, 1_4, 1_8: color is decisive criterion (green object in scene => 0; blue object in scene = 1)
* easy example for proof of concept
*  assumptions:
    *  excatly one object is visible in each image
    *  allover, two objects can occur in the scene
        *  Object 1: green, rectangular, fixed size
        *  Object 2: blue, rectangular, fixed size

Scenario 1_2, 1_3, 1_5, 1_6, 1_7: color and position are decisive criteria (blue object in scene + position lower half of the table (y > scene_height / 2), otherwise 0)
* interesting aspect: Dependency of the features: circular AND position have to be in one rule
*  assumptions:
    *  exactly one object is visible in each image
    *  allover, two objects can occur in the scene
        *  Object 1: green, rectangular, fixed size
        *  Object 2: blue, rectangular, fixed size

* Scenario 1_2 is the basic version.
* Scenario 1_3 is a variant of Scenario 1_2; it includes a non-equivalent distribution, i.e., 333 data sets are labelled negatively and 167 data sets are labelled positively. The 333 negative labelled data covers 166 data sets where a green object is placed and 167 data sets where a blue object is placed in the wrong half of the table (in the upper half). Furthermore, very small noise regarding the label assignment is included: the negative labelled data contains 9 record that should actually be considered positive (= blue object positioned in the lower half of the table but label "0" is assigned).
* Scenario 1_5 is a variant of Scenario 1_2; it includes noise on the feature "size", i.e., the features "Sizes X" and "Sizes Y" vary by -5, -4,.. to ..,+4, +5 points.
* Scenario 1_6 is a variant of Scenario 1_3; it includes noise on the feature "size", i.e., the features "Sizes X" and "Sizes Y" vary by -5, -4,.. to ..,+4, +5 points. IN CONTRAST to Scenario 1_3, there is NO NOISE regarding the LABEL assignement.
* Scenario 1_7 is a variant of Scenario 1_2; in contrast to Scenario 1_2 it contains the double amount of data sets, i.e., 1000 data sets. 

Scenario 2_1, 2_2: shape and position are decisive criteria (circular object in scene + position in upper seventh of table)
* interesting aspect: Dependency of the features: circular AND position have to be in one rule
*  assumptions:
    *  exactly four objects are visible in each image
    *  allover, four objects can occur in the scene
        *  Object 1: red, circular, fixed size
        *  Object 2: red, circular, fixed size
        *  Object 3: red, rectangular, fixed size
        *  Object 4: red, rectangular, fixed size

Note: The data are in the Excel table in the order in which they were inserted (ordered by label). They should be tested ordered by label AND ordered by name.