# Binarization process

## Original data
| # | f1 | f2 | class |
|---|------|------|-------|
| 1 | 5    | 5    | 0     |
| 2 | 5    | 6    | 0     |
| 3 | 10   | 20   | 1     |
| 4 | 10   | 25   | 1     |
| 5 | 5    | 6    | 1     |

### Sorted by `f1`
| # | var1 | class |
|---|------|-------|
| 1 | 5    | 0     |
| 2 | 5    | 0     |
| 5 | 5    | 1     |
| 3 | 10   | 1     |
| 4 | 10   | 1     |

### Transition Mapping for `f1`

| value | classes |
|-------|---------|
| 5     | {0,1}   |
| 10    | {1}     |

> Therefore, exists a single cutpoint between 5 {0} and 10 {1}

### Cutpoints formation for `f1`
$$c_1 = \frac{|5| + |10|}{2} = 7.5$$

### Sorted by `f2`
| # | f2 | class |
|---|----|-------|
| 1 | 5  | 0     |
| 2	| 6	 | 0     |
| 5	| 6	 | 1     |
| 3	| 20 | 1     |
| 4	| 25 | 1     |

### Transition Mapping for `f2`
| value | classes |
|-------|---------|
| 5	    | {0}     |
| 6	    | {0,1}   |
| 20	  | {1}     |
| 25	  | {1}     |

> Therefore, exists a single cutpoint between 5 {0} and 6 {1}

### Cutpoints formation for `f2`
$$c_1 = \frac{|5| + |6|}{2} = 5.5$$